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CNA Seminar
Jared Whitehead
Brigham Young University
Title: Multiple time scales and geophysical fluid dynamics: reduced equation sets and slow manifolds

Abstract: The first accurate numerical weather prediction of the 1950s utilized a model reduction of the full equations of motion for atmospheric flow. This reduction relies on the concept that fast waves in geophysical fluid dynamics have little to no effect on the slower evolving mean flow (often referred to as the slow manifold) of the system. By eliminating the fast waves, Jule Charney and colleagues were able to develop a system of equations amenable to numerical integration. Since that first success, several distinct model reductions have been applied in the community based on the same concept that the fast waves have little to no effect on the more important, slower mean flow of the full system.

In this talk we review these concepts in the context of the rotating, stably stratified Boussinesq system. Using direct numerical simulations we explore the validity of each of these limits, and the relative accuracy of the asymptotic approximation as the small parameter remains finite. Following intuition gained from these numerical observations we use the theory of cancellation of oscillations to demonstrate that the limit of two fast, yet distinct time scales is not the same as if these two scales are identical.

Date: Tuesday, April 22, 2014
Time: 1:30 pm
Location: WEH 7218
Submitted by:  Gautam Iyer