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The Role of Curvature in Modifying Frontal Instabilities. Part I: Review of Theory and Presentation of a Nondimensional Instability Criterion

Journal

JOURNAL OF PHYSICAL OCEANOGRAPHY
Volume 51, Issue 2, Pages 299-315

Publisher

AMER METEOROLOGICAL SOC
DOI: 10.1175/JPO-D-19-0265.1

Keywords

Instability; Ocean dynamics; Potential vorticity; Turbulence; Frontogenesis; frontolysis; Fronts; Vortices; Angular momentum

Categories

Funding

  1. European Commission [798319]
  2. NERC [bas0100033] Funding Source: UKRI
  3. Marie Curie Actions (MSCA) [798319] Funding Source: Marie Curie Actions (MSCA)

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This study examines the impact of curvature on frontal stability and introduces a more general criterion for studying gravitational, centrifugal, and symmetric instabilities at curved density fronts. Through theoretical analysis and calculations, it is found that the criteria applied to low-Richardson-number fronts and vortices in gradient wind balance yield new insights, suggesting highly curved cyclonic fronts and vortices are symmetrically unstable with potential implications for ocean budgets.
In 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. Significance statementConsiderable progress has been made by considering ocean fronts to be in geostrophic balance. By this, we mean that fluid parcels accelerate as a result of horizontal pressure gradients and Earth's rotation. A good example of this is in our efforts to understand symmetric instability, a process thought to impact energy, buoyancy, and tracer budgets in the ocean. However, we wanted to know how the physics might change if we accounted for centrifugal forces, or curvature. It turns out that this same question had been asked and answered nearly 100 years ago. However, the new criteria that we introduce in Part I yield (in Part II) one result that is new: in low-stratified waters, curved cyclonic fronts become strongly unstable and curved anticyclonic fronts become marginally stable. This suggests that highly curved cyclonic fronts and vortices are symmetrically unstable, with potential implications for the aforementioned budgets.

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