Abstract
Abstract. Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motion. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and thus in modelling stably stratified turbulent flows. We obtain a theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE budget equation from atmospheric measurements of other components of the TKE budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science, and microphysics of clouds.
Highlights
Until the present, the dependence of dissipation rate, εK, of turbulent kinetic energy (TKE), EK, on static stability remained insufficiently understood
The dissipation rate is parameterized in terms of a turbulent length scale, lT, as εK ∼ EK3/2/lT
The vertical structure of the Couette flow in terms of z coincides with the vertical structure of the surface-layer flow in terms of z. This allows for showing together the genuine dissipation rate calculated from direct numerical simulation (DNS): εK = ν (∂ui/∂xk)(∂ui/∂xk), where ν is kinematic viscosity, and εK = τ ∂U/∂z + βFz retrieved from atmospheric observations assuming the steady-state TKE budget
Summary
The dependence of dissipation rate, εK, of turbulent kinetic energy (TKE), EK, on static stability remained insufficiently understood. The dissipation rate is parameterized in terms of a turbulent length scale, lT, as εK ∼ EK3/2/lT This solves the problem in neutrally stratified boundary-layer flow, when the only length scale is the distance over the surface, z, so that lT ∼ z. S. Zilitinkevich et al.: Dissipation rate of turbulent kinetic energy fication and well-known log-linear velocity profile in moderately stable stratifications typical of the atmospheric surface layer – up to the coincidence of empirical dimensionless constants. Zilitinkevich et al.: Dissipation rate of turbulent kinetic energy fication and well-known log-linear velocity profile in moderately stable stratifications typical of the atmospheric surface layer – up to the coincidence of empirical dimensionless constants This very lucky empirical finding yields universal formulation of the dissipation rate versus static stability, valid over the whole range of stratifications from neutral to extremely stable. Practically nothing was known about this dependence beyond the interval of stratifications covered by observations in atmospheric surface layer: 0 < Ri < 0.2, which corresponds to 0 < z/L < 10
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