Beyond Long's solution: exploring the rotating and nonhydrostatic mountain wave regimes

For nonrotating flows, Long's analytic model provides a convenient and tractable description of nonlinear mountain-wave dynamics. However, this description is somewhat limited by its restricted parameter space, as attempts to extend the solutions to the rotating problem have proved difficult. The solutions also become difficult if the flow is strongly nonhydrostatic. Recently, a steady solver was developed based on a nonlinear Newton iteration which effectively extends Long's solution space to the rotating regime. In the present study this solver is extended further to include nonhydrostatic effects and then applied to examine wave steepening over the full range of parameter space. The space spanned by the nondimensional mountain height (F=NH/U), rotational parameter (R=fL/U), and aspect ratio (D=U/NL) is explored for the case of flow with constant background N and U. Results include a complete mapping of the surface drag values as well as the curve of critical mountain heights at which wave overturning occurs. Relative to the hydrostatic nonrotating regime, the onset of wavebreaking is shown to occur at increasingly larger mountain heights with both increasing rotation and decreasing horizontal scale. Solutions are also demonstrated for flows with nonconstant background wind and stability. In a companion study, the stability of the mountain waves is explored using a linear instability analysis.