P2.16
Effects of dispersion on zero and fast mode spectra in three-dimensional rotating stratified flows
Jai Sukhatme, University of Wisconsin-Madison, Madison, WI; and L. M. Smith
Utilizing an eigenfunction decomposition, we study the scaling of energy spectra in the zero and fast modes of a three-dimensional (3D) rotating stratified fluid as a function of dispersivity, i.e. of ε = f/N : where f,N are the Coriolis parameter and Brunt-Vaisala frequency. Throughout we work in a unit aspect ratio domain and set these parameters such that the Froude and Rossby numbers are comparable and < < O(1). In fact it is the added possbility of interscale energy transfer by means of fast-fast-fast (near-)resonant interactions in the presence of dispersivity that motivates this inquiry. Starting from the well understood reference state of ε=1, employing a random large scale forcing, we see that the fast modes always transfer energy to small scales. But their scaling steepens from k-1 to k-5/3 for kf < k < kd (where kf,kd are the forcing and dissipation scales) as ε moves away from unity. On the other hand, the zero modes follow a k-3 scaling for kf < k < kε and a k-5/3 form for k ε < k < kd with kε = kd when ε differs from unity --- i.e. in the non-dispersive case, instead of being dissipated a fraction of the energy deposited at small scales by the fast modes appears to be transferred upwards into the zero modes. Further, in all cases the zero mode energy for all k < kf grows indicating a clear inverse transfer of energy. Curiously, we notice an unequal partitioning of energy between the different modes at k=kf --- specifically, the zero modes always have a greater amount of energy at the forcing scale. Ofcourse, this naturally leads to a steep-shallow transition in the total energy spectrum.
Poster Session 2, Atmospheric Dynamics
Tuesday, 26 June 2007, 5:00 PM-6:30 PM, Ballroom North
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