Continuity equations as expressions for local balances of masses in
                        cloudy air

Wacker, Ulrike; Herbert, F.

doi:10.3402/tellusa.v55i3.12097

Cited by 15 publications

(15 citation statements)

References 4 publications

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“…The use of the full mass‐weighted solution for a system where one wishes to keep a ‘gaseous‐type’ state equation may appear counter‐intuitive. Nevertheless, Wacker and Herbert (2003) make the same recommendation: ‘ In a more detailed framework in which the field balance equations of momentum, energy and entropy of the system are also enclosed, a clear physical preference is seen to exist for the barycentric frame of reference. ’.…”

Section: The Microphysical Schemementioning

confidence: 99%

“…Hence it should be no surprise that the subject of a fully consistent set of multiphase dynamical and thermodynamical equations has recently received substantial attention (e.g. Bannon, 2002; Bryan and Fritsch, 2002; Wacker and Herbert, 2003). This happened although the topic could in fact have been addressed already thirty years ago, following for instance some pioneering work of Hinkelmann (developed and published by Zdunkowski and Bott 2003, in chapter 11 of their textbook).…”

Section: Introductionmentioning

confidence: 99%

“…The interaction with the vertical momentum and kinetic energy aspects of the problem are not yet treated in this work. We assume that the equations automatically obey the Green–Ostrogradsky theorem when turbulent fluxes of enthalpy and water species are derived using Reynolds‐type averaging. Wacker and Herbert (2003) indicate that this is a legitimate step when working with a full mass‐weighted system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Flux-conservative thermodynamic equations in a mass-weighted framework

Catry

Geleyn

Tudor

et al. 2007

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C TA set of equations, ready for discretization, is presented for the purely thermodynamic part of atmospheric energetics along a vertical column. Considerations of kinetic energy budgets and detailed turbulence laws are left for further study. The equations are derived in a total mass-based framework, both for the vertical coordinate system and for the conservation laws. This results in the use of the full barycentric velocity as the vector of advection. Under these conditions, the equations are derived from first principles on the basis of an a priori defined set of simplifying hypotheses. The originality of the resulting set of equations is twofold. First, even in the presence of a full prognostic treatment of cloud and precipitation processes, there exists a flux-conservative form for all relevant budgets, including that of the thermodynamic equation. Secondly, the form of the state law that is obtained for the multiphase system allows the flux-conservative form to be kept when going from the hydrostatic primitive equations system to the fully compressible system and projecting then the heat source/sink on both temperature and pressure tendencies.

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Section: The Microphysical Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Flux-conservative thermodynamic equations in a mass-weighted framework

Catry

Geleyn

Tudor

et al. 2007

Tellus A: Dynamic Meteorology and Oceanography

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“…Water mass. Wacker and Herbert (2003) and Wacker et al (2006) studied the budget equations for partial densities of a moist atmosphere, particularly incorporating sedimentation fluxes. Following their approach, the budget of any water component x can be formulated as where σ x is the internal production rate, for example, cloud water from a condensation process, and F x is the turbulent mass flux.…”

mentioning

confidence: 99%

“…Taking the impact of water vapour evaporation and precipitation into account, the barycentric velocity is not zero at the surface. Although the Earth surface is impermeable for dry air, the diffusive flux of water vapour J v and the sedimentation flux of the precipitating particles across the Earth surface account for a non‐vanishing barycentric velocity at ground (Wacker and Herbert, 2003): w s = ( J v − P r − P s − P g )/ρ d . Therefore, the turbulent fluxes and precipitation rates of have to be multiplied by a factor of ρ/ρ d , if the lower surface of the CV is equal to the Earth surface.…”

mentioning

confidence: 99%

Validation of a mesoscale weather prediction model using subdomain budgets

Petrik

Baldauf

Schlünzen

et al. 2011

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C TThe monitoring of conservation properties is essential for model development and for the investigation of the hydrological cycle. This is especially relevant for models that do not solve equations in flux form and do not apply a finite volume discretization. The conservation properties of the mesoscale model COSMO are evaluated by using a finite volume diagnostic approach. That is the subdomain budget of energy, water mass and total mass are diagnosed in a control volume that can be placed at each site in the model domain and is independent of the grid size. Thus, this diagnostic method has the major advantage that it can be applied to realistic simulations. The application of the diagnostic method to the COSMO model reveals a good preservation of the water mass, but large errors in energy and total mass conservation. The analysis shows to which extent errors in the treatment of thermodynamical processes, numerical filters and moisture advection schemes contaminate the subdomain budgets. In this paper we will show that the application of a saturation adjustment scheme under a fixed volume condition is required for models, which use the non-hydrostatic equations and height-based coordinates. Also, a further extension of the model physics will be introduced and discussed for a realistic test case.

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How is local material entropy production represented in a numerical model?

Gaßmann

Herzog²

2014

Quart J Royal Meteoro Soc

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Numerical models of the atmosphere should fulfil fundamental physical laws. The second law of thermodynamics is associated with positive local entropy production and dissipation of available energy. In order to guarantee this positivity in numerical simulations, subgridscale turbulent fluxes of heat, water vapour and momentum are required to depend on numerically resolved gradients in a unique way. The task of parametrization remains to deliver phenomenological coefficients.Inspecting commonly used parametrizations for subgrid fluxes, we find that some of them obey the second law of thermodynamics and some do not. The conforming approaches are Smagorinsky momentum diffusion, phase changes and sedimentation fluxes for hydrometeors. Conventional turbulent heat-flux parametrizations do not conform with the second law. A new water-vapour flux formulation is derived from the requirement of locally positive entropy production. The conventional and new water-vapour fluxes are compared using high-resolution radiosonde data. Conventional water-vapour fluxes are wrong by up to 10% and exhibit a negative bias. Two numerical tests (the Boulder windstorm test case and a convective boundary-layer experiment) are performed with the Icosahedral Nonhydrostatic model at the Institute for Atmospheric Physics (ICON-IAP). The experiments compare conventional and entropyconsistent heat-flux parametrizations. Both test cases indicate that negative thermal dissipation can occur for the conventional heat flux. Obviously, the additional energy made available by this negative dissipation to the resolved turbulence is later on dissipated by friction, so that the total dissipation is again comparable, at least for the boundary-layer experiment. To avoid confusion, dissipation here means a local entropy source multiplied by temperature, which has the dimension [energy/(volume unit × time unit)] = J/(m 3 × s) = kg/(m × s 3 ).

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Continuity equations as expressions for local balances of masses in cloudy air

Cited by 15 publications

References 4 publications

Flux-conservative thermodynamic equations in a mass-weighted framework

Flux-conservative thermodynamic equations in a mass-weighted framework

Validation of a mesoscale weather prediction model using subdomain budgets

How is local material entropy production represented in a numerical model?

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