Abstract
Cumulus clouds involve processes on a vast range of scales—including cloud droplets, turbulent mixing, and updrafts and downdrafts—and it is often difficult to determine how processes on different scales interact with each other. In this article, several multiscale asymptotic models are derived for cumulus cloud dynamics in order to (i) provide a systematic scale analysis on each scale and (ii) clarify the nature of interactions between different scales. In terms of scale analysis, it is shown that shallow cumulus updrafts can be described by balanced dynamics with a balance between source terms and ascent/descent; this is a cloud-scale version of so-called weak-temperature-gradient models. In terms of multiscale interactions, a model is derived that connects these balanced updrafts to the fluctuations within the balanced updraft envelope. These fluctuations describe parcels and updraft pulses, and this model encompasses some of the multiscale aspects of entrainment. In addition to this shallow cumulus model, to provide a broad picture of general cumulus dynamics, multiscale models are also derived for other scales; these include models for parcels and subparcel turbulent mixing and models for deep cumulus. Broadly speaking, the differences between the shallow and deep cases convey the notion that shallow cumulus dynamics are parcel dominated, whereas deep cumulus dynamics are updraft dominated; this is largely due to the difference in the apparent magnitude of the background temperature stratification. In addition to their use in guiding theory, the multiscale models also provide a framework for multiscale numerical simulations.
* Current affiliation: Department of Mathematics, University of Wisconsin—Madison, Madison, Wisconsin
Corresponding author address: Samuel Stechmann, Department of Mathematics, University of Wisconsin—Madison, 480 Lincoln Dr., Madison, WI 53706. Email: stechmann@wisc.edu
