Editorial Type:
Article
Article Type:
Research Article

A Theoretical and Numerical Study of Density Currents in Nonconstant Shear Flows

Ming Xue Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma

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Qin Xu Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

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Kelvin K. Droegemeier School of Meteorology and Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma

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Print Publication:
01 Aug 1997
DOI:
https://doi.org/10.1175/1520-0469(1997)054<1998:ATANSO>2.0.CO;2
Page(s):
1998–2019
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Abstract

The previous idealized two-fluid model of a density current in constant shear is extended to the case where the inflow shear is confined to the low levels. The analytical solution is determined by the conservation of mass, momentum, vorticity, and energy. It is found that a low-level shear acts in a similar manner to a uniform vertical shear in controlling the depth of a steady-state density current. When the shear enhances the low-level flow against the density current propagation, the current is deeper than half of the domain depth. Time-dependent numerical experiments are conducted for a variety of parameter settings, including various depths and strengths of the shear layer. The numerical results agree closely with the theoretical analyses.

Numerical experiments are also performed for a case where the initial depth of the density current is set to be comparable to the low-level shear, which is much shallower than that given by the steady-state solution. The circulation at the density current head remains shallow and is nonsteady in this case, whereas the time-averaged flow still exhibits a deep jump updraft pattern that is close to the theoretical solution, suggesting the applicability of the theoretical results to even more transient flows.

The simulated flow features are discussed in terms of balanced and unbalanced dynamics, and in the context of forcing and uplifting at the frontal zone in long-lived convective systems. Here the term balance refers to a flow configuration that satisfies the steady-state solution of the idealized theoretical model.

Corresponding author address: Dr. Ming Xue, CAPS, University of Oklahoma, Sarkeys Energy Center, Suite 1110, 100 East Boyd, Norman, OK 73019.

Abstract

The previous idealized two-fluid model of a density current in constant shear is extended to the case where the inflow shear is confined to the low levels. The analytical solution is determined by the conservation of mass, momentum, vorticity, and energy. It is found that a low-level shear acts in a similar manner to a uniform vertical shear in controlling the depth of a steady-state density current. When the shear enhances the low-level flow against the density current propagation, the current is deeper than half of the domain depth. Time-dependent numerical experiments are conducted for a variety of parameter settings, including various depths and strengths of the shear layer. The numerical results agree closely with the theoretical analyses.

Numerical experiments are also performed for a case where the initial depth of the density current is set to be comparable to the low-level shear, which is much shallower than that given by the steady-state solution. The circulation at the density current head remains shallow and is nonsteady in this case, whereas the time-averaged flow still exhibits a deep jump updraft pattern that is close to the theoretical solution, suggesting the applicability of the theoretical results to even more transient flows.

The simulated flow features are discussed in terms of balanced and unbalanced dynamics, and in the context of forcing and uplifting at the frontal zone in long-lived convective systems. Here the term balance refers to a flow configuration that satisfies the steady-state solution of the idealized theoretical model.

Corresponding author address: Dr. Ming Xue, CAPS, University of Oklahoma, Sarkeys Energy Center, Suite 1110, 100 East Boyd, Norman, OK 73019.

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  • Benjamin, B. T., 1968: Gravity current and related phenomena. J. Fluid Mech.,31, 209–248.

  • Bluestien, H. B., and M. H. Jain, 1985: Formation of mesoscale lines of precipitation: Severe squall lines in Oklahoma during the spring. J. Atmos. Sci.,42, 1711–1732.

  • Britter, R. E., and J. E. Simpson, 1978: Experiments on the dynamics of a gravity current head. J. Fluid Mech.,88, 223–240.

  • Carbone, R. E., 1982: A severe frontal rainband. Part I: Stormwide hydrodynamic structure. J. Atmos. Sci.,39, 258–279.

  • Chen, C., 1995: Numerical simulations of gravity currents in uniform shear flows. Mon. Wea. Rev.,123, 3240–3253.

  • Clark, T. L., 1977: A small-scale dynamic model using a terrain-following coordinate transformation. J. Comput. Phys.,24, 186–215.

  • Crook, N. A., and M. J. Miller, 1985: A numerical and analytical study of atmospheric undular bores. Quart. J. Roy. Meteor. Soc.,111, 225–242.

  • Droegemeier, K. K., 1985: The numerical simulation of thunderstorm outflow dynamics. Ph.D. dissertation, University of Illinois at Urbana–Champaign, 695 pp. [Available from Dept. of Atmospheric Science, University of Illinois at Urbana–Champaign, 105 S. Gregory Avenue, Urbana, IL 81801.].

  • ——, and R. P. Davies-Jones, 1987: Simulation of thunderstorm microbursts with a super-compressible numerical model. Preprint, Fifth Int. Conf. on Numerical Methods in Laminar and Turbulent Flow, Montreal, Quebec, Canada, Concordia University, Pratt and Whitney, Canada, and the National Science and Engineering Research Council of Canada, 1386–1397.

  • ——, and R. Wilhelmson, 1987: Numerical simulation of thunderstorm outflow dynamics. Part I: Outflow sensitivity experiments and turbulence dynamics. J. Atmos. Sci.,44, 1180–1210.

  • ——, M. Xue, K. Johnson, M. O’Keefe, A. Sawdey, G. Sabot, S. Wholey, N. T. Lin, and K. Mills, 1995: Weather prediction: A scalable storm-scale model. High Performance Computing, G. Sabot, Ed., Addison-Wesley, 45–92.

  • ——, and ——, A. Sathye, K. Brewster, G. Bassett, J. Zhang, Y. Lui, M. Zou, A. Crook, V. Wong, R. Carpenter, and C. Mattocks, 1996: Real-time numerical prediction of storm-scale weather during VORTEX-95. Part I: Goals and methodology. Preprints, 18th Conf. on Severe Local Storms, San Francisco, CA, Amer. Meteor. Soc., 6–10.

