Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes

Wetzel, Alfredo N.; Smith, Leslie; Stechmann, Samuel N.; Martin, Jonathan E.

doi:10.1007/s11401-019-0170-4

Cited by 14 publications

(17 citation statements)

References 40 publications

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“…To do so, it has been suggested by Smith & Stechmann (2017, § 9) that additional slow variables arise in association with additional cloud variables such as , or (see also Wetzel et al. 2019 b , 2020). Even in the basic set-up of the present paper, the fast waves already have an influence on the slow components of the flow.…”

Section: Concluding Discussionmentioning

confidence: 99%

“…In addition, for the moist system described in § 2.1, a second slow variable has been found and named (Smith & Stechmann 2017; Wetzel et al. 2019 b , 2020).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The velocity associated with is found from inversion, where Relation (2.69) is one of the formulae to prescribe the transformation between and , with the wave complement set equal to zero, and is the analogue of inversion in the dry dynamics (Smith & Stechmann 2017; Wetzel et al. 2019 b , 2020). Once has been found from inversion, one may compute , and then use (2.67) to compute .…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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

2021

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Section: Concluding Discussionmentioning

confidence: 99%

“…In addition, for the moist system described in § 2.1, a second slow variable has been found and named (Smith & Stechmann 2017; Wetzel et al. 2019 b , 2020).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

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

2021

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“…since it would be proportional to the Boussinesq definition of M in the special case of constant N 2 u and N 2 s . An alternative definition of an anelastic M variable was proposed by Wetzel et al (2019). An advantageous property of M aneastic here is its physical interpretation: it is related to convective available potential energy (CAPE) (e.g., Moncrieff and Miller 1976;Emanuel 1994;Hernandez-Duenas et al 2019).…”

Section: Alternative Energy Anelastic M and Connection With Bousmentioning

confidence: 99%

Energy Decompositions for Moist Boussinesq and Anelastic Equations with Phase Changes

Marsico

Smith

Stechmann

2019

Journal of the Atmospheric Sciences

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To define a conserved energy for an atmosphere with phase changes of water (such as vapor and liquid), motivation in the past has come from generalizations of dry energies—in particular, from gravitational potential energy ρgz. Here a new definition of moist energy is introduced, and it generalizes another form of dry potential energy, proportional to θ2, which is valuable since it is manifestly quadratic and positive definite. The moist potential energy here is piecewise quadratic and can be decomposed into three parts, proportional to bu2Hu, bs2Hs, and M2Hu, which represent, respectively, buoyant energies and a moist latent energy that is released upon a change of phase. The Heaviside functions Hu and Hs indicate the unsaturated and saturated phases, respectively. The M2 energy is also associated with an additional eigenmode that arises for a moist atmosphere but not a dry atmosphere. Both the Boussinesq and anelastic equations are examined, and similar energy decompositions are shown in both cases, although the anelastic energy is not quadratic. Extensions that include cloud microphysics are also discussed, such as the Kessler warm-rain scheme. As an application, empirical orthogonal function (EOF) analysis is considered, using a piecewise quadratic moist energy as a weighted energy in contrast to the standard L2 energy. By incorporating information about phase changes into the energy, the leading EOF modes become fundamentally different and capture the variability of the cloud layer rather than the dry subcloud layer.

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“…Namely, the vortical mode of dry dynamics will be augmented in the moist system with additional low-frequency moist modes. These additional moist modes, which we call M modes or M variables, prove vital in describing the moist balanced flow (Wetzel et al 2019). In particular, the balanced PV and M variables are both needed together to specify an invertibility principle, which we call PV-and-M inversion, to diagnostically recover balanced components of all other dynamic variables, including moisture.…”

Section: Introductionmentioning

confidence: 99%

Potential Vorticity and Balanced and Unbalanced Moisture

Wetzel

Smith

Stechmann

et al. 2020

Journal of the Atmospheric Sciences

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Atmospheric flows are often decomposed into balanced (low frequency) and unbalanced (high frequency) components. For a dry atmosphere, it is known that a single mode, the potential vorticity (PV), is enough to describe the balanced flow and determine its evolution. For a moist atmosphere with phase changes, on the other hand, balanced–unbalanced decompositions involve additional complexity. In this paper, we illustrate that additional balanced modes, beyond PV, arise from the moisture. To support and motivate the discussion, we consider balanced–unbalanced decompositions arising from a simplified Boussinesq numerical simulation and a hemispheric-sized channel simulation using the Weather Research and Forecasting (WRF) Model. One important role of the balanced moist modes is in the inversion principle that is used to recover the moist balanced flow: rather than traditional PV inversion that involves only the PV variable, it is PV-and-M inversion that is needed, involving M variables that describe the moist balanced modes. In examples of PV-and-M inversion, we show that one can decompose all significant atmospheric variables, including total water or water vapor, into balanced (vortical mode) and unbalanced (inertio-gravity wave) components. The moist inversion, thus, extends the traditional dry PV inversion to allow for moisture and phase changes. In addition, we illustrate that the moist balanced modes are essentially conserved quantities of the flow, and they act qualitatively as additional PV-like modes of the system that track balanced moisture.

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Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes

Cited by 14 publications

References 40 publications

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

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

Energy Decompositions for Moist Boussinesq and Anelastic Equations with Phase Changes

Potential Vorticity and Balanced and Unbalanced Moisture

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