Slide 1

High rotation rate effects - Taylor Columns

Triply periodic rotating and stratified Boussinesq equations

Method of Multiple Scale -- Embid and Majda style.

The equations for the slow dynamics are, ,
u, v, w all functions of (x,y) only.

Numerical Simulations

Numerical simulations - Globally integrated total and slow potential enstrophy.

Take home message

The Nondimensional Boussineseq Equations

Boussinesq equations In non-local form

In operator form

Method of Multiple scales - write the abstract form with epsilon and tau.

Method of multiple of time scales

Separation of time scales - Fast wave averaging equation

By direct computation the fast wave averaging equation

Example of a linear operator

The nonlinear operator

Find the equations for the slow dynamics

The null space of the fast operator

The leading order conservation laws in the absence of dissipation,

Analysis of the fast operator

Do the horizontal and vertical kinetic energies decouple?