# A local diagnostic energy to study diabatic effects on a class of degenerate Hamiltonian systems with application to mixing in stratified flows

@article{Scotti2017ALD, title={A local diagnostic energy to study diabatic effects on a class of degenerate Hamiltonian systems with application to mixing in stratified flows}, author={Alberto Scotti and Pierre-Yves Passaggia}, journal={arXiv: Fluid Dynamics}, year={2017} }

In Hamiltonian systems characterized by a degenerate Poisson algebra, we show how to construct a local energy-like quantity that can be used to study diabatic effects on the evolution of the Available Energy of the system, the latter concept formalizing the original idea of Margules'. We calculate the local diagnostic energy for geophysically relevant flows. For the particular case of stratified Boussinesq flows, we show that under moderately general conditions, in inertial frames where the…

## References

SHOWING 1-10 OF 34 REFERENCES

### Selective decay by Casimir dissipation in inviscid fluids

- Physics
- 2013

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional (2D) incompressible turbulence. The…

### On the interpretation of energy and energy fluxes of nonlinear internal waves: an example from Massachusetts Bay

- Environmental Science, PhysicsJournal of Fluid Mechanics
- 2006

A self-consistent formalism to estimate baroclinic energy densities and fluxes resulting from the propagation of internal waves of arbitrary amplitude is derived using the concept of available…

### A unified theory of available potential energy 1

- Physics
- 1993

Abstract Traditional derivations of available potential energy, in a variety of contexts, involve combining some form of mass conservation together with energy conservation. This raises the questions…

### Available potential energy and mixing in density-stratified fluids

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 1995

A conceptual framework for analysing the energetics of density-stratified Boussinesq fluid flows is discussed. The concept of gravitational available potential energy is used to formulate an energy…

### On the calculation of the available potential energy of an isolated perturbation in a density-stratified fluid

- PhysicsJournal of Fluid Mechanics
- 2008

Two methods for calculating the available potential energy (APE) of an isolated feature in a density-stratified fluid, such as an internal solitary wave or an eddy, are compared. The first…

### Diagnosing mixing in stratified turbulent flows with a locally defined available potential energy

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2014

Abstract A local available potential energy (APE) density useful as suitable diagnostic tool in turbulent stratified flows is considered under the Boussinesq approximation. The local APE is positive,…

### Energetics of a symmetric circulation including momentum constraints

- Physics
- 2017

A theory of available potential energy (APE) for symmetric circulations, which includes momentum constraints, is presented. The theory is a generalization of the classical theory of APE, which…

### The slowly evolving background state of the atmosphere

- Physics, Environmental Science
- 2015

The theory of wave–mean flow interaction requires a partition of the atmospheric flow into a notional background state and perturbations to it. Here, a background state, known as the Modified…

### Available Potential Energy and Exergy in Stratified Fluids

- Physics, Environmental Science
- 2013

Lorenz's theory of available potential energy (APE) remains the main framework for studying the atmospheric and oceanic energy cycles. Because the APE generation rate is the volume integral of a…

### VERTICAL MIXING, ENERGY, AND THE GENERAL CIRCULATION OF THE OCEANS

- Environmental Science
- 2004

▪ AbstractThe coexistence in the deep ocean of a finite, stable stratification, a strong meridional overturning circulation, and mesoscale eddies raises complex questions concerning the circulation…