PRELIMINARY STUDY OF TRANSVERSE BARS

Prévia do material em texto

Marine Geology'- Elsevier Publishing Company, Amsterdam - Printed in The Netherlands 
P R E L I M I N A R Y STUDY OF TRANSVERSE BARS 1 
A. W. NIEDORODA AYD W. F. TANNER 
Geology Department, Geophysieal Fluid Dynamics Institute, Florida State University, Tallahassee, 
Fla. (U.S.A.) 
(Received July 31, 1968) 
SUMMARY 
Transverse bars (finger bars) are extremely common along sandy beaches 
in low-to-moderate wave energy regimes. They are typically oriented normal or 
nearly normal to the beach toe. Each transverse bar acts as a "focusing lens" for 
advancing waves, controlling wave refraction Jn such a way that: (1) the trans- 
verse bar is maintained; (2) sediment is transported along the long axis of the bar; 
and (3) a subtle but nevertheless effective circulation pattern is established, whereby 
water is transported seaward from the surf, without rip currents. 
In areas where transverse bars are numerous and well developed, the onshore 
or offshore transport of sand along the bar axes may be more important than 
littoral drift. 
Field experiments delineated a subtle nearshore current pattern, caused by 
unequal distribution of wave energy over the foreshore. Currents of this type were 
studied also in model wave tanks, These studies indicate that a transverse bar 
causes shallow waves to be refracted so that wave energy increases over the bar 
and decreases between the bars. Bottom friction reduces the wave energy more 
rapidly over the crest than in the adjacent deeper water. If the bars are relatively 
short this loss of energy through bottom friction has little effect. The wave energy 
concentrated over the crest results in an onshore current along the axis. The onshore 
current divides near the breaker zone and returns seaward slowly between the 
bars. The currents form two meshed gyres of horizontal circulation, one on each 
side of each relatively short transverse bar. 
Over relatively long transverse bars, the greater loss of wave energy through 
bottom friction over the crests, compared with the deeper wave between the bars, 
results in a reduced amount of wave energy over the shoreward portions. The 
areas between these bars provide a greater capacity for onshore movement of 
water caused by the mass transport associated with shallow water waves. The 
1 This project was partially supported through Contract Number N-00014-68-A-0159, Project 
Themis, Department of Defense. Contribution no. 26 of the Geophysical Fluid Dynamics Institute. 
Marine Geol., 9 (1970 41-62 
42 A . W . NIEDORODA AND W. F. TANNER 
seaward return of this water takes place over the crests of relatively long transverse 
bars. These bars produce four meshed horizontally circulating gyres with an off- 
shore current over the shoreward portions and an onshore current at their seaward 
ends. 
Preliminary data indicate that current strength is a direct function of the 
depth of water over the bars and an exponential function of the initial wave height. 
Additional work is in progress. 
PREVIOUS WORK 
SHEPARD (1952) defined transverse bars as, " . . . the bars which extend at 
right angles to shorelines". Furthermore he stated that, " . . . they have been 
described elsewhere as 'sand w a v e s ' . . , and as 'giant r i p p l e s ' . . . , but these terms 
fail to indicate their important relationship to the shoreline". This feature is a 
distinctive member of a continuous series of features which are genetically related 
to each other. 
TANNER (1960a, b) described similar bars which are maintained, or aug- 
mented, as a result of the refraction which they cause, and extended these observa- 
tions (TANNER, 1961) to larger features. MooDY (1964) reported transverse bars 
3,350 m long; and lengths less than 100 m have been observed. These bars are 
characterized by gentle slopes and relief of a few meters (BRUUN, 1955; MOODY, 
1964) to almost nothing. There is a crudely rhythmic spacing between bars, 
ranging from 300 to 2,000 m (BRUUN, 1955; HOM-MA and SONy, 1963). BRUUN 
(1955) reported an annual rate of migration in the direction of littoral drift of 
700 m for transverse bars on the Danish North Sea coast. From his studies of these 
features at several places on the North Sea coast he found that the rate of migration 
varies between 0 and 1,000 m a year. HOM-MA and SONU (1963) reported several 
occurrences where no migration could be observed. They also reported examples 
on gravel beaches. 
EVANS (1938) described "large cusps" which have their apexes continuing 
out into the lake as ridges of sand on the lake bottom, in Silver Lake, Michigan. 
His paper appears to be the first published account of suspected sediment move- 
ment, normal to the shore, along transverse bars. 
TANNER (1960a, b) and HOM-MA and SONU (1963) noted zones of convergence 
and divergence of waves due to refraction over these bars. The zone of convergence 
is located over the crest. 
Transverse bars have been reported from Brazil (TANNER, 1967), Canada, 
Denmark, Japan, the Soviet Union, and the United States. In general, their 
occurrences are restricted to areas of an abundant supply of sand, wide gently 
sloping foreshores and low average annual breaker heights. 
