2004 LOM Workshop

Monday 10:50 - 11:10 a.m.

Some Idealized Thermobaric Solutions

Roland de Szoeke and Scott Springer
Oregon State University
szoeke@coas.oregonstate.edu

ABSTRACT

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We discretized the equations of motion and thermodynamics, written in terms of orthobaric specific volume (reciprocal of density) as vertical coordinate, following the principles of Hsu and Arakawa (1990), so that no spurious forces or energy sources are created. Because orthobaric sp. vol. is not materially conserved, even in the absence of diffusion and friction, there are unavoidable, but thermodynamically reversible, mass fluxes across orthobaric isopycnals (or discrete layer interfaces), because of the thermobaric character of seawater, coupled with geographic variation of the ocean's T-S relation. We will show some idealized test solutions designed to highlight thermobaric effects and T-S variation. First of all, we show rest states (stable, level in situ and orthobaric isopycnals) in which potential density isopycnals exhibit quite bizarre behavior. We show time-dependent, nonlinear solutions, such as solitary waves and hydraulic jumps, in which the essential nonlinearity is supplied by the thermobaricity of the equation of state. Variants of such behavior can be demonstrated in both the low-frequency planetary-wave realm, and in the ultra-Coriolis frequency band of internal gravity waves. The thermobaric behavior is evident even in simple two-layer idealizations. These tests should be useful benchmarks for numerical model codes that include thermobaric effects in their equations of state.

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LOM Users' Workshop, February 9-11, 2004