Inherent dissipation of upwind-biased potential temperature advection and its feedback on model dynamics

<p>Higher order upwind biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and anti-diffusive fluxes are interpreted here as the effect of irreversible sub-gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes.</p><p>The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one-dimensional advection-dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core.</p>

Rapid extreme meteorological events detected by daily regional GRACE solutions

<p>We investigate the possibility to use the Low-Earth Orbiter mission well known as GRACE to detect sudden regional variations of water mass storage caused by heavy precipitation and flooding episodes caused by the passage of tropical hurricanes of categories 4-5 (from day to a week). For this purpose, daily water mass solutions are produced from along-track GRACE geopotential anomalies to catch the signatures of these intense meteorological events. These geopotential variations are derived from accurate inter-satellite K-Band Range Rate (KBRR) measurements made along the 5-second orbits by imposing the total energy conservation to the twin GRACE vehicles. The determination of these surface sources is made over a regional network of juxtaposed triangular tiles of quasi-constant areas, and they are refreshed by a Kalman filtering for integrating progressively daily geopotential observations. These latter data have been previously reduced from known gravitational effects of atmosphere and oceanic masses (including periodic tides) for isolating the continental hydrology contribution. Our estimates of regional hydrological impacts are also compared to the ones obtained by synthesis of daily degree-40 Stokes coefficients provided by ITSG, Graz.</p>

Incorporating the Work Done by Vertical Density Fluxes in Both Kinetic and Thermal Energy Conservation Equations to Satisfy Total Energy Conservation

Conservation of total, kinetic, and thermal energy in the atmosphere is revisited, and the derived thermal energy balance is examined with observations. Total energy conservation (TEC) provides a constraint for the sum of kinetic, thermal, and potential energy changes. In response to air thermal expansion/compression, air density variation leads to vertical density fluxes and potential energy changes, which in turn impact the thermal energy balance as well as the kinetic energy balance due to the constraint of TEC. As vertical density fluxes can propagate through a large vertical domain to where local thermal expansion/compression becomes negligibly small, interactions between kinetic and thermal energy changes in determining atmospheric motions and thermodynamic structures can occur when local diabatic heating/cooling becomes small. The contribution of vertical density fluxes to the kinetic energy balance is sometimes considered but that to the thermal energy balance is traditionally missed. Misinterpretation between air thermal expansion/compression and incompressibility for air volume changes with pressure under a constant temperature would lead to overlooking important impacts of thermal expansion/compression on air motions and atmospheric thermodynamics. Atmospheric boundary layer observations qualitatively confirm the contribution of potential energy changes associated with vertical density fluxes in the thermal energy balance for explaining temporal variations of air temperature.

Thermodynamic Consistency of a Pseudoincompressible Approximation for General Equations of State

In soundproof model equations for geophysical fluid dynamics, the momentum and mechanical energy budgets decouple from the thermodynamics for adiabatic flows. In applying such models to nonadiabatic flows of fluids with general equations of state, thermodynamic consistency of the soundproof approximations needs to be ensured. Specifically, a physically meaningful total energy conservation law should arise as an integral of adiabatic dynamics, while for diabatic flows the effective energy source terms should be related through thermodynamic relationships to the rates of change of entropy and other pertinent internal degrees of freedom. Complementing earlier work by one of the authors on the Lipps and Hemler-type anelastic approximation, this paper discusses the thermodynamic consistency of an extension of Durran’s pseudoincompressible model to moist atmospheric motions allowing for a general equation of state.

Self-consistent spectra from GRMHD simulations with radiative cooling A link to reality for Sgr A*

Cosmos++ (Anninos et al. 2005) is one of the first fully relativistic magneto-hydro-dynamical (MHD) codes that can self-consistently account for radiative cooling, in the optically thin regime. As the code combines a total energy conservation formulation with a radiative cooling function, we have now the possibility to produce spectra energy density from these simulations and compare them to data. In this paper, we present preliminary results of spectra calculated using the same cooling functions from 2D Cosmos++ simulations of the accretion flow around Sgr A*. The simulation parameters were designed to roughly reproduce Sgr A*'s behavior at very low (10−8–10−7 M⊙/yr) accretion rate, but only via spectra can we test that this has been achieved.

Total energy conservation in ALE schemes for compressible flows

The numerical prediction of interaction phenomena between a compressible flow model with a moving domain and other physical models requires that the work performed on the fluid is properly translated into total fluid energy variation. We present a numerical model relying on an Arbitrary Lagrangian-Eulerian (ALE) unstructured vertex-centered finite volume that satisfies this condition together with the Geometric Conservation Law. We apply this numerical scheme to the solution of a 3D fluid-structure interaction problem. The results are contrasted with those obtained by the energy non-conservative counterpart.