| 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 |
| 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 |
| 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? |