Boundary-Layer Meteorology

, Volume 3, Issue 3, pp 273–283 | Cite as

Periodic solutions of the set of equations governing the nonadiabatic convection of dry isolated thermals

  • V. Andreev


The changes with timet of a temperature deviation δT(t,α) and of a vertical velocityWi(t,α) of an isolated dry thermal have been investigated theoretically. Solutions for the functionWi(t, α) have been derived for stable and unstable environmental stratifications. Comparing these solutions with the corresponding ones for the rise of an adiabatic thermal yield some interesting conclusions.

Firstly, there is the evident relation between the rate of entrainment of environmental air (expressed by the parameter α=(1/Mi) dMi/dz whereMi is the mass of the thermal) and the vertical velocity of the thermal: an increase in α decreases the velocity.

Two similar thermals in stably stratified surroundings, one of them moving adiabatically (α=0) the other nonadiabatically (α>0), would rise for the same length of timet2=π/N, whereN is a typical Brunt-Väisälä frequency, but with different velocities and to different heights: the ascent timet2 depends only on environmental parameters. In an unstable stratification, the vertical non-adiabatic velocity of the thermal, instead of increasing without limit, tends towards a finite asymptotic velocity
$$W_t (\infty ) = (\sqrt { - \mathcal{N}^2 } )/\alpha $$
the value of which depends upon both the stratification of the surroundings and upon the entrainment rate α. In a real atmosphere, where additional retarding forces exist, the motion will certainly be damped.


Atmosphere Convection Stratification Temperature Deviation Periodic Solution 
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Copyright information

© D. Reidel Publishing Company 1973

Authors and Affiliations

  • V. Andreev
    • 1
  1. 1.Department of MeteorologyUniversity of SofiaSofiaBulgaria

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