Internal Waves 3 - High frequency


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.


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


Movie and text - Barry Ruddick
Digitization of movie - Dave Hebert

Load and run high frequency internal waves movie