Chengzhu (William) Xu
Applied Mathematics, University of Waterloo
Wave-Mean Flow Interaction and Its Applications
A common practice in the study of environmental and geophysical fluid dynamics is to divide the overall flow field into a mean flow and a departure from the mean flow, often referred to as a wave. Because of the various length and time scales involved, interaction between the waves and the mean flow leads to a number of phenomena. Here, we study wave-mean flow interaction in two different areas, internal wave dynamics and large-scale atmospheric circulation. For internal waves, the mathematical formulation is based on the WKB theory. It is well developed for a weakly nonlinear environment, but less so for a fully nonlinear environment. For this part of the project, we investigate internal wave dynamics with numerical simulations performed of a fully nonlinear background flow, which cannot be expressed in analytical form. For large-scale atmospheric circulation, wave-mean flow interaction leads to the Eliassen-Palm theorem, which describes the dynamics controlling the response of the extratropical atmospheric circulation to climate perturbations, for example wave teleconnections originating in the tropics. In this part of the project, we examine two different topics, the linear interference effects and Rossby wave critical layer dynamics. While wave-mean flow interaction is used to describe fluid flow in different context, the general conclusion is the same in both cases: energy exchange between the waves and the mean flow occurs while the wave action (or wave activity) is conserved.