Abstract
The relationship of lateral eddy viscosity depending on length scale is estimated with the decay rate of mesoscale eddies identified from sea level anomaly of satellite observations. The eddy viscosity is expressed in terms of the mesoscale eddy parameters according to vortex dynamics. The census of mesoscale eddies shows, in general, that the eddy numbers obey the e-folding decay laws in terms of their amplitude, area and lifetime. The intrinsic values in the e-folding laws are used to estimate the lateral eddy viscosity. Dislike the previous theory that diffusivities are proportional to the length square, the eddy mixing rates (diffusivity and viscosity) from satellite mesoscale eddy datasets are proportional to rs to power of 1.8 (slightly less than 2), where rs is the radius of eddy with radius larger than the Batchelor scale. Additionally, the extrapolation of the eddy mixing to the molecule scale implies that the above power laws may hold until the value of rs is less than O (1 m). These mixing rates with the new parameterizations are suggested to use in numerical schemes. Finally, the climatological distributions of eddy viscosity are calculated.
Highlights
The relationship of lateral eddy viscosity depending on length scale is estimated with the decay rate of mesoscale eddies identified from sea level anomaly of satellite observations
Dislike the previous theory that diffusivities are proportional to the length square, the eddy mixing rates from satellite mesoscale eddy datasets are proportional to rs to power of 1.8, where rs is the radius of eddy with radius larger than the Batchelor scale
Since such parameterization is valid from very small scale to very large scale, the mixing rates with the new parameterizations are suggested to use in numerical schemes
Summary
The eddy mixing rates (diffusivity and viscosity) are parameterized with a simple relationship proportional to the length square and independent of the time and space [7]. Such simple relationship is not fully supported by the previous field observations and recent parameterizations. For passive tracers from the oceanic observations, the isopycnal eddy diffusivity and viscosity may is on the order of 103 m2/s [7], it varies from 102 m2/s [8] [9] [10] to more than 104 m2/s [11] [12] [13]. One problem is the appropriate choice of parameterizations for the eddy properties, e.g., “what is the appropriate choice of the parameterizations and numerical schemes?” [6]
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