The Theory and Theology of Nonlinear Balance

Monday, February 11, 2002 - 11:00am - 12:00pm
Keller 3-180
James McWilliams (University of California, Los Angeles)
A didactic presentation will be given on the premises, mathematical structure, regimes of validity, historical experience, evolutionary singularities, and unbalanced instabilities for the reduced fluid-dynamical system, the Balance Equations. The Balance Equations are an asymptotically consistent (but nonunique) set of approximations for rotating, stably stratified flows, built around the quasi-static momentum balances of hydrostacy in the vertical and gradient-wind balance in the horizontal divergence.

It is widely agreed that the vast majority of the energy in the general circulations of the ocean and atmosphere is in balanced motions. In this context, the organizing focus of the talk will be on the mystery of large-scale energy dissipation in the ocean and atmosphere: planetary forcing energizes large-scale balanced motions, including balanced instabilities of the directly forced flows; balanced flows are asymptotically characterized by an inverse energy cascade towards larger scales, but there are few and relatively inefficient dissipation mechanisms available are large scales (e.g., bottom drag and radiative cooling); thus, somehow the route to dissipation at small scales remains to be elucidated.