Entrainment Through the Top of a Heavy Gas Cloud
After termination of the slumping phase of a heavy gas cloud, the height slowly starts to grow again. It is shown that this volume increase cannot be the result of entrainment through the side wall hut must be due to entrainment through the cloud top. An entrainment relation is derived from the turbulence kinetic energy equation, and it is shown that the entrainment is driven by the turbulence in the gas cloud rather than the ambient atmospheric turbulence. As hazardous releases of heavy gases to the atmosphere is most often related to failure of pressurized vessels, the gas typically is quite cold relative to the ground. Thus, thermal convection in the cloud is the dominant turbulent mechanism, the strength of which is controlled by a surface temperature-jump Ri-number. The entrainment on the other hand is controlled by a density-jump Ri-number, and both Ri-numbers are coupled to the heat transfer at the surface and to entrainment of atmospheric air. The paper gives an approximate solution to this complex problem.
KeywordsTurbulent Kinetic Energy Surface Heat Transfer Turbulent Kinetic Energy Budget Entrainment Speed Turbulence Kinetic Energy Equation
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