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 empiricallybased 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.
