**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Friday, April 29, 2016 — 2:00 PM EDT

MC-6496

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.

- Lecture (1)

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.