Gravity currents in a deep anelastic atmosphere

AMS Citation:
Bryan, G. H., and R. Rotunno, 2008: Gravity currents in a deep anelastic atmosphere. Journal of the Atmospheric Sciences, 65, 536-556, doi:10.1175/2007JAS2443.1.
Resource Type:article
Title:Gravity currents in a deep anelastic atmosphere
Abstract: This study presents analytic results for steady gravity currents in a channel using the deep anelastic equations. Results are cast in terms of a nondimensional parameter H/H₀ that relates the channel depth H to a scale depth H₀ (the depth at which density goes to zero in an isentropic atmosphere). The classic results based on the incompressible equations correspond to H/H₀ = 0. For cold gravity currents (at the bottom of a channel), assuming energy-conserving flow, the nondimensional current depth h/H is much smaller, and nondimensional propagation speed C/(gH)½ is slightly smaller as H/H₀ increases. For flows with energy dissipation, C/(gH)½ decreases as H/H₀ increases, even for fixed h/H. The authors conclude that as H/H₀ increases the normalized hydrostatic pressure rise in the cold pool increases near the bottom of the channel, whereas drag decreases near the top of the channel; these changes require gravity currents to propagate slower for steady flow to be maintained. From these results, the authors find that steady cold pools have a likely maximum depth of 4 km in the atmosphere (in the absence of shear). For warm gravity currents (at the top of a channel), h/H is slightly larger and C/(gH)½ is much larger as H/H₀ increases. The authors also conduct two-dimensional numerical simulations of "lock-exchange flow" to provide an independent evaluation of the analytic results. For cold gravity currents the simulations support the analytic results. However, for warm gravity currents the simulations show unsteady behavior that cannot be captured by the analytic theory and which appears to have no analog in incompressible flow.
Subject(s):Currents, Cold pools, Model evaluation/performance
Peer Review:Refereed
Copyright Information:Copyright 2008 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be "fair use" under Section 107 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Law (17 USC, as revised by P.L. 94-553) does not require the Society's permission. Republication, systematic reproduction, posting in electronic form on servers, or other uses of this material, except as exempted by the above statements, requires written permission or license from the AMS. Additional details are provided in the AMS Copyright Policies, available from the AMS at 617-227-2425 or Permission to place a copy of this work on this server has been provided by the AMS. The AMS does not guarantee that the copy provided here is an accurate copy of the published work.
OpenSky citable URL: ark:/85065/d7pr7w61
Publisher's Version: 10.1175/2007JAS2443.1
  • George Bryan - NCAR/UCAR
  • Richard Rotunno - NCAR/UCAR
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