Related papers: Non-conservation and conservation for different fo…
Many definitions of moist potential vorticity (PV) have been proposed to extend the dry theory of Ertel PV. None of the moist PV definitions seem to have all of the desirable properties of the dry Ertel PV. For instance, dry PV is not only…
One of the most important conservation laws in atmospheric and oceanic science is conservation of potential vorticity. The original derivation is approximately a century old, in the work of Rossby and Ertel, and it is related to the…
A new potential vorticity is derived by using a specific entropy formulation expressed in terms of a moist-air entropy potential temperature. The new formulation is compared with Ertel's version and with others based on virtual and…
The aim of this note is to describe several meteorological properties shown in a conference talk (Marquet, January 2022) for the moist-air specific entropy, the associated potential temperature ($\theta_s$) defined in Marquet (2011) and the…
A framework is introduced to compare moist `potential' temperatures. The equivalent potential temperature, $\theta_e,$ the liquid water potential temperature, $\theta_\ell,$ and the entropy potential temperature, $\theta_s$, are all shown…
Ertel's potential vorticity theorem is essentially a clever combination of two conservation principles. The result is a conserved scalar $q$ that accurately reflects possible vorticity values that fluid parcels can possess and acts as a…
The precipitating quasi-geostrophic equations go beyond the (dry) quasi-geostrophic equations by incorporating the effects of moisture. This means that both precipitation and phase changes between a water-vapour phase (outside a cloud) and…
The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring…
Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint to the dynamical evolution of plasmas in complex…
Condensible substances are nearly ubiquitous in planetary atmospheres. For the most familiar case-water vapor in Earth's present climate-the condensible gas is dilute, in the sense that its concentration is everywhere small relative to the…
A moist entropy potential temperature -- denoted by ${\theta}_{s}$ -- is defined analytically in terms of the specific entropy for moist air. The expression for ${\theta}_{s}$ is valid for a general mixing of dry air, water vapour and…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
Internal energy, enthalpy and entropy are the key quantities to study thermodynamic properties of the moist atmosphere, because they correspond to the First (internal energy and enthalpy) and Second (entropy) Laws of thermodynamics. The aim…
Recent work giving a classification of kinematic and vorticity conservation laws of compressible fluid flow for barotropic equations of state (where pressure is a function only of the fluid density) in $n>1$ spatial dimensions is extended…
Using a four-dimensional manifestly covariant formalism suitable for classical fluid dynamics, it is shown that the conservation of potential vorticity is not associated with any symmetry of the equations of motion but is instead a trivial…
It is important to be able to calculate the moist-air entropy of the atmosphere with precision. A potential temperature has already been defined from the third law of thermodynamics for this purpose. However, a doubt remains as to whether…
Molecular clouds are supported by thermal pressure, magnetic pressure, and turbulent pressure. Each of these can be modeled with a polytropic equation of state, so that overall the total pressure is the sum of the individual components. We…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
We consider a rotating non-hydrostatic flow with arbitrary stratification and argue that 1) the appropriate form of potential vorticity (PV) for this system is in terms of isopycnal deviation and 2) the decomposition into energetically…
The helicity is a topological conserved quantity of the Euler equations which imposes significant constraints on the dynamics of vortex lines. In the compressible setting the conservation law only holds under the assumption that the…