Transients in the Nonlinear Adjustment to Geostrophy
The consequences of nonlinearity on the character of the waves generated during the adjustment to geostrophic equilibrium of a layer of incompressible fluid are investigated by comparing the results of a linear analysis to the approximate solution to the full nonlinear problem obtained numerically. The calculations show that when nonlinear advection and rotation are both important to the dynamics, the evolution of the flow is quite different from that found in the linear, rotating problem of Cahn and the nonlinear, nonrotating problem of Stoker. Solutions presented demonstrate that the adjustment is accomplished by the formation of a large amplitude jump in layer depth which propagates in the opposite direction to that of the initial discontinuity, i.e. towards high pressure. Comparison of this solution to that for the linear problem suggests that the jump is formed by the steepening of Poincare waves and that nonlinear effects have little influence on the rate of approach to the final geostrophic state.
KeywordsLayer Depth Coastal Current Hydraulic Jump Buoyant Plume Nonlinear Advection
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