On the Influence of a Lower Layer on the Propagation of Nonlinear Oceanic Eddies

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
  • | 2 Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire
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Abstract

The one-layer, reduced-gravity, also called equivalent-barotropic, model has been widely used in countless applications. Although its validity is based on the assumption that a second, lower layer is sufficiently deep to be dynamically inactive, the question of how deep that second layer ought to be has not yet received thorough examination. When one considers the importance of the two processes excluded from the reduced-gravity model, namely barotropic motion and baroclinic instability, the conventional choice of a second layer much deeper than the first might be too simplistic.

A scaling analysis aimed at covering all two-layer regimes, geostrophic as well as ageostrophic, leads to a double criterion, requiring that the total depth of fluid be much larger than either of two values. These values, resulting from f-plane and β-plane dynamics, apply to the shorter and longer scales, respectively. A number of numerical experiments on the propagation of eddies on the β-plane with various eddy radii and lower-layer depths verify the applicability of the criterion. A final set of experiments with dipoles on the f-plane and β-plane also clearly illustrates the two sides of the criterion.

The rule for the validity of the reduced-gravity model can be summarized as follows. For characteristic horizontal length scales of motion (e.g., eddy radius, wavelength, …) up to the deformation radius, it is sufficient that the lower layer be much deeper (e.g., by a factor ten or so) than the upper layer. For length scales increasing beyond the deformation radius, on both the f- and β-planes, the reduced-gravity model rapidly loses its validity. The model recovers its validity toward larger scales on the β-plane.

Abstract

The one-layer, reduced-gravity, also called equivalent-barotropic, model has been widely used in countless applications. Although its validity is based on the assumption that a second, lower layer is sufficiently deep to be dynamically inactive, the question of how deep that second layer ought to be has not yet received thorough examination. When one considers the importance of the two processes excluded from the reduced-gravity model, namely barotropic motion and baroclinic instability, the conventional choice of a second layer much deeper than the first might be too simplistic.

A scaling analysis aimed at covering all two-layer regimes, geostrophic as well as ageostrophic, leads to a double criterion, requiring that the total depth of fluid be much larger than either of two values. These values, resulting from f-plane and β-plane dynamics, apply to the shorter and longer scales, respectively. A number of numerical experiments on the propagation of eddies on the β-plane with various eddy radii and lower-layer depths verify the applicability of the criterion. A final set of experiments with dipoles on the f-plane and β-plane also clearly illustrates the two sides of the criterion.

The rule for the validity of the reduced-gravity model can be summarized as follows. For characteristic horizontal length scales of motion (e.g., eddy radius, wavelength, …) up to the deformation radius, it is sufficient that the lower layer be much deeper (e.g., by a factor ten or so) than the upper layer. For length scales increasing beyond the deformation radius, on both the f- and β-planes, the reduced-gravity model rapidly loses its validity. The model recovers its validity toward larger scales on the β-plane.

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