Theoretical Expressions for the Ascent Rate of Moist Deep Convective Thermals
Abstract
An approximate analytic expression is derived for the ratio λ of the ascent rate of moist deep convective thermals and the maximum vertical velocity within them; λ is characterized as a function of two nondimensional buoyancydependent parameters y and h and is used to express the thermal ascent rate as a function of the buoyancy field. The parameter y characterizes the vertical distribution of buoyancy within the thermal, and h is the ratio of the vertically integrated buoyancy from the surface to the thermal top and the vertical integral of buoyancy within the thermal. Theoretical λ values are calculated using values of y and h obtained from idealized numerical simulations of ascending moist updrafts and compared to λ computed directly from the simulations. The theoretical values of [Formula: see text] 0.4–0.8 are in reasonable agreement with the simulated λ (correlation coefficient of 0.86). These values are notably larger than the [Formula: see text] from Hill’s (nonbuoyant) analytic spherical vortex, which has been used previously as a framework for understanding the dynamics of moist convective thermals. The relatively large values of λ are a result of net positive buoyancy within the upper part of thermals that opposes the downwarddirected dynamic pressuremore »
 Authors:

 National Center for Atmospheric Research, Boulder, Colorado
 Department of Meteorology, U.S. Naval Postgraduate School, Monterey, California
 Publication Date:
 Research Org.:
 University Corporation for Atmospheric Research, Boulder, CO (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1437523
 Alternate Identifier(s):
 OSTI ID: 1541830
 Grant/Contract Number:
 SC0016476
 Resource Type:
 Published Article
 Journal Name:
 Journal of the Atmospheric Sciences
 Additional Journal Information:
 Journal Name: Journal of the Atmospheric Sciences Journal Volume: 75 Journal Issue: 5; Journal ID: ISSN 00224928
 Publisher:
 American Meteorological Society
 Country of Publication:
 United States
 Language:
 English
 Subject:
 54 ENVIRONMENTAL SCIENCES; Meteorology & Atmospheric Sciences
Citation Formats
Morrison, Hugh, and Peters, John M. Theoretical Expressions for the Ascent Rate of Moist Deep Convective Thermals. United States: N. p., 2018.
Web. doi:10.1175/JASD170295.1.
Morrison, Hugh, & Peters, John M. Theoretical Expressions for the Ascent Rate of Moist Deep Convective Thermals. United States. doi:10.1175/JASD170295.1.
Morrison, Hugh, and Peters, John M. Tue .
"Theoretical Expressions for the Ascent Rate of Moist Deep Convective Thermals". United States. doi:10.1175/JASD170295.1.
@article{osti_1437523,
title = {Theoretical Expressions for the Ascent Rate of Moist Deep Convective Thermals},
author = {Morrison, Hugh and Peters, John M.},
abstractNote = {An approximate analytic expression is derived for the ratio λ of the ascent rate of moist deep convective thermals and the maximum vertical velocity within them; λ is characterized as a function of two nondimensional buoyancydependent parameters y and h and is used to express the thermal ascent rate as a function of the buoyancy field. The parameter y characterizes the vertical distribution of buoyancy within the thermal, and h is the ratio of the vertically integrated buoyancy from the surface to the thermal top and the vertical integral of buoyancy within the thermal. Theoretical λ values are calculated using values of y and h obtained from idealized numerical simulations of ascending moist updrafts and compared to λ computed directly from the simulations. The theoretical values of [Formula: see text] 0.4–0.8 are in reasonable agreement with the simulated λ (correlation coefficient of 0.86). These values are notably larger than the [Formula: see text] from Hill’s (nonbuoyant) analytic spherical vortex, which has been used previously as a framework for understanding the dynamics of moist convective thermals. The relatively large values of λ are a result of net positive buoyancy within the upper part of thermals that opposes the downwarddirected dynamic pressure gradient force below the thermal top. These results suggest that nonzero buoyancy within moist convective thermals, relative to their environment, fundamentally alters the relationship between the maximum vertical velocity and the thermaltop ascent rate compared to nonbuoyant vortices. Implications for convection parameterizations and interpretation of the forces contributing to thermal drag are discussed.},
doi = {10.1175/JASD170295.1},
journal = {Journal of the Atmospheric Sciences},
number = 5,
volume = 75,
place = {United States},
year = {2018},
month = {5}
}
DOI: 10.1175/JASD170295.1
Web of Science