Potential Vorticity and Balanced and Unbalanced Moisture

Abstract

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.

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

“…2006; Wetzel et al. 2020). In particular, the goal is to create some initial conditions that are somewhat simple while also involving the influence of a turbulent flow.…”

“…Majda (2003), Marquet (2014), Wetzel et al. (2020) and references therein). 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.…”

“…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).…”

“…For instance, a moist variable based on potential temperature, , or on virtual potential temperature, , is not slowly varying (Wetzel et al. 2020). The variable, based on , is one definition of that is slowly varying, and it is therefore well-suited for the present study.…”

“…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 .…”