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Richard Rotunno
,
Glen S. Romine
, and
Howard B. Bluestein

Abstract

A recent study found that surface hodographs over the Great Plains of the United States turn in a counterclockwise direction with time. This observed turning is opposite of the clockwise turning observed (and expected, based on theory) at higher altitudes. Using a mesoscale forecast model, the same study shows that it has the same hodograph behavior as found in the observations. The study further shows that the reason for this anomalous counterclockwise turning is the decoupling of the surface layer from the boundary layer after sunset and its recoupling after sunrise. The present paper presents a simple model for this behavior by extending a recent analytical model for the diurnal oscillation to include the surface-layer effect. In addition, selected solution features are analyzed in terms of several of the nondimensional input parameters.

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Richard Rotunno
,
Joseph B. Klemp
, and
Morris L. Weisman

Abstract

We study herein the mechanics of long-lived, line-oriented, precipitating cumulus convection (squall lines) using two- and three-dimensional numerical models of moist convection. These models, used in juxtaposition, enable us to address the important theoretical issue of whether a squall line is a system of special, long-lived cells, or whether it is a long-lived system of ordinary, short-lived cells. Our review of the observational literature indicates that the latter is the most consistent paradigm for the vast majority of cases but, on occasion, a squall line may be composed of essentially steady, supercell thunderstorms. The numerical experiments presented herein show that either type of squall line may develop from an initial line-like disturbance depending on the magnitude and orientation of the environmental shear with respect to the line. With shallow shear, oriented perpendicular to the line, a long-lived line evolves containing individually short-lived cells. Our analysis of this type of simulated squall line suggests that the interaction of a storm cell's cold surface. outflow with the low-level shear produces much-deeper and less-inhibited lifting than is possible without the low-level shear, making it easier for new cells to form and grow as old cells decay. Through interecomparsion of two- and three-dimensional squall-line simulations, we conclude that the essential physics of this type of squall line is contained in the two- dimensional framework. We argue that these results describe the physics of both midlatitude and tropical squall lines. Under conditions of deep strong shear at an angle to the supposed line, a line of supercells develops in which their respective three-dimensional circulations do not interfere with one another.

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Morris L. Weisman
,
Joseph B. Klemp
, and
Richard Rotunno

Abstract

Using a three-dimensional numerical cloud model, we investigate the effects of vertical wind shear on squall-line structure and evolution over a wide range of shear magnitudes, depths, and orientations relative to the line. We find that the simulated squall lines are most sensitive to the magnitude of the component of shear perpendicular to the line, and that we may reproduce much of the range of observed structures by varying this single parameter. For weak shear, a line of initially upright-to-downshear-tilted short-lived cells quickly tilts upshear, producing a wide band of weaker cells extending behind the surface outflow boundary. For moderate-to-strong shear, the circulation remains upright-to-downshear tilted for longer periods of time, with vigorous, short-lived cells confined to a relatively narrow band along the system's leading edge. At later times, however, these systems may also weaken as the circulation tilts upshear. For strong, deep shears oriented obliquely to the line, the squall line may be composed of quasi-steady, three-dimensional supercells. The squall-line lifecyle that occurs in most of the simulations is dependent on both the strength of the developing cold pool, which induces an upshear-tilted circulation, and the strength of the ambient low-level shear ahead of the line, which promotes a circulation tilting the system downshear. When these two factors are in balance, the overall system circulation remains upright, and we obtain the optimal conditions for deep lifting that promotes the regeneration of strong cells along the outflow boundary. In the current experiments, this optimal state occurs with 15–25 m s−1 of velocity change over the lowest 2.5 km AGL.

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Richard Rotunno
,
Joseph B. Klemp
, and
Morris L. Weisman

Abstract

Abstract not available.

