In this work, the reconstruction of sub-grid scales in large eddy simulation (LES) of turbulent
flows in stratocumulus clouds is addressed. The approach is based on the fractality
assumption of turbulent velocity field. The fractal model reconstructs sub-grid velocity
field from known filtered values on LES grid, by means of fractal interpolation, proposed
by Scotti and Meneveau (Physica D 127, 198–232 1999). The characteristics of the
reconstructed signal depend on the stretching parameter d, which is related to the fractal
dimension of the signal. In many previous studies, the stretching parameter values were
assumed to be constant in space and time. To improve the fractal interpolation approach,
we account for the stretching parameter variability. The local stretching parameter is calculated
from direct numerical simulation (DNS) data with an algorithm proposed by Mazel
and Hayes (IEEE Trans. Signal Process 40(7), 1724–1734, 1992), and its probability density
function (PDF) is determined. It is found that the PDFs of d have a universal form when
the velocity field is filtered to wave-numbers within the inertial range. In order to investigate
Reynolds number (Re) dependence, we compare the inertial-range PDFs of d in DNS
and large eddy simulation (LES) of stratocumulus cloud-top and experimental airborne data
from Physics of Stratocumulus Top (POST) research campaign. Next, fractal reconstruction
of the subgrid velocity is performed and energy spectra and statistics of velocity increments
are compared with DNS data. It is assumed that the stretching parameter d is a random variable
with the prescribed PDF. We show that the agreement with the DNS is in such case
better and the error in mass conservation is smaller compared to the use of constant values
of d. The motivation of this study is to reproduce effect of sub-grid scales on a motion of
Lagrangian particles (e.g. droplets) in clouds.