  • Fovell, R. G., and Y. Ogura, 1988: Numerical simulation of a midlatitude squall line in two dimensions. J. Atmos. Sci.,45, 3846–3879.

  • Johnson, K. W., J. Bauer, G. A. Riccardi, K. K. Droegemeier, and M. Xue, 1994: Distributed processing of a regional prediction model. Mon. Wea. Rev.,122, 2558–2572.

  • Klemp, J. B., and R. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci.,35, 1070–1096.

  • ——, R. Rotunno, and W. C. Skamarock, 1994: One the dynamics of gravity currents in a channel. J. Fluid Mech.,269, 169–198.

  • Liu, C., and M. W. Moncrieff, 1996a: An analytical study of density currents in sheared, stratified flow and the effects of latent heating. J. Atmos. Sci.,53, 3303–3312.

  • ——, and ——, 1996b: A numerical study of the effects of ambient flow and shear on density currents. Mon. Wea. Rev.,124, 2282–2303.

  • Mitchell, K. E., and J. B. Hovermale, 1977: A numerical investigation of the severe thunderstorm gust front. Mon. Wea. Rev.,105, 657–675.

  • Moncrieff, M. W., 1978: The dynamic structure of two-dimensional steady convection in constant shear. Quart. J. Roy. Meteor. Soc.,104, 543–567.

  • ——, 1992: Organized convective systems: Archetypal dynamical models, momentum flux theory, and parameterization. Quart. J. Roy. Meteor. Soc.,118, 819–850.

  • ——, and D. K. So, 1989: A hydrodynamic theory of conservative bounded density currents. J. Fluid Mech.,198, 177–197.

  • Mueller, C., and R. Carbone, 1987: Dynamics of a thunderstorm outflow. J. Atmos. Sci.,44, 1879–1898.

  • Parker, D. J., 1996: Cold pools in shear. Quart. J. Roy. Meteor. Soc.,122, 1655–1674.

  • Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong long-lived squall lines. J. Atmos. Sci.,45, 463–485.

  • Shapiro, A., 1992: A hydrodynamical model of shear flow over semi-infinite barriers with application to density currents. J. Atmos. Sci.,49, 2293–2305.

  • Simpson, J. E., 1969: A comparison between laboratory and atmospheric density currents. Quart. J. Roy. Meteor. Soc.,95, 758–765.

  • ——, D. A. Mansfield, and J. R. Milford, 1977: Inland penetration of sea-breeze fronts. Quart. J. Roy. Meteor. Soc.,103, 47–76.

  • Skamarock, W. C., and J. B. Klemp, 1992: The stability of time-splitting numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon. Wea. Rev.,120, 2109–2127.

  • ——, and ——, 1993: Adaptive grid refinement for two-dimensional and three-dimensional nonhydrostatic atmospheric flow. Mon. Wea. Rev.,121, 788–804.

  • Thorpe, A. J., M. J. Miller, and M. W. Moncrieff, 1980: Dynamic models of two-dimensional downdraft. Quart. J. Roy. Meteor. Soc.,106, 463–484.

  • ——, ——, and ——, 1982: Two-dimensional convection in non-constant shear: A model of mid-latitude squall lines. Quart. J. Roy. Meteor. Soc.,108, 739–762.

  • von Karman, T., 1940: The engineer grapples with non-linear problems. Bull. Amer. Math. Soc.,46, 615–683.

  • Wakimoto, R. M., 1982: The life cycle of thunderstorm gust fronts as viewed with Doppler radar and rawinsonde data. Mon. Wea. Rev.,110, 1060–1082.

  • Xu, Q., 1992: Density currents in shear flows—A two-fluid model. J. Atmos. Sci.,49, 511–524.

  • ——, and L. P. Chang, 1987: On the two-dimensional steady upshear-sloping convection. Quart. J. Roy. Meteor. Soc.,113, 1065–1088.

  • ——, and M. W. Moncrieff, 1994: Density current circulations in shear flows. J. Atmos. Sci.,51, 434–446.

  • ——, F. S. Zhang, and G. P. Lou, 1992:Finite-element solutions of free-interface density currents. Mon. Wea. Rev.,120, 230–233.

  • ——, M. Xue, and K. K. Droegemeier, 1996: Numerical simulation of density currents in sheared environments within a vertically confined channel. J. Atmos. Sci.,53, 770–786.

  • Xue, M., and A. J. Thorpe, 1991: A mesoscale numerical model using the nonhydrostatic sigma coordinate equations: Model experiments with dry mountain flows. Mon. Wea. Rev.,119, 1168–1185.

  • ——, K. K. Droegemeier, and V. Wong, 1995a: Advanced Regional Prediction System (ARPS) and real-time storm prediction, Preprints, Int. Workshop on Limited-Area and Variable Resolution Models, Beijing, China, World Meteorological Organization, 23–27.

  • ——, ——, ——, A. Shapiro, and K. Brewster, 1995b: Advanced Regional Prediction System (ARPS) Version 4.0 User’s Guide, 380 pp. [Available from Center for Analysis and Prediction of Storms, University of Oklahoma, 100 E. Boyd, Norman, OK 73019.].

  • ——, K. Brewster, K. K. Droegemeier, F. Carr, V. Wong, Y. Liu, A. Sathye, G. Bassett, P. Janish, J. Levit, and P. Bothwell, 1996: Real time prediction of storm-scale weather during VORTEX-95, Part II: Operation summary and example cases. Preprints, 18th Conf. on Severe Local Storms, San Francisco, CA, Amer. Meteor. Soc., 178–182.

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