Abstract
For a thermal starting from rest, the scales of motion consistent with the initial conditions are given. An alternative time scale based on the motion of the thermal is derived. The anticipated similarity solutions for thermals are summarised and possible qualitative differences between solutions are given. Within this consistent framework previously published laboratory and numerical models of thermals are discussed. Reasons why numerical models have not rigorously demonstrated the existence of a self-similarity solution are considered. Comparisons of all available results show that a single similarity solution valid for all thermals does not exist.
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References
Daley, R. andMerilees, P. (1971),A spectral model of bubble convection, J. Atmos. Sci.28, 933–943.
Drake, R. L., Coyle, P. D. andAnderson, D. P. (1974),The effects of non-linear Eddy coefficients on rising line thermals. J. Atmos. Sci.31, 2046–2057.
Drake, R. L., Coyle, P. D. andAnderson, D. P. (1975),Interactive line thermals in a convective layer: a numerical simulation, J. Atmos. Sci.32, 375–379.
Dutton, J. L. andFichtl, G. H. (1969),Approximate equations of motion for gases and liquids, J. Atmos. Sci.26, 241–254.
Fox, D. G. (1972),Numerical simulation of three-dimensional, shape-preserving convective elements, J. Atmos. Sci.29, 322–341.
Lilly, D. K. (1962),On the numerical simulation of buoyant convection, Tellus14, 148–172.
Lilly, D. K. (1964),Numerical solutions for the shape-preserving two dimensional thermal convection element, J. Atmos. Sci.21, 83–98.
Molenkamp, C. M. (1968),Accuracy of finite difference methods applied to the advection equation, J. Appl. Meteor.6, 160–167.
Ogura, Y. (1962),Convection of isolated masses of buoyant fluids: a numerical calculation, J. Atmos. Sci.19, 492–502.
Orszag, S. A. (1971),Numerical simulation of incompressible flows within simple boundaries: accuracy, J. Fluid. Mech.49, 75–112.
Pearson, R. A. (1978),A numerical model of a line thermal: the influence of initial conditions, Il Nuovo Cimento C.3, 223–247.
Pearson, R. A. andMcGregor, J. L. (1976)An open boundary condition for models of thermals, J. Atmos. Sci.33, 447–455.
Pearson, R. A. andO'Connor, S. (1977),A numerical-dynamical instability, Mon. Wea. Rev.105, 301–316.
Richards, J. M. (1961), Experiments on the penetration of an interface by buoyant thermals, J. Fluid Mech.11, 367–384.
Richards, J. M. (1963),Comparisons between calculated thermal motions and experiments, J. Atmos. Sci.20, 241–242.
Scorer, R. S. (1957),Experiments on convection of isolated masses of buoyant fluid, J. Fluid Mech.2, 583–594.
Woodward, B. (1959),The motion in and around isolated thermals, Quart. J. Roy. Met. Soc.85, 144–151.
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Pearson, R.A. A discussion on models of thermals. PAGEOPH 118, 913–934 (1980). https://doi.org/10.1007/BF01593040
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DOI: https://doi.org/10.1007/BF01593040