A NOTE ON THE APPLICATION OF LINEAR WAVE THEORY AT A CRITICAL-LEVEL

The purpose of this note is to estimate the accuracy and practical lim itations of applying linear theory at a critical level over a realisti c range of atmospheric stabilities for an idealized surface terrain. T hese estimates are made by comparing the results of a linear model wit h a nonlinear numerical model at a critical level. Essentially similar results are obtained from each model for wave stress, wave breaking h eight and wave dissipation through the critical level. Because gravity waves can be either evanescent or internal depending on the relative sizes of the Scorer parameter and the wavenumber of the ground surface disturbance, the somewhat paradoxical result develops that wave break ing and non-linearity increase with increasing bulk Richardson number. It is recommended that steady linear wave theory be used in gravity w ave drag parameterizations provided near real time profiles of backgro und velocity and temperature are available.