Generation of slow large scales in forced rotating stratified turbulence

Numerical simulations are used to study homogeneous, forced turbulence in three-dimensional rotating, stably stratified flow in the Boussinesq approximation, where the rotation axis and gravity are both in the zˆ-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 ∞, where N is the Brunt–Väisälä frequency and f is twice the rotation rate. For strongly stratified flows (N/f[Gt ]1), the slow large scales generated by the fast small-scale forcing consist of vertically sheared horizontal flow. Quasi-geostrophic dynamics dominate, at large scales, only when 1/2 [les ] N/f [les ] 2, which is the range where resonant triad interactions cannot occur.

[1]  R. Kraichnan.  Inertial Ranges in Two‐Dimensional Turbulence , 1967 .

[2]  Michael Selwyn Longuet-Higgins,et al.  Resonant interactions between planetary waves , 1967, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  O. Phillips.  The interaction trapping of internal gravity waves , 1968, Journal of Fluid Mechanics.

[4]  H. Greenspan.  On the non-linear interaction of inertial modes , 1969, Journal of Fluid Mechanics.

[5]  K. Hasselmann.  Stochastic climate models Part I. Theory , 1976 .

[6]  D. G. Vincent,et al.  Evidence of deep convection as a source of synoptic-scale kinetic energy , 1979 .

[7]  R. Rogallo.  Numerical experiments in homogeneous turbulence , 1981 .

[8]  D. Lilly,et al.  Mesoscale Variability of the Atmosphere , 1983 .

[9]  G. D. Nastrom,et al.  A Climatology of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft , 1985 .

[10]  G. D. Nastrom,et al.  Theoretical Interpretation of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft During GASP , 1986 .

[11]  T. Warn.  Statistical mechanical equilibria of the shallow water equations , 1986 .

[12]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[13]  D. Lilly.  Two-dimensional turbulence generated by energy sources at two scales , 1989 .

[14]  J. Herring,et al.  Numerical experiments in forced stably stratified turbulence , 1989, Journal of Fluid Mechanics.

[15]  M. Maltrud,et al.  Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence , 1991, Journal of Fluid Mechanics.

[16]  J. Riley,et al.  Internal wave—vortical mode interactions in strongly stratified flows , 1991, Journal of Fluid Mechanics.

[17]  Fabian Waleffe,et al.  Inertial transfers in the helical decomposition , 1993 .

[18]  C. Cambon,et al.  Detailed investigation of energy transfers in homogeneous stratified turbulence , 1994 .

[19]  J. Chasnov.  SIMILARITY STATES OF PASSIVE SCALAR TRANSPORT IN ISOTROPIC TURBULENCE , 1994 .

[20]  Irad Yavneh,et al.  Anisotropy and Coherent Vortex Structures in Planetary Turbulence , 1994, Science.

[21]  V. Yakhot,et al.  Finite-size effects in forced two-dimensional turbulence , 1994, Journal of Fluid Mechanics.

[22]  P. Bartello.  Geostrophic Adjustment and Inverse Cascades in Rotating Stratified Turbulence , 1995 .

[23]  Andrew J. Majda,et al.  Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity , 1996 .

[24]  Smith,et al.  Crossover from Two- to Three-Dimensional Turbulence. , 1996, Physical review letters.

[25]  The effect of small-scale forcing on large-scale structures in two-dimensional flows , 1996, chao-dyn/9601012.

[26]  M. Lesieur,et al.  Inverse cascade in stably stratified rotating turbulence , 1996 .

[27]  Andrew J. Majda,et al.  MODEL DYNAMICS AND VERTICAL COLLAPSE IN DECAYING STRONGLY STRATIFIED FLOWS , 1997 .

[28]  Andrew J. Majda,et al.  Averaging over Fast Gravity Waves for Geophysical Flows with Unbalanced Initial Data , 1998 .

[29]  R. Salmon,et al.  Geophysical Fluid Dynamics , 2019, Classical Mechanics in Geophysical Fluid Dynamics.

[30]  Kelvin K. Droegemeier,et al.  Stratified Turbulence in the Atmospheric Mesoscales , 1998 .

[31]  Andrew J. Majda,et al.  Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers , 1998 .

[32]  C. Staquet,et al.  Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics , 1998, Journal of Fluid Mechanics.

[33]  E. Knobloch,et al.  A New Class of Equations for Rotationally Constrained Flows , 1998 .

[34]  P. Tabeling,et al.  Intermittency in the two-dimensional inverse cascade of energy: Experimental observations , 1998 .

[35]  Leslie M. Smith,et al.  Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence , 1999 .

[36]  Vanden Eijnden E,et al.  Models for stochastic climate prediction. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[37]  P. Bartello.  Potential Vorticity, Resonance and Dissipation in Rotating Convective Turbulence , 2000 .

[38]  J. Riley,et al.  Fluid Motions in the Presence of Strong Stable Stratification , 2000 .

[39]  C. Cambon.  Turbulence and vortex structures in rotating and stratified flows , 2001 .

[40]  E. Tabak,et al.  Advances in Wave Interaction and Turbulence , 2001 .

[41]  B. Galperin,et al.  Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere , 2001 .

[42]  L. Smith.  Numerical Study of Two-Dimensional Stratified Turbulence , 2022 .