Effects of clouds and phase changes on fast-wave averaging: a numerical assessment

Zhang, Yeyu; Smith, Leslie; Stechmann, Samuel N.

doi:10.1017/jfm.2021.427

Cited by 5 publications

(16 citation statements)

References 81 publications

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“…The purely saturated simulations have liquid water everywhere. Reprinted with permission from [19]. (Online version in colour.)…”

Section: Results Of Numerical Simulationsmentioning

confidence: 99%

“…The main influence of phase changes can be seen in (2.2), (2.6) and (2.7): the form of the buoyancy is different in unsaturated and saturated phases. This effect is related to latent heating within clouds, which itself can be seen more clearly if the equations are written in terms of potential temperature θ and water vapour mixing ratio qv, as in (1.1), instead of θe and qt; see [19]. Note that the buoyancy, as defined in (2.6), is continuous but not differentiable at the phase interface, as is consistent with common treatments of phase changes in clouds; while one could possibly use a smoother buoyancy definition, it would likely not cause any significant changes in the numerical solutions here, which already inherently include a smoothing effect due to the finite grid resolution.…”

Section: Model Description and Methodsmentioning

confidence: 99%

“…We consider the special case Fr1=Fr2=Ro=ϵ corresponding to false(Fru,Frsfalse)=false(ϵ/2,ϵfalse) with ϵ=false(10−3,10−2,10−1false). Thus the maximum wave frequency is σmax=2ϵ−1 [19]. After calculating normalΔt based on the CFL and wave conditions, we select the smaller of the two time steps.…”

Section: Model Description and Methodsmentioning

confidence: 99%

“…The present paper fits into a growing body of mathematical work on moist dynamics, including asymptotic analyses [17–27], rigorous results [28–36] and additional investigations of PQG dynamics and related topics [17–19,37–44].…”

Section: Introductionmentioning

confidence: 97%

“…Phase changes and latent heating may provide new mechanisms for the generation of waves, which may prevent convergence. Another reason for possible non-convergence is that non-convergence was actually suggested in a recent numerical investigation for a different variation of the PQG limit: the case of unbalanced or ill-prepared initial conditions [18,19]. For unbalanced initial conditions, the effects of phase changes caused complications.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment

Zhang

Smith

Stechmann

2022

Phil. Trans. R. Soc. A.

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The quasi-geostrophic (QG) equations play a crucial role in our understanding of atmospheric and oceanic fluid dynamics. Nevertheless, the traditional QG equations describe ‘dry’ dynamics that do not account for moisture and clouds. To move beyond the dry setting, precipitating QG (PQG) equations have been derived recently using formal asymptotics. Here, we investigate whether the moist Boussinesq equations with phase changes will converge to the PQG equations. A priori , it is possible that the nonlinearity at the phase interface (cloud edge) may complicate convergence. A numerical investigation of convergence or non-convergence is presented here. The numerical simulations consider cases of ϵ = 0.1 , 0.01 and 0.001, where ϵ is proportional to the Rossby and Froude numbers. In the numerical simulations, the magnitude of vertical velocity w (or other measures of imbalance and inertio-gravity waves) is seen to be approximately proportional to ϵ as ϵ decreases, which suggests convergence to PQG dynamics. These measures are quantified at a fixed time T that is O ( 1 ) , and the numerical data also suggests the possibility of convergence at later times. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

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“…The purely saturated simulations have liquid water everywhere. Reprinted with permission from [19]. (Online version in colour.)…”

Section: Results Of Numerical Simulationsmentioning

confidence: 99%

Section: Model Description and Methodsmentioning

confidence: 99%

Section: Model Description and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment

Zhang

Smith

Stechmann

2022

Phil. Trans. R. Soc. A.

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Non‐conservation and conservation for different formulations of moist potential vorticity

Kooloth,

Smith,

Stechmann

2024

Atmospheric Science Letters

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Potential vorticity (PV) is one of the most important quantities in atmospheric science. In the absence of dissipative processes, the PV of each fluid parcel is known to be conserved, for a dry atmosphere. However, a parcel's PV is not conserved if clouds or phase changes of water occur. Recently, PV conservation laws were derived for a cloudy atmosphere, where each parcel's PV is not conserved but parcel‐integrated PV is conserved, for integrals over certain volumes that move with the flow. Hence a variety of different statements are now possible for moist PV conservation and non‐conservation, and in comparison to the case of a dry atmosphere, the situation for moist PV is more complex. Here, in light of this complexity, several different definitions of moist PV are compared for a cloudy atmosphere. Numerical simulations are shown for a rising thermal, both before and after the formation of a cloud. These simulations include the first computational illustration of the parcel‐integrated, moist PV conservation laws. The comparisons, both theoretical and numerical, serve to clarify and highlight the different statements of conservation and non‐conservation that arise for different definitions of moist PV.

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Hamilton's principle with phase changes and conservation principles for moist potential vorticity

Kooloth

Smith

Stechmann

2023

Quart J Royal Meteoro Soc

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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 a globally conserved quantity, but also a material invariant that is conserved along fluid parcel trajectories. Therefore, an open question remains: Is there a moist PV that is a material invariant, if clouds and phase changes of water are present? In prior studies, definitions of moist PV have been proposed based on physical and mathematical intuition. Here, a systematic approach is used. In particular, a particle relabeling symmetry is devised for a moist atmosphere and then Noether's theorem is employed to arrive at the associated conservation laws for a moist PV. A priori, it is not clear whether this systematic approach will be viable, since it relies on variational derivatives in Hamilton's principle, and phase changes introduce singularities that could potentially prevent derivatives at the cloud edge. However, it is shown that the energy and the Lagrangian density are sufficiently smooth to allow variational derivatives, in a moist Boussinesq system with reversible phase transitions between water vapor and liquid cloud water. From the particle relabeling symmetry, a moist Kelvin circulation theorem is found, along with a moist PV conservation law that applies not for each individual parcel but for parcel‐integrated PV, integrated over certain local volumes.

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Effects of clouds and phase changes on fast-wave averaging: a numerical assessment

Abstract: Abstract

Cited by 5 publications

References 81 publications

Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment

Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment

Non‐conservation and conservation for different formulations of moist potential vorticity

Hamilton's principle with phase changes and conservation principles for moist potential vorticity

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