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| Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes |
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Citation： |
Alfredo N. WETZEL,Leslie M. SMITH,Samuel N. STECHMANN,Jonathan E. MARTIN.Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes[J].Chinese Annals of Mathematics B,2019,40(6):1005~1038 |
| Page view： 537
Net amount： 350 |
Authors： |
Alfredo N. WETZEL; Leslie M. SMITH;Samuel N. STECHMANN;Jonathan E. MARTIN |
Foundation： |
This work was supported by the National Science Foundation through grant AGS--1443325 and DMS-1907667 and the University of Wisconsin--Madison Office of the Vice Chancellor
for Research and Graduate Education with funding from the Wisconsin
Alumni Research Foundation. |
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| Abstract： |
Atmospheric variables (temperature, velocity, etc.) are often
decomposed into balanced and unbalanced components that represent
low-frequency and high-frequency waves, respectively. Such
decompositions can be defined, for instance, in terms of eigenmodes
of a linear operator. Traditionally these decompositions ignore
phase changes of water since phase changes create a piecewise-linear operator
that differs in different phases (cloudy versus non-cloudy). Here we
investigate the following question: How can a balanced--unbalanced
decomposition be performed in the presence of phase changes? A
method is described here motivated by the case of small Froude and
Rossby numbers, in which case the asymptotic limit yields
precipitating quasi-geostrophic equations with phase changes. Facilitated by its zero-frequency eigenvalue, the balanced component can be found by potential
vorticity (PV) inversion, by solving an elliptic partial
differential equation (PDE), which includes Heaviside
discontinuities due to phase changes. The method is also compared
with two simpler methods: one which neglects phase changes, and one
which simply treats the raw pressure data as a streamfunction. Tests
are shown for both synthetic, idealized data and data from Weather
Research and Forecasting (WRF) model simulations. In comparisons,
the phase-change method and no-phase-change method produce
substantial differences within cloudy regions, of approximately 5 K
in potential temperature, due to the presence of clouds and phase
changes in the data. A theoretical justification is also derived in
the form of a elliptic PDE for the differences in the two
streamfunctions. |
Keywords： |
Potential vorticity inversion, Moist atmospheric dynamics, Slow-fast systems, Balanced-unbalanced decomposition, Elliptic partial differential equations |
Classification： |
35R05, 86A10 |
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