arXiv subjects

Pascal Marquet

Publications and source records attributed to Pascal Marquet.

42 records · Page 3Linked to original sources

arXiv2014

On the concept of pseudo-energy of T. G. Shepherd. A close link with exergy functions

Shepherd (1993) derived a general expression for the available potential energy for compressible, hydrostatic flow, where the sum of this available energy and the kinetic energy is called pseudo-energy. He demonstrated that for a special basic state the small-amplitude limit of the generalized available potential energy reduces to the well-known approximate form of Lorenz (1955) expressed in a pressure vertical coordinate. Other forms of available energies exist in atmospheric energetics and in thermodynamics, where the name exergy has been coined by Rant (1956) to denote the maximum work that can be extracted from any system when it is subject to some constraints (adiabatic transformations or constant total energy for instance). The purpose of this note is to show that the specific available enthalpy function denoted by $a_h = (h - h_r) - T_r \: (s - s_r)$ in Marquet (1991) can be obtained from the generalized approach of Shepherd for another basic state. This special form of pseudo-energy also leads to the global hydrostatic concepts of Dutton (1973) and Pichler (1977). The function $a_h$ only depends on the specific enthalpy $h$ and entropy $s$ at any point, the values $h_r$ and $s_r$ refer to the special dead state at temperature $T_r$ and pressure $p_r$. It is explained that for another choice of the basic state, the generalized expression of Shepherd reduces with a good accuracy to the approximate functions introduced by Pearce (1978) or Blackburn (1983) in meteorology and Thomson (1853, Lord Kelvin) in thermodynamics.

physics.ao-ph↗

arXiv2014

On the concept of exergy and available enthalpy: Application to atmospheric energetics

The available enthalpy is an early form of the modern thermodynamic concept of exergy, which is the generic name for the amount of work obtainable when some matter is brought to a state of equilibrium with its surroundings by means of reversible processes. It is shown in this paper that a study of the hydrodynamic properties of available enthalpy leads to a generalization of the global meteorological available energies previously introduced by Lorenz, Dutton and Pearce. A local energy cycle is derived without approximation. Moreover, static instabilities or topography do not prevent this theory from having practical applications. The concept of available enthalpy is also presented in terms of the potential change in total entropy. Using the hydrostatic assumption, limited-area energetics is then rigorously defined, including new boundary fluxes and new energy components. This innovative approach is especially suitable for the study of energy conversions between isobaric layers of an open limited atmospheric domain. Numerical evaluations of various energy components are presented for a hemispheric field of zonal-average temperature. It is further shown that this new energetic scheme realizes a hierarchical partition of the components so that the smallest of those available enthalpy reservoirs are almost of the same magnitude as the kinetic energy. This is actually the fundamental property that induced Margules to define the primary concept of available kinetic energy in meteorology.

physics.ao-ph↗

arXiv2014

On the computation of moist-air specific thermal enthalpy

The specific thermal enthalpy of a moist-air parcel is defined analytically following a method in which specific moist entropy is derived from the Third Law of thermodynamics. Specific thermal enthalpy is computed by integrating specific heat content with respect to absolute temperature and including the impacts of various latent heats (i.e., solid condensation, sublimation, melting, and evaporation). It is assumed that thermal enthalpies can be set to zero at $0$ K for the solid form of the main chemically inactive components of the atmosphere (solid-$α$ oxygen and nitrogen, hexagonal ice). The moist thermal enthalpy is compared to already existing formulations of moist static energy (MSE). It is shown that the differences between thermal enthalpy and the thermal part of MSE may be quite large. This prevents the use of MSE to evaluate the enthalpy budget of a moist atmosphere accurately, a situation that is particularly true when dry-air and cloud parcels mix because of entrainment/detrainment processes along the edges of cloud. Other differences are observed when MSE or moist-air thermal enthalpy is plotted on a psychrometric diagram or when vertical profiles of surface deficit are plotted.

physics.ao-ph↗

arXiv2014

Moist-entropic vertical adiabatic lapse rates: the standard cases and some lead towards inhomogeneous conditions

This note is a companion of Marquet and Geleyn (2013, {arXiv:1401.2379 [ao-ph]}), where adiabatic lapse rates $Γ_{ns}$ and $Γ_{sw}$ are derived for non-saturated ($Γ_{ns}$) or saturated ($Γ_{sw}$) parcel of moist-air. They are computed in terms of the vertical derivative of the moist-air entropy potential temperature $θ_s$ defined in Marquet (2011, {arXiv:1401.1097 [ao-ph]}). The saturated value $Γ_{sw}$ is rewritten in this note so that a more compact formulation is obtained. The new formulation for $Γ_{sw}$ is expressed in term of a weighting factor $C$. This factor may represent the proportion of an air parcel being in saturated conditions.

physics.ao-ph↗

arXiv2014

On a general definition of the squared Brunt-Väisälä Frequency associated with the specific moist entropy potential temperature

The squared Brunt-Väisälä Frequency (BVF) is computed in terms of the moist entropy potential temperature recently defined in Marquet (2011). Both homogeneously saturated and non-saturated versions of $N^2$ (the squared BVF) are derived. The method employed for computing these special homogeneous cases relies on the expression of density written as a function of pressure, total water content and specific moist entropy only. The associated conservative variable diagrams are discussed and compared with existing ones. Despite being obtained without any simplification, the formulations for $N^2$ remain nicely compact and are clearly linked with the squared BVF expressed in terms of the adiabatic non-saturated and saturated lapse rates. As in previous similar expressions, the extreme homogeneous solutions for $N^2$ are of course different, but they are not analytically discontinuous. This allows us to define a simple bridging expression for a single general shape of $N^2$, depending only on the basic mean atmospheric quantities and on a transition parameter, to be defined (or parameterized) in connection with the type of application sought. This integrated result remains a linear combination (with complex but purely local weights) of two terms only, namely the environmental gradient of the moist entropy potential temperature and the environmental gradient of the total water content. Simplified versions of the various equations are also proposed for the case in which the moist entropy potential temperature is approximated by a function of both so-called moist-conservative variables of Betts (1973).

physics.ao-ph↗

arXiv2014

On the definition of a moist-air potential vorticity

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 equivalent potential temperatures. The new potential vorticity is subject to conservative properties ensured by the Second Law applied to the moist-air material derivatives. It is shown that the upper tropospheric and stratospheric (dry) structures are nearly the same as those obtained with Ertel's component. Moreover, new structures are observed in the low troposphere, with negative values associated with moist frontal regions. The negative values are observed in the frontal regions where slantwise convection instabilities may take place, but they are smaller than those observed with the equivalent potential vorticity. The main purpose of the article is to diagnose the behaviour of the new potential vorticity from numerical output generated by the ARPEGE NWP model, with the help of isobaric charts and vertical cross-sections. Two inversion methods are suggested. The first method could be based on the invertibility principle verified by the virtual potential vorticity, with a possibility to control and modify separately potential vorticity components in the (dry) upper and (moist) lower atmospheric levels. The other method may consist of an inversion process directly applied to the new moist-air entropy potential vorticity, because the negative values and the solenoidal term are smaller than those observed with equivalent potential vorticity, as shown by numerical evaluations.

physics.ao-ph↗