Internal boundary layer scaling in "two layer" solutions of the thermocline equations

Authors
Citation
Rm. Samelson, Internal boundary layer scaling in "two layer" solutions of the thermocline equations, J PHYS OCEA, 29(8), 1999, pp. 2099-2102
Citations number
10
Categorie Soggetti
Aquatic Sciences","Earth Sciences
Journal title
JOURNAL OF PHYSICAL OCEANOGRAPHY
ISSN journal
00223670 → ACNP
Volume
29
Issue
8
Year of publication
1999
Part
2
Pages
2099 - 2102
Database
ISI
SICI code
0022-3670(199908)29:8<2099:IBLSI">2.0.ZU;2-Z
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 thermocl ine equations in the limit of small vertical diffusivity kappa(v), it must contain an internal boundary layer that collapses to a discontinuity as kap pa(v) --> 0. An asymptotic internal boundary layer equation is derived for this case, and the associated boundary layer thickness is proportional to k appa(v)(1/2). In general, the boundary layer remains three-dimensional and the thermodynamic equation does not reduce to a vertical advective-diffusiv e balance even as the boundary layer thickness becomes arbitrarily small. I f the vertical convergence varies sufficiently slowly with horizontal posit ion, a one-dimensional boundary layer equation does arise, and an explicit example is given for this case. The same one-dimensional equation arose pre viously in a related analysis of a similarity solution that does not itself approach a two-layer solution in the limit kappa(v) --> 0.