Chengzhu Xu , Applied Mathematics, University of Waterloo
Wave-Mean Flow Interaction
A common practice in the study of transitional and turbulent flow is to divide the overall flow field into a mean flow and a departure from the mean flow, often referred to as a wave (or “eddy” in turbulent flow). The interaction between the mean flow and the waves is generally a two-way process, since the mean flow can modify the wave propagation, while the waves themselves can also change the mean flow. We discuss wave-mean flow interaction in small-scale transitional flow as well as in large-scale atmospheric circulation. For small-scale transitional flow, we study internal waves interacting with a parallel shear flow. The mathematical formulation is based on the WKB theory, and numerical simulations are performed when a mean flow 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. We will further discuss the role of linear interference in such teleconnections. 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.