TY - JOUR

T1 - QNSE theory of turbulence anisotropization and onset of the inverse energy cascade by solid body rotation

AU - Sukoriansky, Semion

AU - Galperin, Boris

N1 - Funding Information:
The authors are grateful to Professor Sagaut who contributed figure 4. We are also thankful to the anonymous reviewers for providing insightful comments that helped to improve and clarify the manuscript. S.S. was partially supported by the ISF grant no. 408/15. B.G. and S.S. gratefully acknowledge partial support by ARO grant W911NF-09-1-0018 and ONR grant N00014-07-1-1065.
Publisher Copyright:
© 2016 Cambridge University Press.

PY - 2016/10/25

Y1 - 2016/10/25

N2 - Under the action of solid body rotation, homogeneous neutrally stratified turbulence undergoes anisotropization and onset of the inverse energy cascade. These processes are investigated using a quasi-normal scale elimination (QNSE) theory in which successive coarsening of a flow domain yields scale-dependent eddy viscosity and diffusivity. The effect of rotation increases with increasing scale and manifests in anisotropization of the eddy viscosities, eddy diffusivities and kinetic energy spectra. Not only the vertical (in the direction of the vector of rotation ω) and horizontal eddy viscosities and eddy diffusivities become different but, reflecting both directional and componental anisotropization, there emerge four different eddy viscosities. Three of them decrease relative to the eddy viscosity in non-rotating flows while one increases; the horizontal 'isotropic' viscosity decreases at the fastest rate. This behaviour is indicative of the increasing redirection of the energy flux to larger scales, the phenomenon that can be associated with the energy backscatter or inverse energy cascade. On scales comparable to the Woods's scale which is the rotational analogue of the Ozmidov length scale in stably stratified flows, the horizontal viscosity rapidly decreases, and in order to keep it positive, a weak rotation limit is invoked. Within that limit, an analytical theory of the transition from the Kolmogorov to a rotation-dominated turbulence regime is developed. It is shown that the dispersion relation of linear inertial waves is unaffected by turbulence while all one-dimensional energy spectra undergo steepening from the Kolmogorov to the slope.

AB - Under the action of solid body rotation, homogeneous neutrally stratified turbulence undergoes anisotropization and onset of the inverse energy cascade. These processes are investigated using a quasi-normal scale elimination (QNSE) theory in which successive coarsening of a flow domain yields scale-dependent eddy viscosity and diffusivity. The effect of rotation increases with increasing scale and manifests in anisotropization of the eddy viscosities, eddy diffusivities and kinetic energy spectra. Not only the vertical (in the direction of the vector of rotation ω) and horizontal eddy viscosities and eddy diffusivities become different but, reflecting both directional and componental anisotropization, there emerge four different eddy viscosities. Three of them decrease relative to the eddy viscosity in non-rotating flows while one increases; the horizontal 'isotropic' viscosity decreases at the fastest rate. This behaviour is indicative of the increasing redirection of the energy flux to larger scales, the phenomenon that can be associated with the energy backscatter or inverse energy cascade. On scales comparable to the Woods's scale which is the rotational analogue of the Ozmidov length scale in stably stratified flows, the horizontal viscosity rapidly decreases, and in order to keep it positive, a weak rotation limit is invoked. Within that limit, an analytical theory of the transition from the Kolmogorov to a rotation-dominated turbulence regime is developed. It is shown that the dispersion relation of linear inertial waves is unaffected by turbulence while all one-dimensional energy spectra undergo steepening from the Kolmogorov to the slope.

KW - rotating flows

KW - turbulence theory

UR - http://www.scopus.com/inward/record.url?scp=84988428889&partnerID=8YFLogxK

U2 - 10.1017/jfm.2016.568

DO - 10.1017/jfm.2016.568

M3 - Article

AN - SCOPUS:84988428889

VL - 805

SP - 384

EP - 421

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -