On the Buoyancy Subrange in Stratified Turbulence

This study is motivated by the importance of the stratified turbulence in geophysical flows. We present a theoretical analysis of the buoyancy subrange based on the theory of strongly stratified turbulence. Some important turbulent scales and their relations are explored. Scaling constants of the buoyancy subrange scaling laws for both kinetic and potential energy spectra are derived and analyzed. It is found that these constants are functions of the horizontal Froude number F r h . For the potential energy spectrum, the scaling constant also depends on the turbulent flux coefficient of Γ .

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

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.

An Experimental Study of Turbulent Convection in Air Using PIV Technique

Airside turbulent flow structure in a coupled air-water system has been investigated during natural convection. Two-dimensional velocity field in a plane perpendicular to the surface was measured using particle image velocimetry (PIV). The results show the presence of different flow regimes in turbulent velocity fields which increase the complexity of the phenomena. The spectral analysis shows the existence of two power law regimes in the wavenumber spectra of the horizontal and vertical turbulent velocities. The regime at lower wavenumbers exhibits slopes of −3 which correspond to the buoyancy subrange where the energy loss is due to the work against buoyancy. At relatively higher wavenumbers, the inertial subrange with slopes of −5/3 is manifested. The trends of the wavenumber spectra in the present study are similar to the kinetic energy spectra observed in the geophysical studies over land and oceans, which indicates that laboratory experiments could be used to understand the near-surface dynamics in the lower atmosphere.