Critical Layer Effects on Atmospheric Solitary and Cnoidal Waves

Abstract

The interactions of atmospheric cnoidal waves with a critical level are examined using a two-dimensional numerical model. A cnoidal wave system is generated by applying a bore initial condition to a shallow surface-based inversion; the system is analyzed using various profiles of stability and shear. Under neutral conditions a critical level is shown to cause wave reflection with wave growth, as indicated by the vertical velocity, when the stability is low. Increasing the ambient stability above the cnoidal wave leads to a reduction in the reflective properties of the critical level and an increase in critical level absorption. The division between wave growth and wave decay occurs near a critical level Richardson's number of 0.25 agreeing with instability theory. When a variable profile of stability is assumed, with stable regions both below and above the critical layer and weak stability at the critical level region, the cnoidal wave system again amplifies, but not as strongly. The results conform with past analytical results pertaining to the atmospheric structure required for wave reflection and absorption. However, the occurrence of overreflection cannot be diagnosed from the simulations because of the strongly nonlinear, unsteady behavior of the cnoidal wave systems.