Abstract

This study presents analytic results for steady gravity currents in a channel using the deep anelastic equations. Results are cast in terms of a nondimensional parameter H/H ₀ that relates the channel depth H to a scale depth H ₀ (the depth at which density goes to zero in an isentropic atmosphere). The classic results based on the incompressible equations correspond to H/H ₀ = 0. For cold gravity currents (at the bottom of a channel), assuming energy-conserving flow, the nondimensional current depth h/H is much smaller, and nondimensional propagation speed C/(gH)^1/2 is slightly smaller as H/H ₀ increases. For flows with energy dissipation, C/(gH)^1/2 decreases as H/H ₀ increases, even for fixed h/H. The authors conclude that as H/H ₀ increases the normalized hydrostatic pressure rise in the cold pool increases near the bottom of the channel, whereas drag decreases near the top of the channel; these changes require gravity currents to propagate slower for steady flow to be maintained. From these results, the authors find that steady cold pools have a likely maximum depth of 4 km in the atmosphere (in the absence of shear). For warm gravity currents (at the top of a channel), h/H is slightly larger and C/(gH)^1/2 is much larger as H/H ₀ increases. The authors also conduct two-dimensional numerical simulations of “lock-exchange flow” to provide an independent evaluation of the analytic results. For cold gravity currents the simulations support the analytic results. However, for warm gravity currents the simulations show unsteady behavior that cannot be captured by the analytic theory and which appears to have no analog in incompressible flow.

Abstract

In this study the authors analyze and interpret the effects of parameterized diffusion on the nearly steady axisymmetric numerical simulations of hurricanes presented in a recent study. In that study it was concluded that horizontal diffusion was the most important control factor for the maximum simulated hurricane intensity. Through budget analysis it is shown here that horizontal diffusion is a major contributor to the angular momentum budget in the boundary layer of the numerically simulated storms. Moreover, a new scale analysis recognizing the anisotropic nature of the parameterized model diffusion shows why the horizontal diffusion plays such a dominant role. A simple analytical model is developed that captures the essence of the effect. The role of vertical diffusion in the boundary layer in the aforementioned numerical simulations is more closely examined here. It is shown that the boundary layer in these simulations is consistent with known analytical solutions in that boundary layer depth increases and the amount of “overshoot” (maximum wind in excess of the gradient wind) decreases with increasing vertical diffusion. However, the maximum wind itself depends mainly on horizontal diffusion and is relatively insensitive to vertical diffusion; the overshoot variation with vertical viscosity mainly comes from changes in the gradient wind with vertical viscosity. The present considerations of parameterized diffusion allow a new contribution to the dialog in the literature on the meaning and interpretation of the Emanuel potential intensity theory.

Abstract

Using a time-dependent axisymmetric numerical model, the authors evaluate whether high-entropy air near the surface in hurricane eyes can substantially increase hurricanes’ maximum intensity. This local high-entropy anomaly is ultimately created by surface entropy fluxes in the eye. Therefore, simulations are conducted in which these surface fluxes are set to zero; results show that the high-entropy anomaly is eliminated, yet the axisymmetric tangential wind speed is only slightly weakened (by ∼4%, on average). These results contradict the hypothesis that transport of high-entropy air from the eye into the eyewall can significantly increase the maximum axisymmetric intensity of hurricanes. In fact, all simulations (with or without high-entropy anomalies) have an intensity that is 25–30 m s⁻¹ higher than Emanuel’s theoretical maximum intensity. Further analysis demonstrates that less then 3% of the total surface-entropy input to the hurricane comes from the eye, and therefore the total magnitude of entropy transport between the eye and eyewall is a negligible component of the entropy budget of the simulated hurricanes. This latter finding is consistent with a cursory comparison with observations.