Marine Geol., 9 (1970) 41-62 
PRELIMINARY STUDY OF TRANSVERSE BARS 43 
FIELD STUDIES 
The present project has included an extensive field study of one group of 
transverse bars occurring on the east coast of St. James Island, F rank l in County, 
Florida (Fig. l ) . The low energy condit ions of the study area have allowed the 
current system to be determined more precisely than had been done previously. 
Fig.1. Index map, showing the southeastern states and the location of the primary field 
study area. The latter is shown in relation to the other states (heavy arrow) and as part of an air 
photo. 
The study area has an average breaker height of about 6 cm and is classified 
as a low energy coast (TANNER, 1960C). The offshore limit of the transverse bar 
field is about the 1.5 m bathymetr ic contour. The distance of this contour f rom the 
Marine Geol., 9 (1970) 41-62 
44 A. W. NIEDORODA AND W. F. TANNER 
beach varies between 335 m and 1,000 m: the foreshore slope is 0.15-0.45 °/o. The 
transverse bars have a spacing varying from 64 to 218 m and lengths varying from 
107 to 640 m. 
The maximum relief along a cross-section perpendicular to the axis of a rep- 
resentative bar is 24 cm in 20 m (1.2 }/o slope). Such a bar can be seen on the ground 
only when the tide is below midheight and the crest of the shoreward end is 
exposed. At each point where a transverse bar joins the beach a large cusp-like 
feature is developed on the beach face (but this is not a beach cusp). During two 
years of observation no migration of these features was noted. Air photos covering 
a 25-year period also indicate that these bars do not migrate. 
A series of drogue and dye studies demonstrated the nature of the near-shore 
currents. These studies were limited to days of light winds to avoid significant 
contribution of a wind driven nearshore current component. The contribution of 
a nearshore tidal current component was reduced by attempting the major portion 
of the current measurements during periods of slack tide. Owing to the asym- 
metrical tidal cycle of this portion of the Gulf coast, slack tide occurs at different 
levels on successive days. The current drogues and dye patches established path 
lines of the nearshore currents. Composites of individual measurements made at 
the same tide levels and wave conditions exhibited the general character of the 
nearshore currents in the vicinity of a transverse bar. 
A typical transverse bar was studied in detail. At, or near, high tide, the 
transverse bar was under approximately 60 cm of water and little significant wave 
refraction was caused by the subtle relief on the sediment surface. Tidal and wind- 
driven currents moved essentially parallel to the shoreline.As the tide level fell 
the bar began to cause significant refraction of the waves. Wave crests, approaching 
the beach, developed a V-shaped pattern, as seen from above, with the bar crest 
under the apex of each V. The wave segments on either side of the transverse bar 
approached the axis of the bar. Eventually, these converging wave crest segments 
crossed through each other and produced a zone of spilling waves along the axis 
of a bar (Fig.2). The length of the zone of converging and crossing waves increased 
as the tide height decreased over the gentle slope of the nearshore bottom. Path 
lines determined by the drogues indicated marked shoreward deflection of the 
nearshore currents over the axis of the bar within the zone of converging and 
crossing waves but individual spot measurements could not be so interpreted 
owing to the constantly changing mean water depth. At low tide slack water, the 
shoreward ends of the transverse bars were covered by approximately 10 cm of 
water. 
Two distinct current systems developed over the foreshore. The breaker 
and swash zones together were only about 2.5 m wide; in these zones the littoral 
drift current velocity was about 40 cm/sec to the north. An 80 cm/sec current, 
directed toward the beach, was observed over the axis of the bar. As this current 
neared the shore, it decelerated and divided into two threads, one of which was 
Marine Geol., 9 (1970) 41-62 
PRELIMINARY STUDY OF TRANSVERSE BARS 45 
Fig.2. Crest of a transverse bar, showing crossing waves, breaker augmentation, and 
ripple marks parallel with the crest. The water is about 15 cm deep; the ruler extends above the 
sand about 25 cm. 
deflected to the left, and the other to the right. Each thread returned seaward in 
an area between bars. The shoreward end of the current gyre south o f the bar 
moved opposi te to the l i t toral drift current and mainta ined its identity even when 
only 30 m separated the two flows. The shoreward por t ion o f the current gyre 
Marine Geol., 9 (1970) 41-62 
46 A. W. N I E D O R O D A A N D W . F. TANNER 
north of the bar flowed parallel to the littoral drift current and the two could not 
be differentiated. 
The shoreward current over the bar was restricted to a relatively narrow 
band and maintained the highest velocities of the system. The flow elsewhere was 
spread over a much wider area and, consequently, was of much lower velocity. 
The sediment transporting capacity of the currents over the bars was 
demonstrated in a series of fluorescent sediment studies. The sand which was 
used was originally taken from the study area so that the dynamic properties 
of the tracer were as close to those of the natural sediment as possible; this sand 
was coated with an ultraviolet fluorescent pigment. Fifty pounds of this dyed sand 
were placed on the crest of the bar about 100 m from the beach. Three lines of 
samples were taken across the crest of the bar shoreward of the point where the 
dyed sand was dumped. Numerous marked grains were recovered from the two 
seaward lines of samples, 5, 17 and 37 rain after the dyed sediment was dumped. 
One hour and fifteen minutes after the dyed sand was dumped a final group of 
samples, taken along the line nearest the beach, yielded three marked grains, 
which had travelled at least 40 m. The maximum observed grain velocity was 
about 7 cm/sec. 
Sediment motion studies were also undertaken with a set of ping-pong 
balls (diameter = 4 cm) painted with red stripes and filled with water. These 
rolled on the bot tom in response to current and wave motion. The motion con- 
sisted primarily of small excursions, at right angles to the ripple marks which lie 
on, and parallel, the crest of each bar; these motions result f rom action of the 
water-wave orbits near the bottom. The sum of many back-and-forth movements 
was a net transport toward the beach (short variety of transverse bar; TANNER, 
1960a). 
It is true that a ping-pong ball is much larger, and much easier to move, 
than a quartz sand grain. Nevertheless, the rolling of the ball demonstrates 
bot tom water motion which provides a bias to sand grain transport, once the 
grains have been disturbed by wave action. The ball reveals the vector resultant 
of all the bias effects. Furthermore, results obtained with rolling ping-pong balls 
duplicate, essentially, the results of other methods reported here. 
The authors have been unable to relate the rate of transport of the tracer 
to the actual volume and rate of sand movement along the bar. However, the 
tracers do show that sand is moved along the axis of the bar under the influence 
of the wave driven current system associated with the bar. 
WAVE T A N K EXPERIMENTS 
Despite the advantages of working in a low-energy area, the wave-produced 
currents associated with the bars could not be isolated completely in the field. 
Marine Geol., 9 (1970) 41-62 
PRELIMINARY STUDY OF TRANSVERSE BARS 47 
Model experiments in wave tanks were used to provide informat ion on the be- 
havior of such currents in response to various wave parameters. 
The first series of model experiments was carried out in a 55 x 55 cm glass- 
bot tomed ripple tank (Fig.3). The water depth was only 0.6 cm at the deepest end 
Fig.3. Overhead photo of one experirnent in the ripple tank. The ripple generator is at 
the top of the picture: it has been modified to generate three sets of waves (pattern clearly visible). 
The dye was introduced in two parallel rows, one row close to the model beach, and a second row 
slightly offshore. The photograph was taken after 2 rain of operation. There were no transverse 
bars or other bottom irregularities in this experiment. The dye has been transported seaward in the 
general area of wave interference (inked arrows show current directions), or left almost 
undisturbed (close to the beach). 
and the bo t tom slope was 2.3 ~ . Dye was used to trace water currents. The wave 
generator was arranged to generate two sets of interfering waves. The model 
produced obvious currents which moved offshore, near the beach, along the axes 
of the interference patterns. Addi t ional currents moved toward the shore, in 
deeper water, also along the axes of the interference patterns. Where these two 
currents met, they parted and formed four meshed current gyres per interference 
pattern. It is impor tan t to note that this wave-driven system included a current 
directed toward the shore, as well as a current directed away from the shore, 
a long the axis of each interference pattern. This experiment indicated that the 
nearshore currents in the vicinity of na tura l transverse bars were closely related 
to the converging and intersecting pat tern of the waves. 
Marine GeoL, 9 (1970) 41-62 
48 A . W . N I E D O R O D A A N D W . F. T A N N E R 
A second series of experiments was carried out in the same tank (Fig.3). 
The same depth was used but the bot tom slope was eliminated. Small scale idealized 
models of short transverse bars were constructed of plaster-of-Paris and set in the 
tank. Plane waves were produced by the wave generator. These waves were 
refracted into a crossing pattern by each model bar. A patch of dye originally 
placed at the seaward end of one model bar was rapidly transported toward the 
model beach by the current developed by the waves over the crest. Two meshed 
counter rotating current gyres formed; they were similar to those developed 
closest to the wave generator in the earlier experiments. 
The third series of ripple tank experiments involved a model transverse 
bar having a length which was long relative to its width. Dye originally placed at 
the seaward end of the model bar was carried toward the beach as it was in the 
second series. However, in this experiment this current moved only a relatively 
short distance toward the shore before it divided and formed two meshed counter 
rotatinggyres. The dye patches originally placed near the beach were transported 
seaward along the bar crest. This indicated a current moving offshore along this 
section of the bar which divided to form two additional meshed counter rotating 
gyres. The final pattern of currents was quite similar to the system obtained in the 
first series, where no model bars were used. 
The latter two experiments showed that the relative length of the transverse 
bar and the associated zone of converging and crossing waves appears to control 
the direction of current flow. The natural transverse bars on the east coast of 
St. James Island, Florida, those reported by EVANS (1938) on Silver kake, Michigan, 
and those examined briefly in Brazil (TANNER, 1967), are of the relatively short 
variety. The bars described by MOODY (1964) from Bethany Beach, Delaware, 
as well as those known to occur on the southwest coast of Mansel Island in Hudson 
Bay, Canada, appear to be of the relatively long variety. The former transport 
sediment toward the beach whereas the latter remove sediment from the beach. 
