NDLI: Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

Content Provider	Springer Nature Link
Author	Galperin, Boris Sukoriansky, Semion
Copyright Year	2010
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.
Starting Page	1319
Ending Page	1337
Page Count	19
File Format	PDF
ISSN	16167341
Journal	Deutsche Hydrografische Zeitschrift
Volume Number	60
Issue Number	5
e-ISSN	16167228
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-08-19
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Anisotropic turbulence Dispersive waves Stable stratification Turbulence spectra Okubo diagrams Environmental Monitoring/Analysis Fluid- and Aerodynamics Geophysics/Geodesy Meteorology/Climatology Oceanography
Content Type	Text
Resource Type	Article
Subject	Oceanography

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