Note on the viscous smoothing of the discontinuities in an inviscid model of abyssal circulation

Calculations for the thermohaline circulation for an inviscid model over the slope regions of a homogeneous and of a two-layer system with sloping western and northern boundaries and driven by uniform upwelling through the thermocline were carried out by Andersson and Veronis [2004. Thermohaline circulation in a two-layer model with sloping boundaries and mid-ocean ridge. Deep-Sea Research Part I 51, 93-106]. The results showed discontinuities in certain regions of the flow over the western and northern slopes where inviscid flows from different regions merged. A speculation that those discontinuities would be smoothed over when friction is added to the model is verified here in a numerical calculation for the homogeneous model in which the value of friction ranges over three orders of magnitude. The inviscid solution is approached as friction is reduced. The conclusion is that obtaining a solution using an inviscid model over the slope regions is a valid first step in solving a problem of this type. (c) 2005 Elsevier Ltd. All rights reserved.