The ripple tank models employed small ultra-gravity waves and therefore 
could only provide general qualitative information concerning the behavior of 
the wave-produced nearshore current component associated with natural trans- 
verse bars. In order to obtain measurements of the effect of water depth and wave 
height on the velocity of the wave-produced currents (Fig.4), a 1 :l 3.3 scale model 
of an idealized short transverse bar was constructed in a 4.5 x 7.33 m wave tank 
at the Coastal and Oceanographic Engineering Department of the University of 
Florida. Dye experiments showed that the direction of the currents was essentially 
the same for all depths. Current velocities were obtained by measuring elapsed 
time for balsa surface drogues to pass beneath the lines of a grid suspended above 
the model. The velocity of surface current above the axis of the model bar was 
found by averaging from 40 to 80 individual measurements for each experiment. 
This average was used as the index of the velocity of the wave produced currents. 
The wave tank used in the study had not been constructed specifically for 
Marine Geol., 9 (1970) 41-62 
PRELIMINARY STUDY OF TRANSVERSE BARS 49 
Fig.4. Overhead pho to o f one exper iment in the wave tank. The wave generator is at the 
left of the picture, and the model beach at the right; one transverse bar is outl ined by contours . 
Dye was in t roduced close to the wave generator ; s treaks of colored water (marked with arrows 
showing currents) can be seen. The currents collected near the seaward end of the bar, and 
diverged close to the beach. 
this study. Several design compromises were required in setting up this model 
which resulted in unavoidable shortcomings in the data. The wave tank was narrow 
enough to restrict the current pattern near the boundaries. The scale of the model 
was limited by the lower limit of resolution of the wave measuring instrument. 
Work is presently in progress on another wave tank which will overcome this 
difficulty. However, data presently available are sufficient to examine the general 
relationships between geometry of a transverse bar and the physical processes 
which cause the currents in the vicinity of the bar. 
A total of 26 experiments were conducted with this model, using different 
water depths, wave heights and wave periods. Several experiments were duplicated. 
Semi-log plots of the data suggest that the current velocity varies as an exponential 
ftmction of the wave height and as a direct function of the water depth (the 
velocity increases as the depth decreases; see Fig.5,6). The model experiments 
yield good qualitative agreement with the trends established through field observa- 
tions. The physical reasons for this type of relationship between the currents 
Marine Geol., 9 (1970) 41-62 
50 A . W . NIEDORODA AND W. F. TANNER 
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Fig.6. Semi-logplots of current velocity vs. wave height, in scaled units, for three different 
water depths in the wave tank. The plots are essentially linear; the slope (as shown) is inversely 
proport ional to water depth. Two questionable points appear, one at 12 cm depth and one at 
4.5 cm depth. These points were rejected in drawing the straight lines. 
associated with transverse bars and the wave parameters are discussed in a separate 
section. 
COMPUTER MODELLING 
In order to determine the refraction pattern associated with transverse bars, 
the computer wave orthogonal plotting program written by HARRISON and 
WILSON (1964) and WILSON (1966), was modified for use with an E.A.I. X - Y plotter 
and translated into Fortran IV. Bathymetry similar to the idealized short variety 
of transverse bar in the model wave tank was used in the computer model. The 
resulting orthogonal diagrams appear to agree well with the wave patterns which 
developed in the largest scale model. 
]~4arine Geol., 9 (1970) 4! 62 
PRELIMINARY STUDY OF TRANSVERSE BARS 51 
Fig.7 shows wave orthogonal diagrams for four different water depths. 
These diagrams show that the zone of converging and crossing waves over the 
axis of the bar lengthens and the intensity of the refraction increases as the water 
depth decreases. The concentration of energy over the bar, due to refraction, is 
balanced by a corresponding flux divergence of wave energy over the flanks. 
The sinuous shape of many of the wave orthogonals indicates that once refraction 
has curved a wave segment toward the axis of the bar, the energy associated with 
the adjacent wave segment does not leave the top of the bar. As the wave passes 
over the axis of the bar, it moves into progressively deeper water and is thus 
refracted back toward the axis. A conceptual problem arises when one considers 
the meaning of the crossing of orthogonals. Theoretically, the wave energy must 
be infinite at such a point. PIERSON (1951) and WIEGEL and ARNOLD (1957) have 
studied the use of geometric optics as applied to shallow water wave refraction 
and found good agreement between orthogonal diagrams based on Snell's law 
and model studies. Pierson showed that the increasing wave energy density asso- 
ciated with converging wave orthogonals results in increasing wave height until 
the wave becomes oversteepened and spills as the orthogonals eventually cross. 
Fig.2 illustrates such events. 
The four diagrams of Fig.7 indicate another interesting aspect of the 
converging and intersecting wave orthogonals associated with transverse bars. 
The diagrams for the two shallowest depths show two areas over the axis of the bar 
where there is a relatively high density of crossing wave orthogonals. These may 
be referred to as smeared-out "focal points". They indicate that the wave energy 
density along the axis of the bar is not uniform; this may help explain the sand 
waves which can be seen on the bars in Fig.1. Sediment would tend to move in 
relation to the "focal points" and thus give the top of the bar a wavyprofile. 
