Abstract
AbstractIn this study, we examine the role of curvature in modifying frontal stability. We first evaluate the classical criterion that the Coriolis parameter f multiplied by the Ertel potential vorticity (PV) q is positive for stable flow and that instability is possible when this quantity is negative. The first portion of this statement can be deduced from Ertel’s PV theorem, assuming an initially positive fq. Moreover, the full statement is implicit in the governing equation for the mean geostrophic flow, as the discriminant, fq, changes sign. However, for curved fronts in cyclogeostrophic or gradient wind balance (GWB), an additional term enters the discriminant owing to conservation of absolute angular momentum L. The resulting expression, (1 + Cu)fq < 0 or Lq < 0, where Cu is a nondimensional number quantifying the curvature of the flow, simultaneously generalizes Rayleigh’s criterion by accounting for baroclinicity and Hoskins’s criterion by accounting for centrifugal effects. In particular, changes in the front’s vertical shear and stratification owing to curvature tilt the absolute vorticity vector away from its thermal wind state; in an effort to conserve the product of absolute angular momentum and Ertel PV, this modifies gradient Rossby and Richardson numbers permitted for stable flow. This forms the basis of a nondimensional expression that is valid for inviscid, curved fronts on the f plane, which can be used to classify frontal instabilities. In conclusion, the classical criterion fq < 0 should be replaced by the more general criterion for studies involving gravitational, centrifugal, and symmetric instabilities at curved density fronts. In Part II of the study, we examine interesting outcomes of the criterion applied to low-Richardson-number fronts and vortices in GWB.
Highlights
There has been considerable interest in submesoscale dynamics in the ocean in recent years
We have examined the role of curvature in modifying frontal stability
We first reconsidered the statement that the Coriolis parameter, f, multiplied by the Ertel potential vorticity (PV), q, is positive for stable flow and that instability is possible when this product is negative
Summary
There has been considerable interest in submesoscale dynamics in the ocean in recent years. In the first part of the study (this paper), we review theoretical concepts and present a nondimensional form of an instability criterion valid for curved fronts These largely reflect the authors’ efforts to understand the sufficient criterion in light of the acknowledged importance of PV to symmetric instability (Hoskins 1974, 2015). For a limiting case applicable to symmetric instability, we demonstrate that this is a sufficient criterion In words, this criterion states that, for axisymmetric vortices or curved fronts with symmetry in the alongfront direction, both the Ertel PV and absolute angular momentum play governing roles in the stability of the front. This criterion states that, for axisymmetric vortices or curved fronts with symmetry in the alongfront direction, both the Ertel PV and absolute angular momentum play governing roles in the stability of the front If either of these is negative (but not both), we have the potential for instability.
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