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Naomi Naik
,
Mark A. Cane
,
Semyon Basin
, and
Moshe Israeli

Abstract

A scheme is presented for solving the equation for barotropic ocean circulation, taking into account the special character of the problem: nearly inviscid motion following f/H contours in the ocean interior, with viscous effects closing the flow near western boundaries. Using a special compact finite-difference discretization, the scheme generates boundary layers without spurious oscillations and without demanding very high resolution. Sharp changes in topography and closed f/H contours (e.g., in the vicinity of high sea mounts) are also handled by the scheme in a way that localizes errors due to underresolved topographic features. Strategies are formulated for simplifying the connectedness of the domain by “sinking” the islands.

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Moshe Israeli
,
Naomi H. Naik
, and
Mark A. Cane

Abstract

A finite-difference scheme for solving the linear shallow water equations in a bounded domain is described. Its time step is not restricted by a Courant–Friedrichs–Levy (CFL) condition. The scheme, known as Israeli–Naik–Cane (INC), is the offspring of semi-Lagrangian (SL) schemes and the Cane–Patton (CP) algorithm. In common with the latter it treats the shallow water equations implicitly in y and with attention to wave propagation in x. Unlike CP, it uses an SL-like approach to the zonal variations, which allows the scheme to apply to the full primitive equations. The great advantage, even in problems where quasigeostrophic dynamics are appropriate in the interior, is that the INC scheme accommodates complete boundary conditions.

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