Comparison of the four parts of Fig.7 shows that the "focal points" migrate 
onshore and offshore along the crest of the bar as the tide level changes. 
The wave orthogonal diagrams show that the geometry of the transverse 
bars causes nearshore wave energy to be focused over the bars, and correspondingly 
reduced over the flanks. The intensity of the refraction is solely a function of bar 
geometry and water depth. These diagrams also show that the distribution of 
wave energy is not uniform along the length of the bar. 
THEORY 
The field observations of this study and those of other authors indicate 
that transverse bars are relatively common on many beaches and provide a 
mechanism for the transfer of sediment between the offshore areas and the beach. 
The wave tank studies clearly show that a nearshore current component exists 
which is caused solely by waves as they are refracted into a converging and crossing 
pattern by the subtle geometry of the bars. Dyed sand experiments on natural 
Marine Geol., 9 (1970) 41-62 
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Marine Geol., 9(1970) 41-62 
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Marine Geol., 9 (1970) 41-62 
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54 A . W . NIEDORODA AND W. F, TANNER 
bars showed that this current component becomes sufficient to transport sand 
along the crest of a transverse bar. We must now examine the processes which: 
(1) cause the distinct currents associated with these bars; (2) facilitate sediment 
transport along these bals; and (3) cause and maintain these bars as an avenue 
for nearshore sediment transport. 
There are not enough data to permit the formulation of rigorous quantitative 
relationships which would explain the near shore processes associated with trans- 
verse bars. However, a qualitative discussion of these processes permits exploration 
of the role of transverse bars in the nearshore zone. 
Expressions derived from existing shallow water wave theory can be used 
only as approximations to the nearshore processes related to this study because 
in the field and model studies the wave heights were not small fractions of the 
mean water depths. Nevertheless, these expressions are used to show the general 
factors which produce and maintain transverse bars. Currents stemming from 
nearshore waves arise from the mass transport of water related to the open 
geometric form of the orbitals of deformed nearshore waves. The earliest expression 
for the mass transport velocity (0 ) was worked out by Stokes (see LON~UET- 
HIGG~NS, 1953) as: 
a 2 crk cosh 2k (z - h) 
0 - + c 
2 sinh 2 kh 
where a = wave height/2; h = water depth; z = the depth below the surface at 
which determination is made; L = wave length; T = wave period; a = 2~/T; 
k = 2re~L; c = an arbitrary constant. 
More recent work by LONGUET-HIGGINS (1953) questions some of Stokes' 
assumptions. Longuet-Higgins gave the following expression for the mass trans- 
port velocity (t_~): 
5 a 2 o'k 
t 2 - 
4 sinh 2 kh 
Attempts to experimentally verify these expressions have been somewhat 
limited by the assumptions used in the construction of the wave tanks employed. 
Only trough-type models have been used, forcing the experimenter to assume that 
all currents produced by nearshore waves circulate in vertical planes. Clearly, 
these equations cannot be used with the present study of currents circulating in 
the horizontal plane. However, RUSSELL and OSORIO (1958) showed that in both 
Longuet-Higgins' and Stokes' solutions for the mass transport velocity the terms 
a2¢k give the scale of the velocity whereas the remainder of the expression shows 
Fig.7. Wave or thogona l d iagrams (computer output) for four different water depths 
over a t ransverse bar. As the depth decreases, an increased a m o u n t of wave energy tends to be 
refracted f rom over the flanks to the crest of the bar. (Wave approach f rom the top of each 
d iagram; beach at the bo t tom of each diagram; transverse bar not out l ined on these plots.) 
Marine Geol., 9 (1970) 41-62 
P R E L I M I N A R Y S T U D Y OF TRANSVERSE BARS 55 
how the velocity varies with depth. Dye experiments were carried out in the largest 
wave tank and showed that the direction of the currents was uniform for all 
depths although the velocities differed. At present we are solely interested in the 
relative magnitude of the mass transport velocity for points in the vicinity of a 
transverse bar, and therefore the terms aZ~k are taken as an index of the mass 
transport velocity. 
Shallow water wave theory presumes that the wave period remains constant 
as the other wave parameters are altered. We make the transformations: 
L = r , , & h k - 
2rr 27r 
L Tx/g x/h 
where g = acceleration of gravity. 
