The importance of critical levels in geophysical flows stems from their omnipresence and complex wave/mean-flow interactions in their vicinity. A critical level is a surface at which the intrinsic frequency of a plane wave with the horizontal wavenumber vector and frequency vanishes. For mountain waves resulting from a steady forcing by the flow over topography, and the critical levels arise wherever. The name critical derives from the singularity of the linearized inviscid time-independent equations (and their solutions) at such levels (Miles 1961; Booker and Bretherton 1967), indicating that the transience, momentum and heat diffusion as well as nonlinear steepening and amplification of waves are important in their vicinity (Maslowe 1986; chap 4.11 in Baines 1995). For the local Richardsonnumber Ri>1/4 at a critical level, linear inviscid theory predicts that infinitesimal perturbations are smoothly absorbed and deposit their momentum into the mean flow below the critical level. Whether this occurs in reality, depends on the amplitude of perturbations as well as the effectiveness of viscous processes in preventing nonlinear steepening and wavebreaking.
In atmospheric flows over complex terrain, gravity waves encounter
their critical levels, in general, at different altitudes where
the projection of the mean velocity on a given wavenumber vector
vanishes. A number and location of critical levels depends on
a degree of directional wind shear and topographic spectrum (Shutts
1995). In this study, we address only unidirectional, steady,
constant-shear flows with a critical level located where, and
describe the 3D steady wave pattern forced by a small-amplitude
isolated axisymmetric obstacle. Since linear inviscid solutions
are singular at the critical level, we use a numerical model to
assess the impact of dissipation and local nonlinearities on the
solutions. In the parameter space spanned by the nondimensional
mountain height and the Richardson number Ri, we determine the
bounds of a regime in which our linear solutions are valid everywhere
except in the vicinity of the critical level where numerical solutions,
as well as natural flows, are regularized by viscous dissipation
(Kelly 1977; Worthington and Thomas 1996).
Click here for further information