An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Abstract

The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

Dependence of Turbulent Velocities on Wind Speed and Stratification

“…Grachev et al (2013) find that the inertial subrange is no longer definable in the very stable weak-wind regime. Conversion of perturbation potential energy back to turbulent kinetic energy becomes important (Zilitinkevich et al 2007) and the velocity fluctuations more effectively transfer material in the horizontal than in the vertical (Sukorianski and Galperin 2013). Although the vertical diffusion in the weakwind stably-stratified boundary layer is quite weak, it significantly influences the nocturnal minimum surface temperature, potential fog formation and concentrations of contaminants.…”

Turbulence in the nocturnal boundary layer with light and variable winds

“…Mahrt (2011) inferred that the characteristics of the fluctuations with weak winds and strong stratification vary gradually with scale, suggesting that a sharp separation between turbulence and non-turbulent motions is not possible. This distinction is avoided in Galperin and Sukoriansky (2010), who model the fluctuations as a mix of turbulence and waves that merge in an intermediate buoyancy subrange (Sukorianski and Galperin, 2011). Such spectral approaches in the wave-number domain are difficult to evaluate in the stable atmospheric surface layer because of lack of fine-scale spatial information.…”

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales I

“…The theoretical understanding of this region is not on the same level as that of the inertial range. The article by Sukoriansky & Galperin [4] presents an investigation of the buoyancy subrange using the so-called quasi-normal scale elimination theory of turbulence. The authors show that the theory is analytically tractable in the limit of weak stratification and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities.…”

“…Volume 1 consists of papers by Wang & Peters [1] on turbulence; by Klimenko [2] on thermodynamics and mixing; by Volpert et al [3] on anomalous diffusion; by Sukoriansky & Galperin [4] on analytical modelling of geophysical flows; by Bershadkii [5] on data interpretation in climate modelling; by Lozovatsky & Fernando [6] on measure for stirring efficiency in natural environments; by Majda & Gershgorin [7] on non-local diffusivity in climate variations; by Frederiksen et al [8] on stochastic modelling of geophysical flows; by Shu [9] on application of high-order accurate nonlinear schemes in simulations of compressible flows; by Radtke et al [10] on hybrid atomistic-continuum dynamic simulations of multi-scale kinetic problems; and by Sofieva et al [11] on measurements of stellar scintillations for quantification of atmospheric turbulence. These papers represent the broad variety of themes of the 'Turbulent mixing and beyond' programme [12] and are concerned with the fundamental aspects of turbulence, mixing and nonequilibrium dynamics.…”