To assess the effect of change in wave amplitude and water depth for any 
wave period we can rewrite our expression for the approximation of the magnitude 
of the mass transport velocity, UA: 
OA= a2r; k = a2 2rr 2rr _ a 2 [ 4rr 2 ] _ a2c 
T T,]g ,]h \/h \ ~ x / g ] ,/h 
where: 
4~ 2 
C - - 
T 
This relationship shows that if the amplitude increases while the depth is 
kept constant, the mass transport velocity (UA) increases; and if the depth de- 
creases while the amplitude is kept constant, the mass transport velocity (U-A) 
increases. The bathymetry of a transverse bar is such that the least depth is along 
the axis of the bar. The wave orthogonal diagrams of Fig.7 show that refraction 
causes a marked increase in the wave energy density over the crest of the bar. A 
common expression for the relationship between wave amplitude and energy 
density is given by McLELLAN (1965) as: 
Ea = p g H2/8 
when: E d -= wave energy density; p = water density; g = acceleration of gravity; 
H = 2 a (= 2 x wave-amplitude). Therefore, the concentration of wave energy 
over the crest of a transverse bar caused by wave refraction leads to increased wave 
heights above the bar relative to the areas between the bars. The direct shoaling 
factor also tends to increase the wave heights over the bar. There should be a 
greater potential mass transport velocity over the transverse bar, due to relatively 
higher waves and shallower depths, than in the area between bars. The current 
direction is the same as the vector resultant of the local wave propagation direction. 
Inasmuch as the waves are refracted toward the crest of the bar from over the 
Marine Geol., 9 (1970) 41 62 
56 A . W . NIEDORODA AND W. F. TANNER 
flanks this current should be directed up the flanks and along the crest. Because 
the mass transport velocity is greater over the crest of the bar, the water which is 
piled up at the beach by this current will seek to return offshore where it is opposed 
by the smallest incipient mass transport. It returns offshore in the areas between 
the transverse bars where the wave heights are relatively lower, the depth is 
slightly greater, and the potential shoreward directed mass transport currents are 
the least. The system of two meshed counter rotating current gyres develops to 
provide a horizontal return for the shoreward current which arises in response to 
the increased wave energy over the transverse bar. 
At this point it would be convenient to provide a meaningful mathematical 
expression which would relate the processes of wave refraction, shallow water 
wave propagation and sediment transport to the generation of the wave produced 
currentsystems herein described and the maintainance of the geometry of the bar. 
However, this study is of a preliminary nature and no such meaningful expression 
has yet been devised. Considering the unavoidable shortcomings of much of the 
data obtained from the wave tank experiments it is not presently possible to 
develop relationships through mathematical curve fittings which will provide real 
insight into processes which cause the currents, transport the sand, and maintain 
the bars. However, the wave tank data do supply valuable information which 
shows that the nearshore current system related to the wave pattern over a trans- 
verse bar is driven by the mass transport of non-sinusoidal shallow water waves. 
With relatively short transverse bars the unequal distribution of wave energy in 
the nearshore zone due to refraction of the waves by the geometry of the bars is 
taken to cause net shoreward movement of water over the axis of the bar and 
offshore return of the water between the bars. Thus the nearshore circulation of 
this current system is purely in the horizontal plane. 
The wave tank data show an exponential increase in the index mean current 
velocity with increase in initial wave amplitude. This closely parallels the response 
predicted from the aforementioned expression for the mass transport approxima- 
tion. Wave tank data for the effect of depth on the index mean current velocity 
shows a linear response whereas one would expect an inverse exponential relation 
from the mass transport approximation expression. Nevertheless, the directions 
of the variations are parallel and one neither expects nor requires a simple relation- 
ship between the expression derived for the mass transport velocity with vertical 
current circulation produced for the case of simple straight crested waves in 
trough-type wave tanks and the expression needed for the more complex condition 
of horizontal circulation produced by crossing wave crests over non-planar 
bot tom geometry. 
The hydrodynamics of the condition are presently being studied and it is 
expected that a concept similar to the radiation stress theory derived by LONOUET- 
HIGGINS and STEWART (1962, 1964) and applied within the breaker zone by BOWEN 
(1967) will result. However, the wave tank data appear to agree sufficiently 
Marine Geol., 9 (1970) 41-62 
PRELIMINARY STUDY OF TRANSVERSE BARS 57 
with the relations which can be predicted from the classical derivations for the 
mass transport velocity to lend strong support to the idea that the currents found 
associated with transverse bars are caused by an unequal distribution of wave 
energy in the nearshore zone, and corresponding differences in the local potential 
mass transport capacity. 
The concept of an unequal distribution of wave energy in the nearshore 
area resulting from wave refraction, and unequal wave shoaling which leads to 
distinct currents stemming from local differences in the potential mass transport 
velocities, can also be used to explain the more complicated current system 
associated with the long variety of transverse bars. The two current gyres which 
occur at the seaward end of such a transverse bar originate for the same reasons 
that have been given for the development of the gyres associated with the relatively 
short bar. However, in order to account for the two shoreward gyres associated 
with the long variety of transverse bars, bottom friction must be taken into account. 
PUYNAM (1949) showed that the loss of wave energy due to currents induced in a 
permeable sea bottom, from wave action, varies as the square of the wave height 
and inversely with water depth. PUTNAM and JOHNSON (1949) showed that the 
same parameters control the dissipation of wave energy by bottom friction arising 
from the oscillating motion of the water at the sea bottom. 
When both are considered, Putnam and Johnson predicted a 40 ~ decrease 
in the height of waves arriving on the shore after travelling over a permeable 
foreshore with a 0.33 ~ slope. These relationships indicate that wave energy is 
more rapidly lost on the top of transverse bars than in the deeper areas between 
them. If the bar is long, a point will be reached where the wave energy above the 
bar is lost through friction more rapidly than it is replaced by additional refraction 
of wave energy from the flanks. This results in producing a smaller potential mass 
transport velocity over the transverse bars than in the area between the bars. For 
this reason the flow will be toward shore between the bars with the return over the 
bars, landward of the critical point. This process explains the two additional 
meshed gyres which produce the offshore current over the crest on the shoreward 
end of the long transverse bar. 
The processes of sediment transport by a combination of waves and currents 
are presently not well enough understood to permit the presentation of a quantitative 
relationship which can be related to this study. TANNER (1964) showed that a 
weak current is capable of transporting sediment when it provides a bias to the 
movement of sediments which are being agitated by bottom pressure fluctuations 
under wave action. The dyed sediment studies indicated that the currents associated 
with transverse bars do transport sediment. In order for such a feature to maintain 
itself the sediment must be supplied to the end and up the flanks at a rate which is 
adjusted to the rate at which it is lost at the other end. Whether the sediment is 
transported toward or away from the beach, depends on the relative length of 
the bar. 
Marine Geol., 9 (1970) 41-62 
58 A . W . N1EDORODA AND W. F. TANNER 
This is the critical point in the theory of the function of transverse bars. 
The rates and directions of sediment transport must be so adjusted that a time- 
averaged equilibrium is established which maintains the general geometric form 
of the transverse bar. 
PRICE (1953) correlated the slope of the offshore area with the local breaker 
heights. Long, gentle slopes lead to significant loss of wave height through bot tom 
friction. Therefore, areas with gently sloping offshore areas give rise to low 
average breakers. 
Under these conditions, small irregularities on an elsewise smooth foreshore 
can cause significant refraction of the waves. A watch glass placed in a ripple tank 
will cause an extensive amount of refraction whereas the same watch glass placed 
on the foreshore of a natural beach will have no discernable effect on the waves. 
in shallow water the wave period and the wave height have no effect on refraction. 
Refraction is purely a function of the local difference in depth along a sloping 
bottom. Therefore, the amount of refraction caused by a given slope must be 
inversely related to the depth. 
In the shallow area a small irregularity of the offshore slope will cause 
significant refraction. This refraction will cause an unequal distribution of wave 
energy in the nearshore area which, in turn, will serve to modify the sediment 
transport in that area to increase the original irregularity of the slope. Such a 
process appears to be responsible for the formation of transverse bars. 
A rough spacing between transverse bars has been noted. This somewhat 
irregular spacing may develop because the currents associated with any one 
particular bar influence only a limited area of the foreshore. Beyond the influence 
of the currents associated with one bar, the foreshore provides the environment 
for the formation of another bar. I f the spacing is too close the two current systems 
will interfere and the two bars may merge into a single feature. If the spacing is 
too great another bar may develop between them. 
RESULTS AND DISCUSSION 
From the model studies and the field work it is apparent that the bathymetry 
of the nearshore zone is delicately adjusted, on a time-averaged basis, to the local 
wave characteristics, in areas where transversebars occur. When this balance is 
obtained, the sediment is transported at exactly the proper rate to maintain the 
geometric form of the transverse bars. The interaction of waves, currents, and 
sediment transport tends to perpetuate these bars. This system evolves at the result 
of an unequal distribution of wave energy in the nearshore area due to wave 
refraction and bot tom friction. 
Wave-produced currents move sediment either toward or away from the 
beach depending on the relative lengths of the bars. Relatively short transverse 
bars tend to transport sediment toward the beach. Wave energy is concentrated 
Marine Geol., 9 (1970) 41 62 
PRELIMINARY STUDY OF TRANSVERSE BARS 59 
over the crest of the bar by refraction. This increases the potential mass transport 
relative to the areas of lower waves between the bars. The result is a narrow, 
relatively strong current (toward the beach; over the crest of the bar) which 
eventually returns seaward as a sluggish current between the bars. The current 
toward the beach is sufficiently strong to transport sand to the beach while the 
return currents are not competent to carry sediment away from the beach. The 
result is that relatively short transverse bars carry sediment to the littoral drift 
current along the beach. Where this sediment meets the beach a cusp-like feature 
develops on the beach face. The transverse bar maintains its form by the addition 
of sediment to its seaward end and up its flanks at the same rate at which it is 
delivering sediment to the beach. 
Over long transverse bars, wave energy is lost more rapidly through bottom 
friction over the crest than over the flanks. Therefore, there is a greater capacity 
for mass transport between the bars, in the area near the beach. This results in an 
offshore movement over the crest of the bar for much of its length. Sediment is 
transported from the beach to the offshore areas by the waves and currents 
associated with relatively long transverse bars. 
