We have carried out a numerical investigation of the nature of high-drag states occurring in nonlinear stratified flow over obstacles. In particular, we consider the relative merits of theories which view the drag enhancement as due to linear resonance vs mechanisms which seek to exploit analogies with nonlinear hydraulic theory.
First we examine the behavior of the system as a function of the height of a zero-wind line imposed in the ambient flow. The character of the high-drag states conforms well to the predictions of the internal hydraulic analysis of Smith, and cannot he explained in terms of linear resonance. However, a high-drag state emerges even when the initial critical level height is below the lowest predicted resonant height. In this case an upstream-propagating bore is generated which adjusts conditions so as to allow a high-drag sate. Further experiments with a narrow mountain revealed that nonhydrostatic effects do not appreciably affect the behavior for the lowest resonant position, but considerably reduce drag at the higher order resonances.
In the second series of experiments, the numerical model is initialized with the idealized high-drag states yielded by Smith's theory, subject to uniform upstream wind conditions. When the mountain is high enough to produce wavebreaking in uniform flow, an overturning region develops at the theoretical level of no motion and a vertically propagating wave emerges aloft; nevertheless, the flow near the ground remains substantially unaltered. When the mountain is too low to support wavebreaking, the mixed region in the lee collapses, and the flow reverts to a nonhydraulic Long's model solution subject to a radiation upper boundary condition. Thus, wavebreaking is a crucial part of the dynamics maintaining the high-drag state.
Our results expose some aspects of nonlinear gravity wave critical level behavior that are of general interest. The long term properties of the critical level were found to depend on the phase of the incident wave. Of particular interest are the circumstances in which the critical level acts as an absorber for all time. In this case the convergence of vertical momentum flux is balanced by a divergence of horizontal momentum flux, a state of affairs which can occur only for a horizontally localized wave packet incident an a horizontally unbounded critical level.