Sticky Thermals: Evidence for a Dominant Balance between Buoyancy and Drag in Cloud Updrafts

Abstract

The vertical velocities of convective clouds are of great practical interest because of their influence on many phenomena, including severe weather and stratospheric moistening. However, the magnitudes of forces giving rise to these vertical velocities are poorly understood, and the dominant balance is in dispute. Here, an algorithm is used to extract thousands of cloud thermals from a large-eddy simulation of deep and tropical maritime convection. Using a streamfunction to define natural boundaries for these thermals, the dominant balance in the vertical momentum equation is revealed. Cloud thermals rise with a nearly constant speed determined by their buoyancy and the standard drag law with a drag coefficient of 0.6. Contrary to suggestions that cloud thermals might be slippery, with a dominant balance between buoyancy and acceleration, cloud thermals are found here to be sticky, with a dominant balance between buoyancy and drag.

A Framework for Convection and Boundary Layer Parameterization Derived from Conditional Filtering

“…The moist static energy budget in turn is often broken down into separate budgets for dry static energy and for water vapor and condensed water with corresponding source and sink terms (e.g., Arakawa and Schubert 1974;Tiedtke 1989). Moist static energy is only approximately conserved, both materially and in an integral sense (e.g., Romps 2015), so an approximation is involved in using its budget. Other mass flux schemes work in terms of entropy or related quantities, and the budget may be broken down into separate budgets for potential temperature and moisture quantities (e.g., Gregory and Rowntree 1990;Siebesma et al 2007).…”

“…On the other hand, rising thermals do not in general experience the same pressure gradient as their environment. For example, pressure perturbations above and below a thermal can provide an effective drag (e.g., Romps and Charn 2015). Such small-scale pressure perturbations are included in the conditional-filtering framework but appear in the b i and d ij terms, which must be parameterized.…”

The Impact of Effective Buoyancy and Dynamic Pressure Forcing on Vertical Velocities within Two-Dimensional Updrafts

“…12); 2(›w/›x)(›u/›z) (which tends to be correlated with horizontal vorticity) was associated with locally low p dynam at the level of the ring vortices [ Fig. 12; these features often migrate to the updraft center in sheared environments (e.g., Romps and Charn 2015)]; and 2(›u/›x) 2 2 (›w/›z) 2 was associated with a locally high p dynam below the ring vortices ( Fig. 12; this high tended to be weaker than the one near the updraft top, owing to much smaller ›w/›z here).…”

“…It is well understood, however, that the dynamics of buoyancy-driven ascent in convective updrafts are far more complex than parcel theory would suggest. Numerous authors have demonstrated that the perturbation pressure response to buoyancy (referred to as ''buoyancy perturbation pressure'' p buoy ) in a convective updraft partially cancels the upward absolute buoyancy force and results in weaker updrafts than would otherwise occur if absolute buoyancy alone were to regulate vertical acceleration dw/dt (e.g., Soong and Ogura 1973;Wilhelmson 1974;Yau 1979;Schlesinger 1984;Weisman et al 1997;Morrison 2016a,b;Romps and Charn 2015). Three primary consequences of the perturbation pressure force on dw/dt are commonly discussed in the literature for nearly steady-state updrafts.…”

“…This implies that nonzero dw/dt may result from local horizontal gradients in absolute buoyancy. 1 Recent authors have therefore advocated for the interpretation of buoyancy as the ''statically forced part of the locally nonhydrostatic, upward pressure gradient force,'' or ''effective buoyancy'' (Davies-Jones 2003;Doswell and Markowski 2004;Romps and Charn 2015), which is equivalent to the sum of B and the vertically oriented buoyancy pressure gradient force. …”