By Chia-Shun Yih (Ed.)
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Extra resources for Advances in Applied Mechanics, Vol. 13
T h e inadequate development of the theory of turbulence has resulted in approximate treat- 37 Large Scale Ocean Circulation ments of turbulent transfer. It is customary to draw an analogy between molecular and turbulent processes and to assume that the latter are similar to the former, the only difference being that eddy or Austansch coefficients are used instead of molecular coefficients. This procedure is still by far the most common even though it is known that substantial errors, qualitative as well as quantitative, can result.
4) is independent of the details of the flow. 5b) 2ii= - ( ETY), az where E may be a function of z (because of V) and T is the vertical stress in the surface layer. 4) follows directly, the only requirement being that cc vanish at great depth. An important consequence of the foregoing considerations emerges when the prescribed horizontal velocities (or stresses) have horizontal variations of a scale much larger than the Ekman layer depth (Charney, 1955a). Then the Ekman layer solutions are locally valid near the surface and a vertical flow out of the Ekman layer results when the continuity equation is integrated from z = - 00 to z = 0 with the boundary condition zZo=Oatz=O.
T h e simple Boussinesq system could not lead to the observed distribution because, according to the Boussinesq system, water which is densest at the point of origin would, in the absence of mixing, end up in the deepest part of the ocean. 28 George Veronis V. Scaling of the Equations The equations of motion can be scaled to exhibit important balances for large scale flows. By “large scale” we mean flows whose characteristic horizontal scales are substantially larger than the vertical scale (or depth).
Advances in Applied Mechanics, Vol. 13 by Chia-Shun Yih (Ed.)