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Zhe-Min Tan
,
Fuqing Zhang
,
Richard Rotunno
, and
Chris Snyder
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Wendell T. Welch
,
Piotr Smolarkiewicz
,
Richard Rotunno
, and
Byron A. Boville

Abstract

Airflow over two-dimensional sinusoidal mesoscale topography is studied using simulations from a numerical model, with an eye toward quantification of the net effect on the large-scale flow. Analytic formulas are derived for the amount of form drag, that is, the total slowdown of the flow, as a function of mountain height, and predictions from such formulas are shown to agree well with model results. The vertical distribution of drag, due to gravity wave breaking at various altitudes, is briefly discussed.

The flow is divided into two regimes: a “linear” regime for small mountain heights, and a “blocked” regime for taller mountains. The latter is always accompanied by a layer of stagnant fluid in the valleys. Separate analytic arguments are used in each regime, and together they provide a prediction of form drag over a wide range of parameter space. The cutoff mountain height between the two regimes is also argued analytically.

A key difference from flow over isolated mountains is explained. This suggests that studies of flow over both isolated and periodic topography are needed in the development of orographic parameterizations for large-scale models.

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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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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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Teddie L. Keller
,
Richard Rotunno
,
Matthias Steiner
, and
Robert D. Sharman

Abstract

Previous studies have observed upstream-propagating modes in two-dimensional numerical simulations of idealized flow over topography with moist, nearly neutral conditions in the troposphere, topped by a stable stratosphere. The generation and propagation mechanisms for these modes were attributed to localized and dramatic changes in stability induced by the desaturation of the flow impinging on the mountain. In the present paper it is shown that these modes are transient upstream-propagating gravity waves, which are a fundamental feature of both moist and dry flow over topography of a two-layer troposphere–stratosphere atmospheric profile impulsively started from rest. The mode selection and propagation speeds of these transient waves are highly dependent on the tropospheric stability, as well as the wind speed and tropopause depth. In the moist case these modes appear to propagate according to an effective static stability that is intermediate to the normal dry stability and the lower moist stability. Comparisons with the linear, time-dependent, hydrostatic analytic solution show that these modes are similar to the transients observed in flow of a constant wind and stability layer over topography with a rigid upper boundary.

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Zhe-Min Tan
,
Fuqing Zhang
,
Richard Rotunno
, and
Chris Snyder

Abstract

Recent papers by the authors demonstrated the possible influence of initial errors of small amplitude and scale on the numerical prediction of the “surprise” snowstorm of 24–25 January 2000. They found that initial errors grew rapidly at scales below 200 km, and that the rapid error growth was dependent on moist processes. In an attempt to generalize these results from a single case study, the present paper studies the error growth in an idealized baroclinic wave amplifying in a conditionally unstable atmosphere. The present results show that without the effects of moisture, there is little error growth in the short-term (0–36 h) forecast error (starting from random noise), even though the basic jet used here produces a rapidly growing synoptic-scale disturbance. With the effect of moisture included, the error is characterized by upscale growth, basically as found by the authors in their study of the numerical prediction of the surprise snowstorm.

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Richard Rotunno
,
Paul M. Markowski
, and
George H. Bryan

Abstract

Numerical models of supercell thunderstorms produce near-ground rotation about a vertical axis (i.e., vertical vorticity) after the development of rain-cooled outflows and downdrafts. The physical processes involved in the production of near-ground vertical vorticity in simulated supercells have been a subject of discussion in the literature for over 30 years. One cause for this lengthy discussion is the difficulty in applying the principles of inviscid vorticity dynamics in a continuous fluid to the viscous evolution of discrete Eulerian simulations. The present paper reports on a Lagrangian analysis of near-ground vorticity from an idealized-supercell simulation with enhanced vertical resolution near the lower surface. The parcel that enters the low-level maximum of vertical vorticity has a history of descent during which its horizontal vorticity is considerably enhanced. In its final approach to this region, the parcel’s enhanced horizontal vorticity is tilted to produce vertical vorticity, which is then amplified through vertical stretching as the parcel rises. A simplified theoretical model is developed that exhibits these same features. The principal conclusion is that vertical vorticity at the parcel’s nadir (its lowest point), although helpful, does not need to be positive for rapid near-surface amplification of vertical vorticity.

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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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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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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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