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

Abstract

This research develops simple diagnostic expressions for vertical acceleration dw/dt and vertical velocity w within updrafts that account for effective buoyancy and the dynamic pressure gradient force. Effective buoyancy is the statically forced component of the vertical gradient in the nonhydrostatic pressure field. The diagnostic expressions derived herein show that the effective buoyancy of an updraft is dependent on the magnitude of the temperature perturbation within an updraft relative to the air along the updraft's immediate periphery du 0 y (rather than relative to an arbitrary base state as in u 0 y ), the updraft's height-to-width aspect ratio, and the updraft's slant relative to the vertical.The diagnostic expressions are significantly improved over parcel theory (where pressure forces are ignored) in their portrayal of the vertical profile of w through updrafts from a cloud model simulation and accurately diagnosed the maximum vertical velocity w max within updrafts. The largest improvements to the diagnostic expressions over parcel theory resulted from their dependence on du 0 y rather than u 0 y . Whereas the actual w max within simulated updrafts was located approximately two-thirds to three-fourths of the distance between the updraft base and the updraft top, w max within profiles diagnosed by expressions was portrayed at the updraft top when the dynamic pressure force was ignored. A rudimentary theoretical representation of the dynamic pressure force in the diagnostic expressions improved their portrayal of the simulated w profile. These results augment the conceptual understanding of convective updrafts and provide avenues for improving the representation of vertical mass flux in cumulus parameterizations.

The Dynamical Coupling of Convective Updrafts, Downdrafts, and Cold Pools in Simulated Supercell Thunderstorms

“…However, we also find importance in ( ∂w / ∂x ) ∂u ′ / ∂z + ( ∂w / ∂y ) ∂v ′ / ∂z , which represents horizontal vorticity along and within the horizontal gradient of the updraft (Figure ). The essence of an argument based on these two terms is the same as just described, except involving upward‐directed vertical gradients in horizontal‐rotationally induced low p ′ NL (see also Peters, , his Figure 12). The relative strength of this forcing depends on ‖∇ w ‖, which depends directly on the initial updraft speed and therefore on parcel buoyancy.…”

“…To understand the dynamical effects of these environmental characteristics on draft area, we follow Rotunno and Klemp (1985) and others recently (e.g., Morrison, 2016;Parker, 2017;Peters, 2016) and Figure 11. As in Figure 9, except showing the response to environmental vertical wind shear via hodograph radius (m/s), and the additional response to low (1,000 J/kg), moderate (2,000 J/kg), and high (3,000 J/kg) environmental convective available potential energy.…”

The Vertical Momentum Budget of Shallow Cumulus Convection: Insights From a Lagrangian Perspective

“…We shall explicitly calculate the value of virtual mass and mechanically induced perturbation pressure based on a rather simple cylindrical updraft model. While idealized calculations of the virtual mass is not new in this field (e.g., Davies‐Jones, ; Jeevanjee & Romps, ; Morrison, , ; Peters, ), we are not aware of attempts to apply this in the context of parameterizing the updraft vertical velocity (i.e., equation ).…”

“…For both shallow and deep convection, our simple cloud model captures the virtual mass coefficients better than the mechanical acceleration term. There may be several possible reasons for this: the ensemble number is small, therefore the result can be noisy; the assumed axisymmetric cylinder shape does not work well for mechanical acceleration compared to buoyancy since the former can be more spatially heterogeneous than the later, which implies that a more complicated treatment might be needed to fully account for the dynamic perturbation pressure as in Morrison () and Peters (); our simple model neglects the influence from the subcloud layer, and this might be of greater importance for the mechanical acceleration than the buoyancy force. We will further address subcloud layer and convective organization in the future work.…”

Core and margin in warm convective clouds – Part 1: Core types and evolution during a cloud's lifetime

“…Here we define CAPE to be the vertical integral of buoyancy from the lowest level of positive buoyancy (h 0 ; initiation of vertical velocity) to an arbitrary top height (h). Usually, the CAPE serves as a theoretical upper limit, and the vertical velocity is smaller due to multiple effects (de Roode et al, 2012), most importantly the perturbation pressure gradient force (which opposes the air motion) and mixing with the environment (entrainment or detrainment; de Roode et al, 2012;Morrison, 2016a;Peters, 2016). Recent studies have shown that entrainment effects on vertical velocity are of the second order, and the forces acting on a rising thermal show a balance between buoyancy and the perturbation pressure gradient (Hernandez-Deckers and Sherwood, 2016;Romps and Charn, 2015), the latter acting as a drag force on the updrafts.…”