Abstract

Several studies have shown that the intensity of numerically simulated tropical cyclones can exceed (by 50%) a theoretical upper limit. To investigate the cause, this study evaluates the underlying components of Emanuel’s commonly cited analytic theory for potential intensity (herein referred to as E-PI). A review of the derivation of E-PI highlights three primary components: a dynamical component (gradient-wind and hydrostatic balance); a thermodynamical component (reversible or pseudoadiabatic thermodynamics, although the pseudoadiabatic assumption yields greater intensity); and a planetary boundary layer (PBL) closure (which relates the horizontal gradients of entropy and angular momentum at the top of the PBL to fluxes and stresses at the ocean surface). These three components are evaluated using output from an axisymmetric numerical model. The present analysis finds the thermodynamical component and the PBL closure to be sufficiently accurate for several different simulations. In contrast, the dynamical component is clearly violated. Although the balanced portion of the flow (υ_g , to which E-PI applies) appears to also exceed E-PI, it is shown that this difference is attributable to the method used to calculate υ_g from the model output. Evidence is shown that υ_g for a truly balanced cyclone does not exceed E-PI. To clearly quantify the impact of unbalanced flow, a more complete analytic model is presented. The model is not expressed in terms of external conditions and thus cannot be used to predict maximum intensity for a given environment; however, it does allow for evaluation of the relative contributions to maximum intensity from balanced and unbalanced (i.e., inertial) terms in the governing equations. Using numerical model output, this more complete model is shown to accurately model maximum intensity. Analysis against observations further confirms that the effects of unbalanced flow on maximum intensity are not always negligible. The contribution to intensity from unbalanced flow can become negligible in axisymmetric models as radial turbulence (i.e., viscosity) increases, and this explains why some previous studies concluded that E-PI was an accurate upper bound for their simulations. Conclusions of this study are also compared and contrasted to those from previous studies.

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.

Abstract

This study examines properties of gravity currents in confined channels with sheared environmental flow. Under the assumptions of steady and inviscid flow, two-dimensional analytic solutions are obtained for a wide range of shear values. The slope of a gravity current interface just above the surface increases as environmental shear α increases, which is consistent with previous studies, although here it is shown that the interface slope can exceed 80° for nondimensional shear α > 2. Then the inviscid-flow analytic solutions are compared with two- and three-dimensional numerical model simulations, which are turbulent and thus have dissipation. The simulated current depths are systematically lower, compared to a previous study, apparently because of different numerical techniques in this study that allow for a faster transition to turbulence along the gravity current interface. Furthermore, simulated gravity current depths are 10%–40% lower than the inviscid analytic values. To explain the model-produced current depths, a steady analytic theory with energy dissipation is revisited. It is shown that the numerical model current depths are close to values associated with the maximum possible dissipation rate in the simplest form of the analytic model for all values of α examined in this study. A primary conclusion is that dissipation plays an important and nonnegligible role in gravity currents within confined channels, with or without environmental shear.

Abstract

Laboratory observations of the leeside hydraulic jump indicate it consists of a statistically stationary turbulent motion in an overturning wave. From the point of view of the shallow-water equations (SWE), the hydraulic jump is a discontinuity in fluid-layer depth and velocity at which kinetic energy is dissipated. To provide a deeper understanding of the leeside hydraulic jump, three-dimensional numerical solutions of the Navier–Stokes equations (NSE) are carried out alongside SWE solutions for nearly identical physical initial-value problems. Starting from a constant-height layer flowing over a two-dimensional obstacle at constant speed, it is demonstrated that the SWE solutions form a leeside discontinuity owing to the collision of upstream-moving characteristic curves launched from the obstacle. Consistent with the SWE solution, the NSE solution indicates the leeside hydraulic jump begins as a steepening of the initially horizontal density interface. Subsequently, the NSE solution indicates overturning of the density interface and a transition to turbulence. Analysis of the initial-value problem in these solutions shows that the tendency to form either the leeside height–velocity discontinuity in the SWE or the overturning density interface in the exact NSE is a feature of the inviscid, nonturbulent fluid dynamics. Dissipative turbulent processes associated with the leeside hydraulic jump are a consequence of the inviscid fluid dynamics that initiate and maintain the locally unstable conditions.

Abstract

A case example demonstrating that surface fronts can propagate in a discrete manner is presented. The event occurred as a cold front encountered a mesoscale area of surface-based convectively generated cold air over the central United States. The surface front stalled when it reached the cold anomaly and underwent rapid frontolysis. At the same time, a prefrontal trough formed on the downstream boundary of the convective cold dome, about 300 km ahead of the original front, and underwent rapid intensification. Eventually, the original surface front became impossible to identify while the new boundary became the new surface front.

A careful inspection of surface reports shows that a front did not pass through the area between the original surface front and the new surface front. However, analysis of rawinsonde and profiler data reveals that the midlevel frontal trough propagated continously. Thus, as the midlevel front moved continously over the cold dome, the surface frontal properties (e.g., pressure trough, wind shift, and thermal gradient) dissipated on one side of the cold air while simultaneously developing on the other side.

A conceptual model of the discrete frontal propagation is presented. Simple hydrostatic arguments are applied to explain the sequence of events. Ahead of the front, moist convection generates a surface-based layer of anomalously cold air. Since hydrostatically high pressure is manifested beneath the cold dome, the surface frontal trough is effectively canceled by the high pressure anomaly. Meanwhile, locally lower pressure appears on the downwind side of the cold pool. As the midlevel front moves over the cold dome, the new surface trough deepens and the original surface frontal trough dissipates. Eventually, only the new trough remains. It is argued that discrete frontal propagation can occur in different environmental settings, but that it is generally induced by thermal anomalies in the prefrontal environment.

Abstract

Discrete frontal propagation has been identified as a process whereby a surface front discontinuously moves forward, without evidence of frontal passage across a mesoscale region. Numerical simulations are employed to examine the upper-level evolution of a discrete frontal propagation event and to explore the processes that were responsible for the discrete movement.

Model results indicate that a frontal pressure trough was not able to penetrate through a deep surface-based layer of cool air created by a precipitating convective system several hundred kilometers in advance of the front. Meanwhile, a new low-level baroclinic zone formed well ahead of the front along the southern side of the cool layer. As the midlevel front moved continuously over the cool layer, a new low-level front developed in the new baroclinic zone and the original low-level front dissipated. At the surface, the simulated front did not pass through the cool layer.

Frontogenesis terms reveal that the prefrontal circulation that becomes the new frontal circulation initially forms directly from diabatic frontogenesis. Daytime heating in the prefrontal boundary layer and cooling from thunderstorms combine to create a thermal gradient and a mesoscale pressure perturbation. Winds turn in response to the altered pressure field and form a convergent boundary, resulting in kinematic frontogenesis. The boundary subsequently undergoes rapid intensification.

Sensitivity studies were conducted in which latent heating due to precipitation was withheld and the influence of clouds on the radiation scheme was ignored. In a simulation with both of these effects withheld, the original front passes continuously through the region, that is, there is no discrete propagation. Thus, diabatic processes associated with a large complex of thunderstorms were necessary to induce the discrete frontal propagation in this case. This conclusion contrasts with previous studies, where fronts were observed to propagate discretely in dry environments.

Abstract

Horizontal homogeneity is typically assumed in the design of planetary boundary layer (PBL) parameterizations in weather prediction models. Consistent with this assumption, PBL schemes with predictive equations for subgrid turbulence kinetic energy (TKE) typically neglect advection of TKE. However, tropical cyclone (TC) boundary layers are inhomogeneous, particularly in the eyewall. To gain further insight, this study examines the effect of advection of TKE using the Mellor–Yamada–Nakanishi–Niino (MYNN) PBL scheme in idealized TC simulations. The analysis focuses on two simulations, one that includes TKE advection (CTL) and one that does not (NoADV). Results show that relatively large TKE in the eyewall above 2 km is predominantly attributable to vertical advection of TKE in CTL. Interestingly, buoyancy production of TKE is negative in this region in both simulations; thus, buoyancy effects cannot explain observed columns of TKE in TC eyewalls. Both horizontal and vertical advection of TKE tends to reduce TKE and vertical viscosity in the near-surface inflow layer, particularly in the eyewall of TCs. Results also show that the simulated TC in CTL has slightly stronger maximum winds, slightly smaller radius of maximum wind, and ~5% smaller radius of gale-force wind than in NoADV. These differences are consistent with absolute angular momentum being advected to smaller radii in CTL. Sensitivity simulations further reveal that the differences between CTL and NoADV are more attributable to vertical advection (rather than horizontal advection) of TKE. Recommendations for improvements of PBL schemes that use predictive equations for TKE are also discussed.