Abstract
Abstract A Jacobian formulation of the pressure gradient force for use in models with topography-following coordinates is proposed. It can be used in conjunction with any vertical coordinate system and is easily implemented. Vertical variations in the pressure gradient are expressed in terms of a vertical integral of the Jacobian of density and depth with respect to the vertical computational coordinate. Finite difference approximations are made on the density field, consistent with piecewise linear and continuous fields, and accurate pressure gradients are obtained by vertically integrating the discrete Jacobian from sea surface. Two discrete schemes are derived and examined in detail: the first using standard centered differencing in the generalized vertical coordinate and the second using a vertical weighting such that the finite differences are centered with respect to the Cartesian z coordinate. Both schemes achieve second-order accuracy for any vertical coordinate system and are significantly more a...
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