The flux Richardson number
New insight for inferring diapycnal diffusivity in stably stratified turbulent flows is obtained based on physical scaling arguments and tested using highresolution direct numerical simulation data. It is shown that the irreversible diapycnal diffusivity can be decomposed into a diapycnal length scale that represents an inner scale of turbulence and a diapycnal velocity scale. Furthermore, it is shown that the diapycnal length scale and velocity scale can be related to the measurable Ellison length scale (LE) that represents outer scale of turbulence and vertical turbulent velocity scale (w′) through a turbulent Froude number scaling analysis. The turbulent Froude number is defined as Fr=ε/Nk, where ε is the rate of dissipation of turbulent kinetic energy, N is the buoyancy frequency, and k is the turbulent kinetic energy. The scaling analysis suggests that the diapycnal diffusivity Kρ∼w′LE in the weakly stratified regime (Fr >1) and Kρ∼(w′LE)×Fr for the strongly stratified regime (Fr <1).
more » « less NSFPAR ID:
 10439968
 Publisher / Repository:
 American Institute of Physics
 Date Published:
 Journal Name:
 Physics of Fluids
 Volume:
 34
 Issue:
 9
 ISSN:
 10706631
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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