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8: Equations of Motion with Viscosity

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    Throughout most of the interior of the ocean and atmosphere friction is relatively small, and we can safely assume that the flow is frictionless. At the boundaries, friction, in the form of viscosity, becomes important. This thin, viscous layer is called a boundary layer. Within the layer, the velocity slows from values typical of the interior to zero at a solid boundary. If the boundary is not solid, then the boundary layer is a thin layer of rapidly changing velocity whereby velocity on one side of the boundary changes to match the velocity on the other side of the boundary. For example, there is a boundary layer at the bottom of the atmosphere, the planetary boundary layer I described in Chapter 3. In the planetary boundary layer, velocity goes from many meters per second in the free atmosphere to tens of centimeters per second at the sea surface. Below the sea surface, another boundary layer, the Ekman layer described in Chapter 9, matches the flow at the sea surface to the deeper flow.

    In this chapter I consider the role of friction in fluid flows, and the stability of the flows to small changes in velocity or density.

    • 8.1: The Influence of Viscosity
      Definition of molecular viscosity and its influence on the frictional force term of the momentum equation.
    • 8.2: Turbulence
      Defining turbulent vs. laminar flow, using the Reynolds number. The role of Reynolds Stress in transferring momentum in turbulent flow.
    • 8.3: Calculation of Reynolds Stress
      Calculating Reynolds stresses through experiments, through Prandtl's analogy with molecular velocity, and through statistical theory of turbulence.
    • 8.4: Mixing in the Ocean
      Average and measured vertical mixing, and measured horizontal mixing, for simple flows in the ocean.
    • 8.5: Stability
      Three forms of instability besides turbulent flow that commonly occur in the ocean. Includes discussion of static stability (associated with change of density with depth), dynamic stability (associated with velocity shear), and double-diffusion (associated with salinity and temperature gradients).
    • 8.6: Important Concepts
      Summary of important concepts covered in this chapter.

    This page titled 8: Equations of Motion with Viscosity is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Robert H. Stewart via source content that was edited to the style and standards of the LibreTexts platform.