Numerical Simulation of Flow around a Tall Isolated Seamount. Part I: Problem Formulation and Model Accuracy

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  • 1 Institut für Meereskunde, Theoretische Ozeanographie, Kiel, Germany
  • | 2 Institute for Marine and Coastal Sciences, Rutgers University, New Brunswick, New Jersey
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Abstract

A sigma coordinate ocean circulation model is employed to study flow trapped to a tall seamount in a periodic f-plane channel. In Part I, errors arising from the pressure gradient formulation in the steep topography/strong stratification limit are examined. To illustrate the error properties, a linearized adiabatic version of the model is considered, both with and without forcing, and starting from a resting state with level isopycnals.

The systematic discretization errors from the horizontal pressure gradient terms are shown analytically to increase with steeper topography (relative to a fixed horizontal grid) and for stronger stratification (as measured by the Burger number). For an initially quiescent unforced ocean, the pressure gradient errors produce a spurious oscillating current that, at the end of 10 days, is approximately 1 cm s−1 in amplitude. The period of the spurious oscillation (about 0.5 days) is shown to be a consequence of the particular form of the pressure gradient terms in the sigma coordinate system.

With the addition of an alongchannel diurnal forcing, resonantly generated seamount-trapped waves are observed to form. Error levels in these solutions are less than those in the unforced cases; spurious time-mean currents are several orders of magnitude less in amplitude than the resonant propagating waves. However, numerical instability is encountered in a wider range of parameter space. The properties of these resonantly generated waves is explored in detail in Part II of this study.

Several new formulations of the pressure gradient terms are tested. Two of the formulations—constructed to have additional conservation properties relative to the traditional form of the pressure gradient terms (conservation of JEBAR and conservation of energy)—are found to have error properties generally similar to those of the traditional formulation. A corrected gradient algorithm, based upon vertical interpolation of the pressure field, has a dramatically reduced error level but a much more restrictive range of stable behavior.

Abstract

A sigma coordinate ocean circulation model is employed to study flow trapped to a tall seamount in a periodic f-plane channel. In Part I, errors arising from the pressure gradient formulation in the steep topography/strong stratification limit are examined. To illustrate the error properties, a linearized adiabatic version of the model is considered, both with and without forcing, and starting from a resting state with level isopycnals.

The systematic discretization errors from the horizontal pressure gradient terms are shown analytically to increase with steeper topography (relative to a fixed horizontal grid) and for stronger stratification (as measured by the Burger number). For an initially quiescent unforced ocean, the pressure gradient errors produce a spurious oscillating current that, at the end of 10 days, is approximately 1 cm s−1 in amplitude. The period of the spurious oscillation (about 0.5 days) is shown to be a consequence of the particular form of the pressure gradient terms in the sigma coordinate system.

With the addition of an alongchannel diurnal forcing, resonantly generated seamount-trapped waves are observed to form. Error levels in these solutions are less than those in the unforced cases; spurious time-mean currents are several orders of magnitude less in amplitude than the resonant propagating waves. However, numerical instability is encountered in a wider range of parameter space. The properties of these resonantly generated waves is explored in detail in Part II of this study.

Several new formulations of the pressure gradient terms are tested. Two of the formulations—constructed to have additional conservation properties relative to the traditional form of the pressure gradient terms (conservation of JEBAR and conservation of energy)—are found to have error properties generally similar to those of the traditional formulation. A corrected gradient algorithm, based upon vertical interpolation of the pressure field, has a dramatically reduced error level but a much more restrictive range of stable behavior.

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