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# Numerical simulations of the flow of a continuously-stratified inertial effects

preprint

posted on 2006-02-06, 16:13 authored by A. Aigner, Roger GrimshawA high-resolution spectral numerical scheme is developed to solve the
two-dimensional equations of motion for the
ow of a density stratified,
incompressible and inviscid
fluid. It incorporates the inertial terms ne-
glected in the Boussinesq approximation. Thus it aims, inter alia , to
extend the numerical simulations of Rottman et. al. [12] and Aigner et.
al. [1].To test its validity, the code is used for two applications. One is the
resonant
flow over isolated bottom topography in a channel of finite depth,
which has been studied extensively in the Boussinesq approximation. The
inclusion of inertial effects, that is the influence of the stratification on the
acceleration terms, discarded in the Boussinesq approximation, allows the
comparison of the solution to the unsteady governing equations with the
fully nonlinear, but weakly dispersive resonant theory of Grimshaw and
Yi [7]. The focus is on topography of small to moderate amplitude and
slope, and for conditions such that the
flow is close to linear resonance for
either of the first two internal wave modes. We also determine the ver-
tical position where wave-breaking occurs. The other application is the
propagation of large-amplitude internal solitary waves with vortex cores,
again in a channel of finite depth. We aim to verify the existence and
permanence of these types of waves derived by Derzho and Grimshaw [5].
Furthermore the time-dependent solution provides measurements of the
structure of the vortex core and maximum adverse velocity at the top
boundary.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

1025638 bytes## Publication date

2000## Notes

This is a pre-print.## Language

- en