NONLINEAR INTERNAL WAVES OVER VARIABLE TOPOGRAPHY

A nonlinear two-layered fluid system on a variable bottom with freely moving upper surface and abrupt density change at the interface is con sidered. The two stably stratified layers with constant densities are assumed to be immiscible. Starting from the continuity and the mometum equations of an incompressible inviscid fluid for each layer and asso ciated boundary and transition conditions at the free upper surface, t he interface and the bottom surface, vertically averaged equations are deduced that incorporate nonlinear advection and dispersion. The appr oximate equations are deduced by scaling the governing equations accor dingly and by using a limit analysis for small aspect ratios (shallown ess) and small amplitude disturbances. The limiting equations extend k nown model equations and include finite amplitude nonlinearities, disp ersion and variable topography. In a second step viscous effects and w ind forcing are also incorporated. These equations permit numerical in tegration and allow us to predict time series of the free surface and of the interface with given initial conditions. While the deduction of the numerical scheme is given elsewhere, we present here a descriptio n of the experimental set-up and compare experimentally derived interf ace time series with corresponding ones obtained from the computations . Agreement is generally excellent except where the experimental condi tions are not in conformity with the prerequisites of the theory. Anot her application of the derived theory can be found in wind forced exci tation of the barotropic and first baroclinic modes. We also present l ime series in this case.