Analytical approximations to spurious short-wave baroclinic instabilities in ocean models. (October 2017)

• Record Type: Journal Article
• Authors: Bell, Michael J.; White, Andrew A.
• Is Part Of: Ocean modelling. Volume 118(2017:Oct.)
• Page Start: 31
• Page End: 40
• Publication Date: 2017-10
• Subjects: Baroclinic instability -- Lorenz grid -- Potential vorticity -- Charney–Phillips grid; Oceanography -- Periodicals; Océanographie -- Périodiques; Oceanography; Periodicals; 551.46
• DOI: 10.1016/j.ocemod.2017.08.001
• Languages: English
• ISSNs: 1463-5003

Abstract

Highlights: Spurious short-wave baroclinic instabilities on the Lorenz grid grow as fast as the Eady mode. They can be simulated by equations which reduce to a quadratic for the phase speed. They only occur near horizontal boundaries where the mean flow has vertical shear. There is a simple expression for their horizontal wavelength. They result from vertical averaging of advection of relative vorticity. Abstract: Most community ocean models that use z - or s -coordinates stagger their variables in the vertical using a Lorenz grid. Spurious short-wave baroclinic instabilities have been shown to occur on that grid by Arakawa and Moorthi. As the vertical resolution of the grid is improved, the wavelength of the spurious modes decreases and they become more and more trapped near one of the boundaries but they continue to grow at almost the same rate as the deep Eady/Charney modes. The spurious instabilities in the case of the Eady problem are here shown to be accurately reproduced by an analytical calculation which reduces the stability problem to a quadratic equation for their complex phase speeds. The interpretation of these spurious instabilities as resulting from spurious sheets of potential vorticity is revisited. A new interpretation is presented using a finite difference analogue of the Charney–Stern–Pedlosky integral constraint. This indicates that the spurious instabilities result from a vertical averaging of the advection of the relative vorticity which leads to a spurious interior source term in the finite difference potential vorticity equation.