Classes of Ocean & Hydro Linear Waves

Prévia do material em texto

1 
Ocean & Hydro 
MECH 7008 
Linear Waves 
Sea and Swell 
• Winds blowing across the water surface 
generate waves 
• Waves generated are a function of 
– Wind Velocity 
– Fetch 
– Time 
Sea and Swell 
• Waves still under the action of the winds that 
created them are referred to as a sea 
• These are forced waves, rather than free 
waves 
2 
Sea and Swell 
• When waves leave the generating area 
– They become smoother 
– Smaller waves on top of bigger waves disappear 
• These waves are are known as a swell 
Sea and Swell 
• In practice the situation is more complex 
– Waves leaving a generating area will encounter 
winds as they travel 
– Waves also encounter other waves 
• Thus wave troughs and crests appear and 
disappear 
Sea and Swell 
• In a wave system 
– Long wave components move toward the front of 
the system 
– Shorter wave components drop to the rear of the 
system 
• This is known as dispersion 
3 
Linear Waves 
Wave Formula 
Graphical Solution 
4 
Phase Velocity c 
Deep Water Approximation 
Deep Water Approximation 
5 
Shallow Water Wavelength 
Shallow Water Velocity 
Shoaling Waves 
6 
Particle Velocities 
Deep Water Approximations 
Shallow Water Approximations 
7 
Wave Energy 
Wave Group 
Phase and Group Velocity 
8 
Phase and Group Velocity 
Phase and Group Velocity 
Linear Wave Theory 
• Applies where height/wavelength is 1/50 or 
less 
• Non-linear wave theory is also utilised in some 
instances 
9 
Non- Linear Wave 
Trochoidal Wave 
Stoke’s Wave 
10 
Particle Velocity - Linear 
Particle Velocity - Stokes 
Break - Linear 
11 
Break - Stokes 
Break - Stokes 
Significant Wave Height 
 
• Height of the highest of 1/3 of the waves 
• Denoted H1/3 or Hs 
 
12 
Ocean Wave Spectra 
• An idealised representation of the distribution 
of wave frequencies 
• Function of 
– Wind speed 
– Fetch 
– Time 
Ocean Wave Spectra 
• Idealised because 
– Wind rarely blows at constant velocity 
– Rarely blows in same direction for long period 
– Influence of waves generated elsewhere is rarely 
absent 
Pierson-Moskowitz Spectrum 
• Assumptions 
– Wind blowing steadily 
• For a long period 
• Over a large area 
– Waves come into equilibrium with the wind 
• ‘Fully Developed Sea’ 
13 
Pierson-Moskowitz Spectrum 
• Derived from 
– Wave measurements from weather ships 
– North Atlantic 
– Wave data selected for wind 
• Blowing for long periods 
• Over large areas 
 
 
Pierson-Moskowitz Spectrum 
Pierson-Moskowitz Spectrum 
14 
Pierson-Moskowitz Spectrum 
Pierson-Moskowitz Spectrum 
Pierson-Moskowitz Spectrum 
 
• Waves in spectrum are travelling faster than 
wind! 
15 
JONSWAP Spectrum 
• Joint North Sea Wave Observation Project 
• Wave spectrum is never fully developed 
• A peak enhancement factor is added to the 
Pierson-Moskowitz Spectrum 
JONSWAP Spectrum 
JONSWAP Spectrum 
16 
JONSWAP Spectrum 
JONSWAP Spectrum