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Internal Boundary Layer Scaling in “Two Layer” Solutions of the Thermocline Equations

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Abstract
  • The diffusivity dependence of internal boundary layers in solutions of the continuously stratified, diffusive thermocline equations is revisited. If a solution exists that approaches a two-layer solution of the ideal thermocline equations in the limit of small vertical diffusivity kᵥ, it must contain an internal boundary layer that collapses to a discontinuity as kᵥ → 0. An asymptotic internal boundary layer equation is derived for this case, and the associated boundary layer thickness is proportional to kᵥ¹/². In general, the boundary layer remains three-dimensional and the thermodynamic equation does not reduce to a vertical advective–diffusive balance even as the boundary layer thickness becomes arbitrarily small. If the vertical convergence varies sufficiently slowly with horizontal position, a one-dimensional boundary layer equation does arise, and an explicit example is given for this case. The same one-dimensional equation arose previously in a related analysis of a similarity solution that does not itself approach a two-layer solution in the limit kᵥ → 0.
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  • Samelson, R. M., 1999: Internal Boundary Layer Scaling in “Two Layer” Solutions of the Thermocline Equations. Journal of Physical Oceanography, 29, 2099–2102.
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  • 29
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  • 8
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  • This research was supported by the National Science Foundation, Division of Ocean Sciences (Grants OCE94-15512 and OCE98-96184).
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