Numerical Study of the Collapse of a Perturbation in an Infinite Density Stratified Fluid

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Abstract
The problem of finding the time‐dependent flow resulting from perturbing a small quantity of fluid in an infinite two‐dimensional fluid having a vertical density stratification is discussed. Since nonturbulent flow in an incompressible fluid is well described by the Navier‐Stokes equations in the Boussinesq approximation, these partial differential equations were approximated by an appropriate set of finite difference equations which were then solved numerically on a computer for a number of physically interesting cases. The equations to be solved and the algorithm to solve them are described and a comparison is made between the computational results and some experimental results. A collapsing perturbation is an efficient generator of internal waves, and these are clearly depicted in film images produced directly by the computer. Physical experiments with collapsing mixed regions in a fluid with linear density stratification have revealed distinctive patterns of internal wave propagation and flow of the mixed fluid; patterns that are accurately duplicated in corresponding numerical computations that are discussed.

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