# Population of Slow Manifolds in Strongly Stratified, Rotating Flows with Unbalanced Turbulent Forcing

Tuesday, February 12, 2002 - 9:30am - 10:30am

Keller 3-180

Leslie Smith (University of Wisconsin, Madison)

Numerical simulations are used to study the population of slow manifolds in rotating, stably stratified flow in the Boussinesq approximation, with rotation and stratification both in the vertical direction. Energy is injected through a three-dimensional, isotropic, white-noise forcing localized at small scales. The parameter range studied corresponds to Froude numbers smaller than an O(1) critical value, below which energy is transferred to scales larger than the forcing scales. The values of the ratio N/f range from 1/2 to infinity.

For purely stratified flows, there exist two distint classes of non-wave modes: the Vertically Sheared Horizontal Flow (VSHF) modes with dependence only on the vertical wavenumber, and the Potential Vorticity (PV) modes, existing for all wavevectors and with zero vertical velocity. For strongly stratified flows with N/f >> 1, the only non-wave modes are the PV modes, while the VSHF modes have (small) wave frequency f or -f. Somewhat surprisingly, for all strongly stratified flows including the purely stratified case, our simulations show that the large scales generated by the turbulence are the VSHF modes. In this case, the PV modes play a secondary role, acting to inhibit the transfer of energy to large scales. On the other hand, for N/f between 1/2 and 2, our simulations show that the inertial-gravity waves are insignificant and that the dynamics are completely dominated by the PV modes. This is quasi-geostrophic turbulence characterized by the inviscid conservation of two quadratic invariants and a -5/3 inverse energy cascade. The region 1/2

For purely stratified flows, there exist two distint classes of non-wave modes: the Vertically Sheared Horizontal Flow (VSHF) modes with dependence only on the vertical wavenumber, and the Potential Vorticity (PV) modes, existing for all wavevectors and with zero vertical velocity. For strongly stratified flows with N/f >> 1, the only non-wave modes are the PV modes, while the VSHF modes have (small) wave frequency f or -f. Somewhat surprisingly, for all strongly stratified flows including the purely stratified case, our simulations show that the large scales generated by the turbulence are the VSHF modes. In this case, the PV modes play a secondary role, acting to inhibit the transfer of energy to large scales. On the other hand, for N/f between 1/2 and 2, our simulations show that the inertial-gravity waves are insignificant and that the dynamics are completely dominated by the PV modes. This is quasi-geostrophic turbulence characterized by the inviscid conservation of two quadratic invariants and a -5/3 inverse energy cascade. The region 1/2