Chapter 8  Equations of Motion With
Viscosity
8.6 Important Concepts
 Friction in the ocean is important only over distances of a few millimeters.
For most flows, friction can be ignored.
 The ocean is turbulent for all flows whose typical dimension exceeds a
few centimeters, yet the theory for turbulent flow in the ocean is poorly
understood.
 The influence of turbulence is a function of the Reynolds number of the
flow. Flows with the same geometry and Reynolds number have the same streamlines.
 Oceanographers assume that turbulence influences flows over distances greater
than a few centimeters in the same way that molecular viscosity influences
flow over much smaller distances.
 The influence of turbulence leads to Reynolds stress terms in the momentum
equation.
 The influence of static stability in the ocean is expressed as a frequency,
the stability frequency. The larger the frequency, the more stable the water
column
 The influence of shear stability is expressed through the Richardson number.
The greater the velocity shear, and the weaker the static stability, the
more likely the flow will become turbulent.
 Molecular diffusion of heat is much faster than the diffusion of salt.
This leads to a doublediffusion instability which modifies the density distribution
in the water column in many regions of the ocean.
 Instability in the ocean leads to mixing. Mixing across surfaces of constant
density is much smaller than mixing along such surfaces.
 Horizontal eddy diffusivity in the ocean is much greater than vertical
eddy diffusivity.
 Measurements of eddy diffusivity indicate water is mixed vertically near
oceanic boundaries such as above seamounts and midocean ridges.
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