Physical Oceanography Surface Gravity Waves Properties Dispersion Refraction & Diffraction Group velocity Generation Assignment: Read Chapter 16 of Stewart: Intro to PO

Importance of Surface Waves ✔ Mediate the transfer of momentum from winds to currents ✔ generate internal waves ✔ provide means to estimate wind stress via scatterometer ✔ provide means to map ocean currents via radar

Practical Importance of Surface Waves

Wavelength (L) or Period (T) Basic Wave Parameters Height (H) Amplitude (A) Crest Trough  (x) = A cos ( [2  /L] x ) = A cos ( k x )  (t) = A cos ( [2  /T] t ) = A cos (  t ) k: wavenumber,  frequency

Propagating Waves x

Note the following limits: kD small means tanh(kD)  kD kD large means tanh(kD)  1

Wave Dispersion

Two waves of slightly different wavenumber and frequency, chosen with the dispersion relation appropriate to short gravity waves. As you watch the animation, note how the waves go in and out of phase, meaning that what you observe will be twice as big – or zero! Note also that as the “blue” wave runs out ahead of the “red” wave, this pattern itself propagates.

Example: superposition of two waves

We’ll now look at group speed from a bit different view …

GROUP SPEED IS FUNDAMENTAL! If there is a storm, do you see the energy when the “phase” reaches you, or when the energy does? Obviously the energy, right? So when you work the exercises involving storms and propagation times, group speed is the important thing!

How to represent the ocean wave field? The wave energy density spectrum

Wave spectra for fully developed sea

A Fully Developed Sea Suppose the wind starts blowing over some region. What controls how big the waves get? Wind speed, duration, and fetch. What limits how big the waves get? When the waves are fast enough that they leave the area before getting more energy input; i.e., when the period is relatively long. As time passes, short (slow) waves transfer energy to longer (faster) waves …

Wave spectra for fully developed sea

Wave spectra for different fetches

PAU

So now we know how to propagate the energy from storms to the beaches, but how does the storm (i.e., the wind) generate the waves in the first place? We don’t really know the answer to this, but we do have some empirical relations that allow us to relate wind speed, duration and fetch to wave heights and dominant periods. That’s what we’ll talk about for the remainder of the today.

Coming Attractions Continue with surface gravity waves next time Group velocity, very important Brief discussion of wave generation and prediction Next lecture is on Internal Waves Similar to surface waves in some ways, not so similar in other ways

Particle Orbits

Last Time Deep water formation Water masses Deep circulation Today Surface gravity wave properties Dispersion relations Refraction and Diffraction