Internal waves in a contained rotating stratified fluid

Abstract

Small-amplitude time-dependent motions of a uniformly rotating, density-stratified, Boussinesq non-dissipative fluid in a rigid container are examined for the case of the rotation axis parallel to gravity. We consider a variety of container shapes, along with arbitrary values for the (constant) Brunt-Väisälä and rotation frequencies. We demonstrate a number of properties of the eigenvalues and eigenfunctions of square-integrable oscillatory motions. Some of these properties hold generally, while others are shown for specific classes of containers (such as with symmetry about the container axis). A full solution is presented for the response of fluid in a cylindrical container to an arbitrary initial disturbance. Features of this solution which are different from the cases of no stratification or no rotation are emphasized. For the situation when Brunt-Väisälä and rotation frequencies are equal, characteristics of the oscillation frequencies and modal structures are found for containers of quite general shape. This situation illustrates, in particular, effects which are possible when rotation and stratification act together and which have been overlooked in previous investigations that assume that the vertical length scale is much smaller than the horizontal scales.

Completeness of inertial modes of an incompressible inviscid fluid in a corotating ellipsoid

“…For these oscillations buoyancy and Coriolis force are the restoring forces at work. They make gravito-inertial waves possible [2,3].…”

Meridional trapping and zonal propagation of inertial waves in a rotating fluid shell

“…Results for a homogeneous rotating shell are modified locally when radial stratification is present, where curved rays replace the straight characteristics considered here and where turning surfaces may limit the part of the fluid domain accessible to waves (Friedlander & Siegmann, 1982;Friedlander, 1982;Dintrans et al, 1999); on the other hand, the pure inertial problem summarizes many of the difficulties and the features of the gravito-inertial problem, and findings in this partial case are supposed to have general validity.…”

Asymptotic behaviour of decay rates of internal waves in a rotating stratified spherical shell

“…the semidiurnal frequency and the rotation frequency are equal. In this case the whole spectrum of the inertial gravity waves coalesces into a single mode whose frequency is the common value of these natural frequencies (Friedlander & Siegmann 1982a). This confluence mode is remarkable because the entire mode persists until the long diffusive time-scale is achieved.…”