Local balance and cross-scale flux of available potential energy

Abstract

Gravitational available potential energy is a central concept in an energy analysis of flows in which buoyancy effects are dynamically important. These include, but are not limited to, most geophysical flows with persistently stable density stratification. The volume-integrated available potential energy ap is defined as the difference between the gravitational potential energy of the system and the potential energy of a reference state with the lowest potential energy that can be reached by adiabatic material rearrangement; ap determines how much energy is available for conservative dynamical exchange with kinetic energy k. In this paper we introduce new techniques for computing the local available potential energy density Eap in numerical simulations that allow for a more accurate and complete analysis of the available potential energy and its dynamical balances as part of the complete energy cycle of a flow. In particular, the definition of Eap and an associated gravitation disturbance field permit us to make a spectral decomposition of its dynamical balance and examine the cross-scale energy flux. Several examples illustrate the spatial structure of Eap and its evolutionary influences. The greatest attention is given to an analysis of a turbulent-equilibrium simulation Eady-like vertical-shear flow with rotation and stable stratification. In this regime Eap exhibits a vigorous forward energy cascade from the mesoscale through the submesoscale range – first in a scale range dominated by frontogenesis and positive buoyancy-flux conversion from ap to k and then, after strong frontal instability and frontogenetic arrest, in a coupled kinetic-potential energy inertial-cascade range with negative buoyancy-flux conversion – en route to fine-scale dissipation of both energy components.