Potential Vorticity and the Conservation Laws of Energy and Momentum for a Stratified Incompressible Fluid

2013 ◽  
pp. 13-21
Author(s):  
Felix V. Dolzhansky
Keyword(s):  
Incompressible Fluid ◽  
Conservation Laws ◽  
Potential Vorticity ◽  
Energy And Momentum ◽  
Conservation Laws Of Energy

Some vorticity theorems and conservation laws for non-barotropic fluids

1981 ◽  
Vol 108 ◽  
pp. 475-483 ◽  
Author(s):  
S. D. Mobbs
Keyword(s):  
Thermodynamic Properties ◽  
Conservation Laws ◽  
Potential Vorticity ◽  
Time Dependent ◽  
Dissipative Effects ◽  
Perfect Fluids ◽  
Barotropic Fluids ◽  
Complete Set ◽  
Circulation Theorem

Some theorems concerning the vorticity in barotropic flows of perfect fluids are generalized for non-barotropic flows. The generalization involves replacing the velocity in certain parts of the equations by a time-dependent quantity which is a function of the velocity and thermodynamic properties of the fluid. Results which are generalized include Kelvin's circulation theorem and conservation laws for potential vorticity and helicity. It is shown how the results can be further generalized to include dissipative effects. The possibility of using some of the results in deriving a complete set of Lagrangian conservation laws for perfect fluids is discussed.

scholarly journals A Framework for Parameterizing Eddy Potential Vorticity Fluxes

2012 ◽  
Vol 42 (4) ◽  
pp. 539-557 ◽  
Author(s):  
David P. Marshall ◽  
James R. Maddison ◽  
Pavel S. Berloff
Keyword(s):  
Stress Tensor ◽  
Potential Vorticity ◽  
Large Scale ◽  
Eddy Diffusivity ◽  
Linear Instability ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Conservation Of Energy ◽  
The Mean ◽  
Energy And Momentum

Abstract A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed.

A Theoretical Framework for Energy and Momentum Consistency in Subgrid-Scale Parameterization for Climate Models

2009 ◽  
Vol 66 (10) ◽  
pp. 3095-3114 ◽  
Author(s):  
Tiffany A. Shaw ◽  
Theodore G. Shepherd
Keyword(s):  
Conservation Laws ◽  
Climate Models ◽  
Multiple Scale ◽  
Theoretical Framework ◽  
Momentum Conservation ◽  
Wave Activity ◽  
Subgrid Scale ◽  
Conservation Of Energy ◽  
Planetary Scale ◽  
Energy And Momentum

Abstract A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes—which represents a generalization of the second Eliassen–Palm theorem—is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

scholarly journals THE SUPERLUMINAL NEUTRINOS FROM DEFORMED LORENTZ INVARIANCE

2012 ◽  
Vol 27 (33) ◽  
pp. 1250196 ◽  
Author(s):  
YUNJIE HUO ◽  
TIANJUN LI ◽  
YI LIAO ◽  
DIMITRI V. NANOPOULOS ◽  
YONGHUI QI ◽  
...  
Keyword(s):  
Energy Conservation ◽  
Conservation Laws ◽  
Conservation Law ◽  
Lorentz Invariance ◽  
Momentum Conservation ◽  
Neutrino Energy ◽  
Dispersion Relations ◽  
Energy And Momentum ◽  
Energy Conservation Law ◽  
Neutrino Momentum

We study two superluminal neutrino scenarios where [Formula: see text] is a constant. To be consistent with the OPERA, Borexino and ICARUS experiments and with the SN1987a observations, we assume that δvν on the Earth is about three-order larger than that on the interstellar scale. To explain the theoretical challenges from the Bremsstrahlung effects and pion decays, we consider the deformed Lorentz invariance, and show that the superluminal neutrino dispersion relations can be realized properly while the modifications to the dispersion relations of the other Standard Model particles can be negligible. In addition, we propose the deformed energy and momentum conservation laws for a generic physical process. In Scenario I the momentum conservation law is preserved while the energy conservation law is deformed. In Scenario II the energy conservation law is preserved while the momentum conservation law is deformed. We present the energy and momentum conservation laws in terms of neutrino momentum in Scenario I and in terms of neutrino energy in Scenario II. In such formats, the energy and momentum conservation laws are exactly the same as those in the traditional quantum field theory with Lorentz symmetry. Thus, all the above theoretical challenges can be automatically solved. We show explicitly that the Bremsstrahlung processes are forbidden and there is no problem for pion decays.

SOME CONSIDERATIONS REGARDING THE PRINCIPLE OF PHASE INVARIANCE

1955 ◽  
Vol 33 (8) ◽  
pp. 436-440
Author(s):  
F. A. Kaempffer
Keyword(s):  
Conservation Laws ◽  
Complex Field ◽  
Conservation Of Energy ◽  
Self Consistent ◽  
Energy And Momentum ◽  
Ether Theories

Taking the view that "particles" are in fact excitations of the motion of an all-pervading medium (or "ether"), it is shown that the conservation laws characterizing the ether, which are different from the well-known laws of conservation of energy and momentum, flow from a single principle, the principle of phase invariance, provided a complex field is used to describe the ether. There are at least two different self-consistent types of Lorentz-invariant ether theories which satisfy the principle of phase invariance.

Invariants and Conserved Quantities for the Helically Symmetric Flows of an Inviscid Gas and Fluid with Variable Density

2019 ◽  
Vol 74 (3) ◽  
pp. 245-251
Author(s):  
Oleg Bogoyavlenskij
Keyword(s):  
Incompressible Fluid ◽  
Conservation Laws ◽  
Ideal Incompressible Fluid ◽  
Variable Density ◽  
Conserved Quantities ◽  
Inviscid Gas ◽  
New Material ◽  
Material Conservation ◽  
Compressible Gas

AbstractNew material conservation laws and conserved quantities are derived for the helically symmetric flows of an inviscid compressible gas and an ideal incompressible fluid with variable density$\rho(\mathbf{x},\;t)$.

scholarly journals Annihilation of relativistic positrons in single crystal with production of one photon

2015 ◽  
Vol 30 (22) ◽  
pp. 1550137 ◽  
Author(s):  
N. P. Kalashnikov ◽  
E. A. Mazur ◽  
A. S. Olczak
Keyword(s):  
Conservation Laws ◽  
Single Crystal ◽  
Single Photon ◽  
Momentum Conservation ◽  
Transverse Motion ◽  
Annihilation Process ◽  
Channeled Particle ◽  
Energy And Momentum ◽  
Photon Annihilation

The energy and momentum conservation laws prohibit positron–electron single-photon annihilation in vacuum. It is shown that the situation is different in a single crystal with one of the leptons (e.g. positron) moving in the channeling (or in the quasi-channeling) mode. The transverse motion of an oriented or channeled particle may sharply increase the probability of the single-photon annihilation process.

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