Chapter 8 - Equations of Motion With Viscosity

 Chapter 8 Contents (8.1) The Influence of Viscosity (8.2) Turbulence (8.3) Calculation of Reynolds Stress (8.4) Stability (8.5) Mixing in the Ocean (8.6) Important Concepts

8.6 Important Concepts

1. Friction in the ocean is important only over distances of a few millimeters. For most flows, friction can be ignored.

2. 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.

3. 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.

4. 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.

5. The influence of turbulence leads to Reynolds stress terms in the momentum equation.

6. 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

7. 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.

8. Molecular diffusion of heat is much faster than the diffusion of salt. This leads to a double-diffusion instability which modifies the density distribution in the water column in many regions of the ocean.

9. Instability in the ocean leads to mixing. Mixing across surfaces of constant density is much smaller than mixing along such surfaces.

10. Horizontal eddy diffusivity in the ocean is much greater than vertical eddy diffusivity.

11. Measurements of eddy diffusivity indicate water is mixed vertically near oceanic boundaries such as above seamounts and mid-ocean ridges.

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