TY - GEN
T1 - Turbulence energetics in stably stratified atmospheric flows
AU - Zilitinkevich, S. S.
AU - Elperin, T.
AU - Kleeorin, N.
AU - L’vov, V.
AU - Rogachevskii, I.
N1 - Publisher Copyright:
© 2010, Springer Science and Business Media, LLC. All rights reserved.
PY - 2010/1/1
Y1 - 2010/1/1
N2 - We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic energy (TKE), turbulent potential energy (TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of the turbulent total energy (TTE = TKE + TPE), we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model permits the existence of turbulence at any gradient Richardson number, Ri. For the stationary, homogeneous regime the turbulence closure model yields universal dependencies of the flux Richardson number, turbulent Prandtl number, anisotropy of turbulence, and normalized vertical fluxes of momentum and heat on the gradient Richardson number, Ri. We also take into account an additional vertical flux of momentum and additional productions of turbulent kinetic energy, turbulent potential energy and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). Accounting for the internal gravity waves, the Ri-dependencies of the flux Richardson number, turbulent Prandtl number, anisotropy of turbulence, vertical fluxes of momentum and heat lose their universality. In particular, with increasing wave energy, the maximal value of the flux Richardson number (attained at very large Ri) decreases. In contrast to the mean wind shear which generates only the horizontal TKE, IGW generate both horizontal and vertical TKE, and thus lead to a more isotropic turbulence at very large Ri. IGW also increase the share of TPE in the turbulent total energy. A well-known effect of IGW is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), it either strengthens of weakens the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations (DNS) and large-eddy simulations (LES).
AB - We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic energy (TKE), turbulent potential energy (TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of the turbulent total energy (TTE = TKE + TPE), we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model permits the existence of turbulence at any gradient Richardson number, Ri. For the stationary, homogeneous regime the turbulence closure model yields universal dependencies of the flux Richardson number, turbulent Prandtl number, anisotropy of turbulence, and normalized vertical fluxes of momentum and heat on the gradient Richardson number, Ri. We also take into account an additional vertical flux of momentum and additional productions of turbulent kinetic energy, turbulent potential energy and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). Accounting for the internal gravity waves, the Ri-dependencies of the flux Richardson number, turbulent Prandtl number, anisotropy of turbulence, vertical fluxes of momentum and heat lose their universality. In particular, with increasing wave energy, the maximal value of the flux Richardson number (attained at very large Ri) decreases. In contrast to the mean wind shear which generates only the horizontal TKE, IGW generate both horizontal and vertical TKE, and thus lead to a more isotropic turbulence at very large Ri. IGW also increase the share of TPE in the turbulent total energy. A well-known effect of IGW is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), it either strengthens of weakens the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations (DNS) and large-eddy simulations (LES).
UR - http://www.scopus.com/inward/record.url?scp=85034637680&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-02225-8_19
DO - 10.1007/978-3-642-02225-8_19
M3 - Conference contribution
AN - SCOPUS:85034637680
SN - 9783642022241
T3 - Springer Proceedings in Physics
SP - 83
EP - 86
BT - Progress in Turbulence III - Proceedings of the iTi Conference in Turbulence 2008
A2 - Oberlack, Martin
A2 - Peinke, Joachim
A2 - Talamelli, Alessandro
PB - Springer Science and Business Media, LLC
T2 - 3rd Conference on Turbulence, iTi 2008
Y2 - 1 January 2008 through 1 January 2008
ER -