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David J. Muraki
and
Richard Rotunno

Abstract

This work is motivated by an unusual feature associated with the start-up of a moist nearly neutral atmospheric flow over a mountain ridge that was previously observed in a full-physics numerical model. In that study, the upstream propagation of a wave of subsidence precluded the establishment of upward-displaced and saturated flow that might be expected upstream of the topography. This phenomenon was hypothesized to be a consequence of the peculiar property of saturated moist neutral flow: an upward air parcel displacement produces zero buoyancy, while a downward displacement desaturates the air parcel and produces a positive buoyancy anomaly. In the present study, this hypothesis is confirmed within numerical solutions to a reduced system of equations that incorporates the saturated-atmosphere property in a particularly simple manner. The relatively uncomplicated nature of these solutions motivates the numerical solution of a further simplified initial-value problem for both nonhydrostatic and hydrostatic flow. Exact analytic solutions are developed for the latter hydrostatic case, which explains the upstream-propagating wave of subsidence as a shock phenomenon.

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Richard Rotunno
and
George H. Bryan

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.

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Mario Marcello Miglietta
and
Richard Rotunno

Abstract

Numerical simulations of conditionally unstable flows impinging on a mesoscale mountain ridge have been performed with an explicitly resolving cloud model to investigate the statistically stationary features of the solution precipitation characteristics. The simulations are performed on a three-dimensional domain and at high resolution (grid spacing: 250 m) to properly resolve cellular-scale features. Although the environmental conditions are specified by a simplified idealized conditionally unstable sounding, there are still quite a few external parameters, so only a limited portion of the parameter space was explored. Numerical solutions were first carried out for different uniform-wind profiles impinging on a bell-shaped ridge 2000 m high. In the experiments with weaker environmental wind speeds (2.5 m s−1), the cold-air outflow, caused by the evaporative cooling of rain from precipitating convective cells, is the main mechanism for cell redevelopment and movement; this outflow produces new convective cells near the head of the up- and downstream density currents, which rapidly propagate far from the ridge so that no rainfall is produced close to the ridge at later times. For larger wind speeds (10 and 20 m s−1), there is less time for upwind, evaporation-induced cold-pool formation before air parcels reach the ridge top and descend downwind. For the intermediate wind speed (10 m s−1), evaporation is effective in generating a cold pool only on the downstream side of the ridge, in a region where the air is unsaturated and slow moving. Further experiments with different ridge heights and half-widths were carried out in order to analyze their effect on the distribution and intensity of precipitation. Dimensional analysis reveals that the maximum (nondimensional) rainfall rate mainly depends on the ratio of mountain height to the level of free convection, the ridge aspect ratio, and a parameter that measures the ratio of advective to convective time scales.

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Mario Marcello Miglietta
and
Richard Rotunno

Abstract

In a recent study, the authors performed numerical simulations of conditionally unstable flows past a mesoscale mountain ridge in order to investigate the statistically stationary features of the solution precipitation characteristics for intermediate-to-high values of convective available potential energy (CAPE). That study proposed a functional dependence of the rain rate on three parameters, related respectively to the triggering and the orographic forcing of convection and to the ratio of the advective to convective time scales. The present study extends that analysis to cover larger regions of the parameter space, including experiments corresponding to a wider range of CAPE. It is found here that the low-CAPE, moderate-wind experiments do not fit the functional dependence for rain rate amount and location proposed in the authors’ previous study. The analysis of the present solutions suggests that two additional nondimensional parameters should be taken into account.

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George H. Bryan
and
Richard Rotunno

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.

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George H. Bryan
and
Richard Rotunno

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 (υg , 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 υg from the model output. Evidence is shown that υg 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.

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Mario Marcello Miglietta
and
Richard Rotunno
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George H. Bryan
and
Richard Rotunno

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.

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George H. Bryan
and
Richard Rotunno

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.

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Yu Du
,
Richard Rotunno
, and
Qinghong Zhang

Abstract

The low-level diurnal winds for different locations of eastern China are documented using the June 2006–11 hourly model data simulated with the Weather Research and Forecasting (WRF) mesoscale model with a 9-km horizontal resolution. A simple 1D model, including both diurnal thermal forcing and diurnally varying boundary layer friction, is found to explain important features of the WRF-simulated diurnal boundary layer winds in eastern China. For example, in northeastern China, at a similar latitude, the maximum velocity parallel to the coastline at a longitude over the ocean occurs earlier than the maximum velocity parallel to the inland chain of coastline-parallel mountains at a longitude over land. This difference can be identified with the well-known Blackadar effect over the land. Off the eastern coast of China, the diurnal winds for different latitudes over the ocean vary in both phase and amplitude, consistent with expectations based on the simple 1D model.

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