Planetary Boundary Layer Turbulence

In previous chapters boundary layers were evident as thin layers across which thermal, dynamic, and material properties of a free interior flow make a transition to their boundary values and/or boundary fluxes. In those cases the thinness of the boundary layer was typically a statement of the smallness of the relevant diffusivity; e.g., the depth h of the laminar Ekman boundary layer scales as ν (Shear Turbulence) and the thermal boundary layer in convection scales as either κ or κ in soft or hard turbulence regimes (Convective Turbulence). Boundary layers are also evident in geophysical flows, for instance at the bottom of the atmosphere, and at the top and bottom of the ocean. And, they serve essentially the same purpose: to match a free or interior flow to the conditions imposed at the surface, i.e., no-slip, fixed temperature, specified material properties, or specified boundary fluxes. Unlike boundary layers in many engineering flows, these planetary boundary layers (or PBLs) are almost always turbulent. The turbulence expresses the instability of the laminar boundary layer solutions, thus giving rise to an effective (eddy) diffusivity that allows the flow to make the transition between its surface and free-flow properties over a much deeper layer than would occur with only molecular diffusion and no turbulent mixing. Through this layer turbulent vertical fluxes, wuh and w′c′, are expected to be significant in shaping the mean vertical profiles, uh(z) and c(z), where c is any material property. To have any asymptotic utility, the concept of a PBL also requires that its depth h remain much smaller than the vertical scale of the free flow. The PBL in the ocean and atmosphere is typically tens or hundreds of meters thick, respectively; this is thin compared to the 3-10 km depth scale of free oceanic and atmospheric flows. Some authors prefer to define the PBL as that layer of the atmosphere that intensively, or actively, mediates the exchanges with the underlying surface (in the case of the atmosphere) or the overlying atmosphere (in the case of the ocean), but such a characterization fails to ensure the thinness of the layer that is fundamental to its identification as a special layer. The basic mechanisms for generating turbulence with in the PBL are familiar: shear and buoyancy. However these usual suspects take on unusual guises in many geophysical situations. Consider the following: