The Optimal State for Gravity Currents in Shear

Abstract

This study examines the lifting of sheared environmental air by gravity currents, focusing primarily on the theoretical ''optimal state'' in which near-surface flow is turned into a vertically oriented jet. Theoretical models are presented from multiple perspectives, including the vorticity perspective that was first presented by Rotunno, Klemp, and Weisman and a flow-force balance perspective based on conservation of mass and momentum. The latter approach reveals a constraint on the depth of the environmental shear layer relative to the depth of the cold pool. Based on these control-volume constraints, a numerical solution for steady, inviscid, isentropic flow is obtained that shows how the cold-pool interface has a slightly concave shape and is nearly (although not strictly) vertical. Then, by initializing a time-dependent numerical model with a stagnant cold pool in an environment with low-level shear, it is shown that a statistically steady flow can be maintained with all the important elements of the analytic solution. Most notably, the front-relative flow is negligible behind the surface gust front at all levels, the interface of the cold pool maintains a predominantly vertical structure, and the net generation of vorticity by buoyancy within a control volume closely matches the horizontal flux of environmental vorticity on the side of the control volume. Sensitivity simulations confirm that the constraints identified by the analytic study must be met for the optimal state to be realized and that lifting of near-surface environmental air is optimized when a vertically oriented jet is created and maintained.

Gravity currents propagating into shear

“…The above reduction in the current height has also been observed by other authors for numerically simulated gravity currents with and without shear (Xu et al 1996;Bryan & Rotunno 2014b). Furthermore, Benjamin (1968) suggests that for the classical case of a gravity current without shear, heights h/H 0.347 should not be expected, due to turbulent dissipation and the resulting diffuse interface between the current and the ambient.…”

“…Bryan & Rotunno (2014b) demonstrate that the gravity current velocity obtained from the inviscid model with imposed energy dissipation agrees well with three-dimensional simulation results (see figure 15 in Bryan & Rotunno 2014b). However, the gravity current height does not track the model predictions closely.…”

“…However, the gravity current height does not track the model predictions closely. We note that in the investigations of Xu et al (1996) and Bryan & Rotunno (2014b), the influence of the Re * -value could not be analysed, since in their simulations the physical viscosity was set to zero, so that they contained only numerical dissipation.…”

Triggering and evolution of a deep convective system in the Mediterranean Sea: modelling and observations at a very fine scale

“…These kinematic conditions prevailed for many hours, contributing to the generation of the convergence line in the lower levels of the atmosphere where the warmer and moister flow over the Ligurian Sea was locally orthogonal to the northerly cold current (Figure ). Furthermore, the interaction between these two flows resembled the kinematic conditions described in Moncrieff and Liu () for an upshear propagating regime, and the dynamic conditions of the interaction of a gravity current with a less dense sheared stratified airflow (Bryan and Rotunno, , hereafter BR14).…”

Characteristics of colliding density currents: A numerical and theoretical study

“…In the lower atmosphere, wind shear (Xu, ; Liu and Moncrieff, ; Parker, ; Lee and Wilhelmson, ; Xue et al. , ; Bryan and Rotunno, ), ambient stratification (Liu and Moncrieff, ; Seigel and van den Heever, ) and three‐dimensional front structure (Droegemeier and Wilhelmson, ; Orf et al. , ; Vermeire et al.…”