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William C. Skamarock
,
Joseph B. Klemp
, and
Richard Rotunno

Abstract

Bends in coastal mountain ranges may diffract propagating atmospheric Kelvin waves and trapped coastal currents. Analytic solutions exist for the diffraction of both linear Kelvin waves and linear nonrotating gravity waves. Within the context of the single-layer shallow-water equations, we examine the diffraction of nonlinear gravity waves and bores in a nonrotating reference frame and nonlinear Kelvin waves and coastally trapped bores in a rotating reference frame. The diffraction process can significantly decrease the amplitude of linear and nonlinear waves and bores in the nonrotating reference frame. Unlike for their linear counterpart, however, the diffraction-related amplitude decay for the nonrotating nonlinear waves takes place entirely within the region of the bend and does not produce a continuous decay after the bend. Moreover, theory predicts a critical bend angle at which bore amplitudes will be zero at the wall after propagation around the bend, but shallow-water model simulations do not confirm the existence of the critical angle. For Kelvin waves and trapped bores in the rotating reference frame, we find robust wave and bore propagation around coastal bends in all cases. No critical angles exist for the waves and bores in the rotating reference frame.

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Scott A. Braun
,
Richard Rotunno
, and
Joseph B. Klemp

Abstract

In this study, the interaction of cold fronts with idealized coastal terrain typical of the western United States and Canada is considered. Two issues are examined. First, what are the factors that determine the strength of the coastal winds, and second, what are the orographic effects on the frontal evolution? To address these issues, the authors utilize a two-dimensional, Boussinesq terrain-following coordinate numerical model in which a uniform prescribed flow is forced to move over a plateau. The resultant across-mountain velocities are characterized by a zone of strongly decelerated flow upstream of the windward slope and a train of inertia-gravity waves downstream. A barrier-jet oriented parallel to the mountain is produced by the Coriolis force. The variations of the magnitude of the upstream deceleration and the barrier jet over a wide range of Froude numbers and Rossby numbers are described. Steady, linear theory applied to flow over a plateau shows that the upstream deceleration is determined largely by the shortwave characteristics of the orography while the barrier-jet strength is related to the longwave characteristics of the orography.

Simulations that include an initially steady, geostrophically balanced front upstream of the coast indicate that the motion of fronts can be significantly retarded along the coast. Across-frontal circulations induced by frontogenesis or frontolysis caused by the mountain are small compared to the changes in the mountain circulation caused by the stability perturbations associated with the front. The strength of the along-mountain winds in the coastal zone during frontal passage are approximately determined by a superposition of the southerly barrier jet and the frontal jets (e.g., a southerly prefrontal jet and/or northerly postfrontal jet). This result implies that a barrier jet forming ahead of a front can combine with a prefrontal jet to produce very strong winds in the coastal zone prior to frontal passage.

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William C. Skamarock
,
Richard Rotunno
, and
Joseph B. Klemp

Abstract

During the spring and summer, the climatological northerly flow along the U.S. west coast is occasionally interrupted by transitions to southerly flow that have a limited offshore scale and appear to be manifestations of marine-layer flow that is rotationally trapped by the coastal mountains. Existing climatological and observational studies suggest that a synoptic-scale offshore flow initiates these coastally trapped disturbances (CTDs). Using idealized simulations produced with a 3D nonhydrostatic model, the authors find that an imposed offshore flow will produce CTDs in idealized coastal environments. The imposed flow first weakens the prevailing northerly flow in the marine layer and lowers the pressure at the coast. The marine-layer flow around this low pressure evolves toward geostrophic balance, but is retarded as it encounters the coastal mountains to the south of the low and subsequently deepens the marine layer in this region. The elevated marine layer then begins progressing northward as a Kelvin wave and later may steepen into a bore or gravity current, this progression being the CTD. Many observed features accompanying CTDs are found in the numerical simulations, including the formation of a mesoscale pressure trough offshore and deep southerlies in the CTD at the coast. Stability in the atmosphere above the marine layer can give rise to topographically trapped Rossby waves and stronger CTD winds. In these stable conditions, propagation of wave energy away from the disturbance does not preclude strong, quasi-steady, propagating CTDs.

