An ocean circulation model based on Eulerian forward-backward difference scheme and three-dimensional, primitive equations and its application in regional simulations

Abstract A global ocean circulation model is formulated in terms of the “residual mean” and used to study eddy–mean flow interaction. Adjoint techniques are used to compute the three-dimensional eddy stress field that minimizes the departure of the coarse-resolution model from climatological observations of temperature. The resulting 3D maps of eddy stress and residual-mean circulation yield a wealth of information about the role of eddies in large-scale ocean circulation. In eddy-rich regions such as the Southern Ocean, the Kuroshio, and the Gulf Stream, eddy stresses have an amplitude comparable to the wind stress, of order 0.2 N m−2, and carry momentum from the surface down to the bottom, where they are balanced by mountain form drag. From the optimized eddy stress, 3D maps of horizontal eddy diffusivity κ are inferred. The diffusivities have a well-defined large-scale structure whose prominent features are 1) large values of κ (up to 4000 m2 s−1) in the western boundary currents and on the equatorial flank of the Antarctic Circumpolar Current and 2) a surface intensification of κ, suggestive of a dependence on the stratification N 2. It is shown that implementation of an eddy parameterization scheme in which the eddy diffusivity has an N 2 dependence significantly improves the climatology of the ocean model state relative to that obtained using a spatially uniform diffusivity.

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An Ocean Circulation Model Based on Operator-Splitting, Hamiltonian Brackets, and the Inclusion of Sound Waves

Journal of Physical Oceanography ◽

10.1175/2009jpo4134.1 ◽

2009 ◽

Vol 39 (7) ◽

pp. 1615-1633 ◽

Cited By ~ 2

Author(s):

Rick Salmon

Keyword(s):

Lattice Boltzmann Method ◽

Ocean Circulation ◽

Lattice Boltzmann ◽

Circulation Model ◽

Sound Waves ◽

Ocean Circulation Model ◽

Time Step ◽

Model Based ◽

Strang Splitting ◽

Boltzmann Method

Abstract This paper offers a simple, entirely prognostic, ocean circulation model based on the separation of the complete dynamics, including sound waves, into elementary Poisson brackets. For example, one bracket corresponds to the propagation of sound waves in a single direction. Other brackets correspond to the rotation of the velocity vector by individual components of the vorticity and to the action of buoyancy force. The dynamics is solved by Strang splitting of the brackets. Key features of the method are the assumption that the sound waves propagate exactly one grid distance in a time step and the use of Riemann invariants to solve the sound-wave dynamics exactly. In these features the method resembles the lattice Boltzmann method, but the flexibility of more conventional methods is retained. As in the lattice Boltzmann method, very short time steps are required to prevent unrealistically strong coupling between the sound waves and the slow hydrodynamic motions of primary interest. However, the disadvantage of small time steps is more than compensated by the model’s extreme simplicity, even in the presence of very complicated boundaries, and by its massively parallel form. Numerical tests and examples illustrate the practicality of the method.

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