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

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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 bythe National Science Foundation, Division of OceanSciences (Grants OCE94-15512 and OCE98-96184).
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  • description.provenance : Made available in DSpace on 2012-02-08T21:04:37Z (GMT). No. of bitstreams: 1SamelsonRM.CEOAS.InternalBoundaryLayer.pdf: 76369 bytes, checksum: 4a2034b84d3aff11d7b7530a67ebdc03 (MD5) Previous issue date: 1999-08
  • description.provenance : Submitted by Deborah Campbell (deborah.campbell@oregonstate.edu) on 2012-02-08T21:04:37ZNo. of bitstreams: 1SamelsonRM.CEOAS.InternalBoundaryLayer.pdf: 76369 bytes, checksum: 4a2034b84d3aff11d7b7530a67ebdc03 (MD5)

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