Internal Waves 2- mode formation
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 wave field fills outwards from
the paddle, reflects from the walls, top, and bottom, and begin to
form modes.
Physics of the phenomenon:
(For discussion of wave crests, phase, and group velocity, see
Internal waves 1- low frequency.)
The wave "crests", or lines of constant phase, are the red and green
bands. The energy moves outwards from the paddle with the group
velocity, and reflects into waves of the same frequency at walls, top,
and bottom. A standing wave would be formed if the frequency were
chosen such that the reflected wave returns to the paddle with just
the right phase so as to reinforce the paddle-generated wave.
This set-up would be even more interesting if the bottom were sloped,
due to the strange reflection properties of internal waves at sloping
top/bottom.
Read about wave reflection from a sloping bottom in Phillips (1966), then
have a look at the interesting consequences at Leo Maas' web-site:
http://www.nioz.nl/nioz_nl/c7e02aab39a9bf4837e6b2a00882809c.php
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 mode formation movie