The currents associated with the wave refraction pattern developed over 
transverse bars are rather distinct when the system is isolated in a model wave 
tank. The data from the model wave tank experiments show that the velocity 
of the wave produced currents over short transverse bars varies as an exponential 
function of the wave height and inversely with water depth. These data support 
the argument that the currents are produced by an increased potential mass 
transport of water over the crest of a short transverse bar, relative to the area 
between the bars, in that the theoretical expression for the mass transport velocity 
can be shown to vary as the square of the wave height and inversely with water 
depth. However, an expression for the mass transport velocityin the case of horizon- 
tal circulation has not yet been developed. 
In the natural environment the wave-produced currents associated with 
transverse bars are but one component of the complex nearshore current system. 
In the field studies here reported, this component was occasionally sufficiently 
dominant to permit documentation of its existence. It is probable that this near- 
shore current component plays a less apparent role in nearshore environments 
where some bottom features are transverse to the beach. SONU et al. (1966) 
reported local variations in the longshore current velocities which are associated 
with secondary circulation cells developed in the vicinity of nearshore lunate 
bars. SONy and RUSSELL (1966) reported transverse sediment transport in the 
vicinity of these features. Lunate bars have one end which lies essentially transverse 
to the beach and it is likely that a current component similar to that studied in 
relation to transverse bars causes the reported deflection of the longshore current 
and the transverse sediment movement associated with lunate bars. As yet, 
insufficient work has been carried out to determine whether this component results 
Marine Geol., 9 (1970) 41-62 
60 A. W. NIEDORODA AND W. F. TANNER 
in a mass transfer or a momentum transfer (or some intermediate ease) between 
the offshore area and the breaker zone in the ease of lunate bars. 
In the event that wave statistics are not available, transverse bars along a 
stretch of beach can be used as an indicator of low average annual breaker height. 
These features also generally indicate a very gently sloping offshore area. 
Extrapolation of the current system, associated with transverse bars, to 
larger scale features requires careful study in that mass transport velocities, wave 
refraction, sediment transport, and other important processes vary non-linearly 
with depth. 
CONCLUSIONS 
(1) The bars control current gyres which provide for a sensible mass 
transport of water f rom the surf zone toward the sea. 
(2) The bars focus wave energy in such a way that sediment motion is 
dominantly back-and-forth across the bar crests; that is, the presence of the bars, 
under certain wave regimes, guarantees their preservation under those regimes. 
Sand is concentrated, up to some limiting value, along the bars, rather than 
removed from the bars, as a result of wave refraction or focusing. 
(3) On a slightly larger scale, sand motion is parallel with the bar crests. 
In some instances, sand transport is toward the beach; under other circumstances, 
it is toward open water, resulting in a spectacular seaward elongation of primitive 
transverse bars. 
(4) Littoral drift may be indicated (as motion on a third scale) where the 
bars do not intersect the average toe line at 90 ° 
(5) Tidal changes modify the circulation patterns somewhat, but are not 
primarily responsible for either the initiation or the maintenance of the bars. 
(6) The seaward currents which develop between short bars are not strong 
enough to produce appreciable sediment transport; over the bars proper, it is a 
current bias, superimposed on wave motion, which provides for net sand grain 
movement. 
(7) Beach cusps may or may not occur along the same stretch of beach 
characterized by transverse bars. Cusps have much shorter spacing than bars, 
and are higher on the beach. 
(8) None of the circulation patterns studied over, or near, transverse bars, 
to date, would qualify as a rip current. 
(9) Oscillation type ripple marks which form along the bar crests are 
generally parallel with the long axes, and are at right angles to the beach toe; 
they bisect the angle between the intersecting wave sets. 
(10) Once a segment of wave crest has crossed a bar, refraction causes a 
curvature of the orthogonal in such a way that the same wave crest segment tends 
to re-approach the bar f rom a different direction. This means that much of the 
Marine Geol., 9 (1970) 41-62 
PRELIMINARY STUDY OF TRANSVERSE BARS 61 
wave energy, along barred beaches, is concentrated on the bars rather than on the 
beaches. 
(11) Very long bars tend to have forked, or split, ends, revealing the current 
pattern. 
(12) The transverse bar is an equilibrium feature, in which geometry is 
produced by a delicate balance between waves, currents, and sediment transport. 
Where this balance is easily destroyed, bars are ephemeral; where this balance 
is easily maintained, bars are more or less permanent. The equilibrium is a dynamic 
one, with both material and energy moving through the system. 
ACKNOWLEDGMENTS 
The work reported herein was supported in part by Office of Naval Research 
contract N-00014-68-A-0159 with Florida State University, through the Geophysical 
Fluid Dynamics Institute. Wave tank facilities were made available by Dr. Robert 
G. Dean of the Coastal and Oceanographic Engineering Department of the 
University of Florida, Gainesville. The authors wish to express their appreciation 
for field assistance provided by Dr. Richard Gentile, William Sinclair, Gary 
Norsworthy, John Ryan, David Poche, George Horvath, Jack Stonebraker and 
Victor Fisher. Robert Holley of theFlorida State University Department of 
Oceanography provided much appreciated assistance with modification of the 
wave orthogonal plotting program. 
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