Large-scale anisotropy in stably stratified rotating flows

Tuesday, 16 December 2014
Raffaele Marino, National Center for Atmospheric Research, Boulder, CO, United States; CNR Institute for Chemical and Physical Processes, Cosenza, Italy, Pablo D. Mininni, University of Buenos Aires, Departamento de Fisica, FCEN,, Buenos Aires, Argentina, Annick Pouquet, University Corporation for Atmospheric Research, Boulder, CO, United States, Duane L. Rosenberg, Oak Ridge National Lab, Oak Ridge, TN, United States and Corentin Herbert, National Center for Atmospheric Research, ASP, Boulder, CO, United States
We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 10243 grid points and Reynolds numbers of ≈ 1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with ∼ k -5/3, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.