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Vorticity dynamics of a convective swirling boundary layer

Published online by Cambridge University Press:  19 April 2006

Richard Rotunno
Richard Rotunno
Affiliation:
Cooperative Institute for Research in Environmental Sciences, University of Colorado/NOAA, Boulder 80309
Present address: National Center for Atmospheric Research, P.O. Box 3000, Boulder 80309. The N.C.A.R. is sponsored by the National Science Foundation.
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Abstract

The vorticity dynamics of a convective swirling boundary layer are studied from the viewpoint of steady, inviscid fluid-dynamics theory. Attention is confined to the region of flow lying directly below and within a circularly shaped updraft. Fluid enters the updraft region without vorticity save for that in the boundary layer upstream of the updraft radius. Solutions of the equation \[ r\eta = r^2\frac{dH}{d\psi}-\frac{d}{d\psi}\bigg(\frac{\Gamma^2}{2}\bigg) \] (e.g. Batchelor 1967, p. 545) are presented. By the nature of this approach it allows one to compute the ‘outer’ flow together with the outer boundary-layer structure and hence side-step the interaction problem. A drawback is that the inner viscous structure is not captured. These solutions are compared to some numerical solutions of the time-dependent, viscous axisymmetric Navier-Stokes equations which are reported elsewhere (Rotunno 1979). Although the agreement is not perfect, model results are close enough whereby a number of useful deductions concerning the effects of viscous diffusion and time-dependence may be made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 3 , 15 April 1980 , pp. 623 - 640
Copyright
© 1980 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions. Washington: National Bureau of Standards.
Ames, W. F. 1969 Numerical Methods for Partial Differential Equations. New York: Barnes & Noble.
Barcilon, A. I. 1967 Vortex decay above a stationary boundary. J. Fluid Mech. 27, 155–175.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, B. 1970 Upstream influence. J. Fluid Mech. 40, 49–79.Google Scholar
Brandes, E. A. 1978 Mesocyclone evolution and tornadogenesis: some observations. Mon. Weath. Rev. 106, 995–1011.Google Scholar
Burgraff, O. R., Stewartson, K. & Belcher, R. 1971 Boundary layer induced by a potential vortex. Phys. Fluids 14, 1821–1833.Google Scholar
Carrier, G. F. 1971 Swirling flow boundary layers. J. Fluid Mech. 49, 133–144.Google Scholar
Davies-jones, R. P. 1979 Tornado dynamics. In Thunderstorms: A Social and Technological Documentary (ed. E. Kessler). University of Oklahoma Press (to be published).
Helmholtz, H. VON 1858 Crelle's J. 55.
Hildebrand, F. B. 1962 Advanced Calculus for Applications. Englewood Cliffs, New Jersey: Prentis-Hall.
Jischke, M. C. & Parang, M. 1975 Fluid dynamics of a tornado-like vortex flow. Final Rep. NOAA Grant N22-200-72 (G) and 04-4-022-13, University of Oklahoma.
Leibovich, S. 1978 The structure of vortex breakdown. Ann. Rev. Fluid Mech. 10, 221–246.Google Scholar
Lewellen, W. S. 1971 A review of confined vortex flows. N.A.S.A. Rep. CR-1772.
Lewellen, W. S. 1976 Theoretical models of a tornado vortex. In Preprints Symposium on Tornadoes, Texas Tech. University.
Lewellen, W. S. & Teske, M. E. 1977 Turbulent transport model of low level winds in a tornado. Preprints 10th Conf. Severe Local Storms, Omaha, Amer. Meteor. Soc., pp. 291–298.
Lilly, D. K. 1969 Tornado Dynamics. NCAR manuscript 69–117.
Long, R. R. 1956 Sources and sinks at the axis of a rotating liquid. Quart. J. Mech. Appl. Math. 9, 385–393.Google Scholar
Mccalla, T. R. 1967 Introduction to Numerical Methods and Fortran Programming. Wiley.
Mcintyre, M. E. 1972 On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow. J. Fluid Mech. 52, 209–243.Google Scholar
Mullen, J. B. & Maxworthy, T. 1977 A laboratory model of dust devils’ vortices. Dyn. Atmos. Oceans 1, 181–214.Google Scholar
Prandtl, L. & Tietjens, O. G. 1957 Fundamentals of Hydro- and Aeromechanics. Dover.
Rott, N. & Lewellen, W. S. 1966 In Progress in Aeronautical Sciences, vol. 7 (ed. P. Kuchemann), cha. 5. Pergammon.
Rotunno, R. 1977 Numerical simulation of a laboratory vortex. J. Atmos. Sci. 34, 1942–1956.Google Scholar
Rotunno, R. 1979 A study in tornado-like vortex dynamics. J. Atmos. Sci. 36, 140–155.Google Scholar
Smith, R. K. & Leslie, L. M. 1978 Tornadogenesis. Q. J. Roy. Met. Soc. 104, 189–199.Google Scholar
Snow, J. T., Chruch, C. R., Baker, G. L. & Agee, E. M. 1977 Characteristics of velocity field measurements associated with single and multiple vortex phenomena. Preprints 10th Conf. Severe Local Storms, Omaha, Amer. Meteor. Soc., 329–336.
Ward, N. B. 1972 The explanation of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci. 49, 1194–1204.Google Scholar