# Internal Waves 3 - High frequency

### Purpose:

To show the unusual, anisotropic phase and group velocity properties
of internal waves in a density-stratified fluid.

### What Happens:

A tank about 30 cm deep is filled with a salt stratification of
buoyancy period, ,
about 6 seconds. A solid cylinder of a
few cm diameter runs across the tank at mid depth, in the right of the
field of view. This cylinder is oscillated horizontally at frequency
less than N, generating internal waves. The flow is visualized with a
schlieren system that shows regions of positive isopycnal slope in
red, and negative isopycnal slope in green. Slopes close to zero show
as yellow. The movie is in time lapse, so that the waves appear to
have higher than real frequency. The movie starts from rest, and
after the paddle motion begins, the wave field starts to fill the tank
outwards from the paddle. The paddle frequency is much higher than
the first sequence, so that the characteristic slope of the rays is
much steeper.

### Physics of the phenomenon:

See "Internal waves 1 - low frequency,
for a discussion of the physics
and dispersion relation for internal waves:
If one considers disturbances of the form
, then
those disturbances must obey the dispersion relation for internal
gravity waves (Phillips, 1966):

This means that the frequency depends on the angle
, which is the
angle the wave crests and the wave energy flux or group velocity make
to the horizontal. Waves of a specific frequency can only propagate
at a specific angle. Note also that since , the
maximum allowed frequency is N, the frequency of the buoyancy
oscillation.

#### d. Effect of paddle frequency

The much higher frequency makes the characteristic angle much steeper.
Energy travels in nearly vertical paths, and phase propagation is
nearly horizontal. If the paddle frequency were to exceed N, internal
waves could not propagate, and the energy would be trapped in the
vicinity of the paddle. The buildup of energy would create a lot of
local mixing.
**References:**

Phillips, O.M. 1966. The dynamics of the upper ocean. Cambridge University
Press.

### Credits:

Movie and text - Barry Ruddick

Digitization of movie - Dave Hebert
Load and run high frequency internal waves movie