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Scott A. Braun
,
Richard Rotunno
, and
Joseph B. Klemp

Abstract

The role of surface friction in modifying cold fronts as they make landfall in regions of steep coastal orography is examined by means of idealized simulations. Both the effects of the surface-roughness change at the coast in the absence of orography and the effects of orography are considered. Flow over a large and abrupt change in surface roughness generates an inertia–gravity wave above the boundary layer with characteristics similar to that associated with flow over a plateau. Deceleration of the cross-coast flow occurs over land, as well as for a short distance upstream, and causes retardation of frontal motion. A prescribed northerly postfrontal jet weakens rapidly after landfall. Maximum vertical motions are several centimeters per second; however, only small rainfall enhancement is expected since the updraft is very narrow and produces only small vertical displacements.

Friction modifies the flow over the orography by increasing the upstream flow deceleration and reducing the magnitude of the barrier jet. The reduction of the barrier-jet strength (when compared to inviscid simulations) by surface friction becomes more pronounced as the mountain forcing of the jet increases. With surface friction, frontal-motion retardation by the orography is strong and upstream frontogenesis is enhanced. The frontal updraft is strongest at the coast and remains strong for a short distance inland along the lower portion of the windward slope. The coastal enhancement of the frontal updraft results from the combined effects of the orography and the surface-roughness change, but large parcel displacements are due mainly to the orographic forcing. Along-coast winds in the coastal zone during frontal passage are approximately determined by a superposition of the southerly barrier jet and the frontal jets.

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Robert G. Nystrom
,
Richard Rotunno
,
Chris A. Davis
, and
Fuqing Zhang

Abstract

Several previous studies have demonstrated the significant sensitivity of simulated tropical cyclone structure and intensity to variations in surface-exchange coefficients for enthalpy (C k ) and momentum (C d ), respectively. In this study we investigate the consistency of the estimated peak intensity, intensification rate, and steady-state structure between an analytical model and idealized axisymmetric numerical simulations for both constant C k and C d values and various wind speed–dependent representations of C k and C d . The present analysis with constant C k and C d values demonstrates that the maximum wind speed is similar for identical C k /C d values less than 1, regardless of whether changes were made to C k or C d . However, for a given C k /C d greater than 1, the simulated and theoretical maximum wind speed are both greater if C d is decreased compared to C k increased. This behavior results because of a smaller enthalpy disequilibrium at the radius of maximum winds for larger C k . Additionally, the intensification rate is shown to increase with C k and C d and the steady-state normalized wind speed beyond the radius of maximum winds is shown to increase with increasing C d . Experiments with wind speed–dependent C k and C d were found to be generally consistent, in terms of the intensification rate and the simulated and analytical-model-estimated maximum wind speed, with the experiments with constant C k and C d .

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Ke Peng
,
Richard Rotunno
,
George H. Bryan
, and
Juan Fang

Abstract

In a previous study, the authors showed that the intensification process of a numerically simulated axisymmetric tropical cyclone (TC) can be divided into two periods denoted by “phase I” and “phase II.” The intensification process in phase II can be qualitatively described by Emanuel’s intensification theory in which the angular momentum (M) and saturated entropy (s*) surfaces are congruent in the TC interior. During phase I, however, the M and s* surfaces evolve from nearly orthogonal to almost congruent, and thus, the intensifying simulated TC has a different physical character as compared to that found in phase II. The present work uses a numerical simulation to investigate the evolution of an axisymmetric TC during phase I. The present results show that sporadic, deep convective annular rings play an important role in the simulated axisymmetric TC evolution in phase I. The convergence in low-level radial (Ekman) inflow in the boundary layer of the TC vortex, together with the increase of near-surface s* produced by sea surface fluxes, leads to episodes of convective rings around the TC center. These convective rings transport larger values of s* and M from the lower troposphere upward to the tropopause; the locally large values of M associated with the convective rings cause a radially outward bias in the upper-level radial velocity and an inward bias in the low-level radial velocity. Through a repetition of this process, the pattern (i.e., phase II) gradually emerges. The role of internal gravity waves related to the episodes of convection and the TC intensification process during phase I is also discussed.

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