Coriolis forces

The Coriolis model controls the manifestation of the term   in the momentum equation.

-plane approximation

Under an -plane approximation^[1] the reference frame in which the momentum and tracer equations are solved rotates at a constant rate.

The traditional -plane approximation

In the traditional -plane approximation, the coordinate system rotates around a vertical axis such that

where is constant and determined by the user.

The arbitrary-axis constant-Coriolis approximation

In this approximation, the coordinate system rotates around an axis in the -plane, such that

where , , and are constants determined by the user.

-plane approximation {#\beta-plane-approximation}

The traditional -plane approximation {#The-traditional-\beta-plane-approximation}

Under the traditional -plane approximation, the rotation axis is vertical as for the -plane approximation, but is expanded in a Taylor series around a central latitude such that

where is the planetary vorticity at some central latitude, and is the planetary vorticity gradient. The -plane model is not periodic in and thus can be used only in domains that are bounded in the -direction.

The non-traditional -plane approximation {#The-non-traditional-\beta-plane-approximation}

The non-traditional -plane approximation accounts for the latitudinal variation of both the locally vertical and the locally horizontal components of the rotation vector

as can be found in the paper by Dellar (2011), where   and   .

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1. The -plane approximation is used to model the effects of Earth's rotation on anisotropic fluid motion in a plane tangent to the Earth's surface. In this case, the projection of the Earth's rotation vector at latitude and onto a coordinate system in which correspond to the directions east, north, and up is    where the Earth's rotation rate is approximately . The traditional -plane approximation neglects the -component of this projection, which is appropriate for fluid motions with large horizontal-to-vertical aspect ratios. ↩︎