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.

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.

scholarly journals Massive surface-plasmon polaritons

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolai B. Chichkov ◽  
Andrey B. Evlyukhin ◽  
Boris N. Chichkov
Keyword(s):  
Conservation Laws ◽  
Surface Plasmon ◽  
Surface Plasmon Polaritons ◽  
Surface Plasmon Polariton ◽  
Rest Mass ◽  
Momentum Conservation ◽  
Surface Phonon ◽  
Plasmon Polariton ◽  
Energy And Momentum ◽  
Plasmon Polaritons

Abstract It is well-known that a quantum of light (photon) has a zero mass in vacuum. Entering into a medium the photon creates a quasiparticle (polariton, plasmon, surface-phonon, surface-plasmon polariton, etc.) whose rest mass is generally not zero. In this letter, devoted to the memory of Mark Stockman, we evaluate the rest mass of light-induced surface-plasmon polaritons (SPPs) and discuss an idea that collisions of two massive SPP quasiparticles can result in changes of their frequencies according to the energy and momentum conservation laws.

Fresnel’s formulae and the Minkowski momentum

2009 ◽  
Vol 87 (4) ◽  
pp. 407-410 ◽  
Author(s):  
A. Hirose ◽  
R. Dick
Keyword(s):  
Electromagnetic Wave ◽  
Conservation Laws ◽  
Oblique Incidence ◽  
Momentum Conservation ◽  
Dielectric Medium ◽  
Energy And Momentum

It is shown that the momentum of an electromagnetic wave in a dielectric medium can be uniquely determined to be the Minkowski momentum by considering oblique incidence of electromagnetic wave on a flat dielectric boundary. The Minkowski momentum is consistent with the Fresnel’s formulae and satifies the energy and momentum conservation laws.

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Total Energy ◽  
Superposition Principle ◽  
Momentum Conservation ◽  
Conserved Quantities ◽  
Angular Momentum Conservation ◽  
Third Law ◽  
The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

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