Geoscience Reference
In-Depth Information
Chapter 4
Similarity for the Ice/Ocean Boundary Layer
Abstract: The concept of similarity is central to nearly all studies of fluid dynam-
ics because it provides a means of reducing a whole class of flows to one set of
equations, after nondimensionalizing with carefully chosen scales. By studying one
instantiation of the class (say, in a laboratory or wind tunnel setting), results can be
applied to other examples, perhaps less amenable to direct measurement. Familiar
applications include testing of scale models to evaluate aerodynamic drag or lift.
In this chapter, similarity in planetary boundary layers is examined in some detail.
Relatively well known concepts (Monin-Obukhov similarity for buoyancy effects
in the atmospheric surface layer and Rossby similarity for the drag exerted by the
atmosphere on the surface) are described and used to illustrate the similarity be-
tween the atmospheric and oceanic boundary layers. We then combine these into a
similarity theory for the IOBL stabilized by positive buoyancy flux at the surface
(melting). The crucial parameters identified in the exercise, including important tur-
bulence scales, then provide the rationale for development of the local turbulence
closure model described in subsequent chapters.
4.1 The Surface Layer
From the first studies of wind structure near the surface in the atmosphere and in
wind tunnels, there was strong evidence that the vertical profile of wind velocity
was often nearly logarithmic, i.e., that
U
∝
log
z
which implies that the wind shear is nearly inversely proportional to distance from
the surface:
U
z
=
∂
U
∂
1
z
z
∝
