Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification |
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Authors: | Boris Galperin Semion Sukoriansky |
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Institution: | (1) College of Marine Science, University of South Florida, St. Petersburg, FL 33701, USA;(2) Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel;(3) Perlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel |
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Abstract: | The quasi-normal scale elimination (QNSE) is an analytical spectral theory of turbulence based upon a successive ensemble
averaging of the velocity and temperature modes over the smallest scales of motion and calculating corresponding eddy viscosity
and eddy diffusivity. By extending the process of successive ensemble averaging to the turbulence macroscale one eliminates
all fluctuating scales and arrives at models analogous to the conventional Reynolds stress closures. The scale dependency
embedded in the QNSE method reflects contributions from different processes on different scales. Two of the most important
processes in stably stratified turbulence, internal wave propagation and flow anisotropization, are explicitly accounted for
in the QNSE formalism. For relatively weak stratification, the theory becomes amenable to analytical processing revealing
just how increasing stratification modifies the flow field via growing anisotropy and gravity wave radiation. The QNSE theory
yields the dispersion relation for internal waves in the presence of turbulence and provides a theoretical reasoning for the
Gargett et al. (J Phys Oceanogr 11:1258–1271, 1981) scaling of the vertical shear spectrum. In addition, it shows that the internal wave breaking and flow anisotropization
void the notion of the critical Richardson number at which turbulence is fully suppressed. The isopycnal and diapycnal viscosities
and diffusivities can be expressed in the form of the Richardson diffusion laws thus providing a theoretical framework for
the Okubo dispersion diagrams. Transitions in the spectral slopes can be associated with the turbulence- and wave-dominated
ranges and have direct implications for the transport processes. We show that only quasi-isotropic, turbulence-dominated scales
contribute to the diapycnal diffusivity. On larger, buoyancy dominated scales, the diapycnal diffusivity becomes scale independent.
This result underscores the well-known fact that waves can only transfer momentum but not a scalar and sheds a new light upon
the Ellison–Britter–Osborn mixing model. It also provides a general framework for separation of the effects of turbulence
and waves even if they act on the same spatial and temporal scales. The QNSE theory-based turbulence models have been tested
in various applications and demonstrated reliable performance. It is suggested that these models present a viable alternative
to conventional Reynolds stress closures. |
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