Generalized Nonlinear Balance Criteria and Inertial Stability

Abstract

The connections between the concept of nonlinear balance and the classical criterion of inertial stability are explored in the context of historical work on this subject. New analytic results are derived establishing that ellipticity and inertial stability are, in general, separate and distinct measures of balanced flows, even in the case of gradient flow. In particular, nonlinear balance is violated more for weaker anticyclonic flows than is inertial balance. These conclusions are supported by analysis of observational data. A hierarchy of nonlinear balance criteria is constructed, which ranges from ellipticity to ?realizability? conditions first obtained by Petterssen and Kasahara. Expressions interrelating all the nonlinear balance criteria and inertial stability are derived, clarifying the relationship between the Petterssen criterion, Kasahara?s realizability, and inertial stability. The balance-criteria hierarchy is tested for cyclonic and anticyclonic conditions using a nonlinear inviscid f-plane trajectory model. The modeling results confirm the analytical ellipticity?inertial stability relationship. In addition, an intercomparison of balance criteria reveals that Petterssen?s realizability (in the form derived here) is the most general and most physically interpretable balance criterion. The implications of this work for generalizations of inertial instability theory are briefly explored.