Dynamical Equations and Turbulent Closures in Geophysics

Based on scaling arguments the governing equations for turbulent flows are classified. The similarity for stratified and rotating flows is characterized and the conditions for a hydrostatic assumption are shown for several flow regimes. For stratified rotating flow a scale analysis of the turbulent stresses exhibits different classes of second order closure. The complete sets of the governing equations for second and third order turbulent closures are presented. The evolution of the equations is embedded into a historical chronology. Received September 15, 1997