Controlling entrainment in the smoke cloud using level set-based front tracking

Although large-eddy simulation (LES) has been shown to produce a reasonable representation of the turbulent circulations within the stratocumulus-topped boundary layer, it has difficulties to accurately predict cloud-top entrainment rates. In this paper, we present a front-tracking algorithm for LES to untangle the numerical and physical contributions to entrainment. Instead of resolving the cloud-top inversion, we treat it as a discontinuity separating the boundary layer from the free atmosphere and use the level set method to track its location. We apply our method to the smoke cloud test case as presented by Bretherton et al. (1999) which is simpler than stratocumulus in that it is only driven by radiative cooling avoiding evaporative feedbacks on entrainment. We present three-dimensional LES results with and without use of the level set method varying the grid resolution and the flux limiter. With the level set method, we prescribe zero entrainment and use this case to evaluate our method's ability to maintain a non-entraining smoke-cloud layer. We use an empirically-based entrainment law to estimate numerical errors. With the level set method, the prescribed entrainment rate was maintained with errors about one order of magnitude smaller than the entrainment errors found in the standard LES. At the same time, the dependence of the entrainment errors on the choice of the limiter was reduced by more than a factor of 10