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Concept
Surface layer
Summary
The surface layer is the layer of a turbulent fluid most affected by interaction with a solid surface or the surface separating a gas and a liquid where the characteristics of the turbulence depend on distance from the interface. Surface layers are characterized by large normal gradients of tangential velocity and large concentration gradients of any substances (temperature, moisture, sediments et cetera) transported to or from the interface.
The term boundary layer is used in meteorology and in physical oceanography. The atmospheric surface layer is the lowest part of the atmospheric boundary layer (typically the bottom 10% where the is valid). The ocean has two surface layers: the benthic, found immediately above the sea floor and the marine surface layer, at the air-sea interface.
A simple model of the surface layer can be derived by first examining the turbulent momentum flux through a surface.
Using Reynolds decomposition to express the horizontal flow in the direction as the sum of a slowly varying component, , and a turbulent component, ,
and the vertical flow, , in an analogous fashion,
we can express the flux of turbulent momentum through a surface, , as the time-averaged magnitude of vertical turbulent transport of horizontal turbulent momentum, :
If the flow is homogeneous within the region, we can set the product of the vertical gradient of the mean horizontal flow and the eddy viscosity coefficient equal to :
where is defined in terms of Prandtl's mixing length hypothesis:
where is the mixing length.
We can then express as:
From the figure above, we can see that the size of a turbulent eddy near the surface is constrained by its proximity to the surface; turbulent eddies centered near the surface cannot be as large as those centered further from the surface. From this consideration, and in neutral conditions, it is reasonable to assume that the mixing length, is proportional to the eddy's depth in the surface:
where is the depth and is known as the von Kármán constant.
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