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Richard Rotunno

Abstract

A three-dimensional numerical simulation is presented for the asymmetric vortex motion which occurs in a Ward-type vortex chamber. The initial state is taken to be one of axisymmetric irrotational flow where the flow enters through the sides at the bottom and exits through the top of the chamber. As tangential velocity is added to the inflowing fluid, the structure of the flow in the meridional plane is modified from a ‘one-celled’ flow(updraft everywhere) to a ‘two-celled’ flow (updraft surrounding a central downdraft). Asymmetric vortices develop in the location of maximum vorticity of the ‘two-celled’ vortex which, it is shown, must be in the gradient between the updraft and the downdraft (but in updraft). Structural features of these asymmetric vortices, such as the tilt with height and propagation rate, are examined. Although the laboratory model upon which the present numerical calculations are based lacks the ability to simulate some important aspects of atmospheric flow, several significant features are shown to resemble the structure of observed tornadoes and mesocyclones.

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Richard Rotunno

Abstract

Given that the earth's atmosphere may be idealized as a rotating, stratified fluid characterized by the Coriolis parameter f and the Brunt–V¨is¨l¨ frequency N, and that the diurnal cycle of heating and cooling of the land relative to the sea acts as a stationary, oscillatory source of energy of frequency ω (=2π day−1), it follows from the linear theory of motion that where f > ω the atmospheric response is confined to within a distance Nh(f −2 – ω −2)−1/2 of the coastline, where h is the vertical scale of the heating. When f < ω, the atmospheric response is in the form of internal-inertial waves which extend to “Infinity” along ray paths extending upward and outward from the coast. Near the ground, the horizontal extent of the sea breeze is given by the horizontal wale of the dominant wave mode, Nh2f −2)−1/2.

Although these concepts are familiar from the linear theory of motion in a rotating, stratified fluid, their relevance with respect to the interpretation of linear models of the land and sea breeze has not been emphasized in the literature. Hence, a critical historical review of extant linear models of the land and sea breeze is presented, and from these varied linear models, a simple model. which allows the above-described conclusions to be reached, is decocted.

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Richard Rotunno

Abstract

An axisymmetric numerical model has been developed to simulate Ward's (1972) laboratory experiments. It was shown by Davies-Jones (1976) that this experiment is more geophysically relevant than all previous experiments in that Ward's experiment exhibits both dynamical and geometrical similarity to actual tornadoes.

Major results are 1) the core size versus inflow angle relationship agrees very nearly with Ward's measurements, 2) the numerical and laboratory surface pressure patterns are in agreement, and 3) it is demonstrated that the core radius is independent of the Reynolds number at high Reynolds number (Ward's data also exhibit this behavior).

Based on this axisymmetric model some speculation concerning the nature of the asymmetric multiple vortex phenomenon is made. Furthermore, the numerical model allows the examination of the interior flow field. As a consequence, an explanation is offered in Section 6 for the double-walled structure sometimes observed in natural vortices.

The experiments with no-slip boundary conditions reveal a very complicated flow structure in the vicinity of r = z = 0. The computed flow field is strongly reminiscent of that described by Benjamin (1962).

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Richard Rotunno

Abstract

Fine-resolution calculations using an axisymmetric numerical model of the flow within a Ward-type vortex chamber are discussed. Particular attention is paid to the vortex-ground interaction. Variations in the swirl ratio S from zero to unity lead to radically different vortex structure in the “corner” region (i.e., near r = z = 0). For S Lt; 1, a concentrated vortex forms in the upper chamber but not in the corner. At moderate S, we observe vortex breakdown, large-amplitude inertial waves, and very intense swirling motion in the corner. When S = 1, the central downdraft penetrates to the lower surface and the vortex breakdown occurs within the boundary layer. These results are consistent with experimental observations and suggest the explanation of a number of observed facets of tornadoes.

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Richard Rotunno

Abstract

In a previous paper a formula was derived for the maximum potential intensity of the tangential wind in a tropical cyclone called PI+. The formula, PI+2 = EPI2 + αrmwmηm , where EPI is the maximum potential intensity of the gradient wind and αrmwmηm represents the supergradient winds. The latter term is the product of the radius rm , the vertical velocity wm , the azimuthal vorticity ηm at the radius and height of the maximum tangential wind (rm , zm ), and the (nearly constant) α. Examination of a series of simulations of idealized tropical cyclones indicate an increasing contribution from the supergradient-wind term to PI+ as the radius of maximum wind increases. In the present paper, the physical content of the supergradient-wind term is developed showing how it is directly related to tropical cyclone boundary layer dynamics. It is found that r m w m η m u min 2 z m ( r m ) / l υ ( z m ) r m , where −u min is the maximum boundary layer radial inflow velocity and lυ (z) is the vertical mixing length.

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Richard Rotunno

Abstract

A vertical velocity field is chosen which imitates that of the initial stages of cloud development as simulated numerically by Wilhelmson and Klemp (1978). Given this, an approximate version of the equation for the vertical component of the vorticity is solved. The vertical velocity is assumed to vary with height as sin πz/H where a is the altitude and H is the depth of the domain. At the level of nondivergence (z=H/2), the solutions indicate the development of a vortex pair which then splits into two vortex pairs one moving to the right of the mean wind and the other to the left (as observed in the numerical model). At lower levels, owing to the convergence in the updraft and divergence in the downdraft, the cyclonic/anticyclonic member of the vortex pair in the rightward/leftward moving storm is greatly enhanced. The vorticity maximum is initially on the maximum gradient of vertical velocity. At mid-levels the maximum vorticity migrates with time close to the position of maximum vertical velocity. However, at lower levels, the maximum vorticity migrates with time past the position of maximum vertical velocity and thereafter resides on the vertical velocity gradient separating updraft from downdraft, as observed in a number of case studies. Some general comparisons of the present theory with an observational case study are made.

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Tetsuya Takemi
and
Richard Rotunno

Abstract

Using the newly developed Weather Research and Forecasting (WRF) model, this study investigates the effects of subgrid mixing and numerical filtering in mesoscale cloud simulations by examining the sensitivities to the parameters in turbulence-closure schemes as well as the parameters in the numerical filters. Three-dimensional simulations of squall lines in both no-shear and strong-shear environments have been performed. Using the Smagorinsky or 1.5-order turbulent kinetic energy (TKE) subgrid model with standard values for the model constants and no explicit numerical filter, the solution in the no-shear environment is characterized by many poorly resolved grid-scale cells. In the past, such grid-scale noise was avoided by adding a numerical filter which, however, produces excessive damping of the physical small-scale eddies. Without using such a filter, it was found that by increasing the proportionality constant in the eddy viscosity coefficient in the subgrid turbulence models, the cells become well resolved, but that further increases in the constant overly smooth the cells. Such solution sensitivity is also found in the strong-shear cases. The simulations using the subgrid models with viscosity coefficients 1.5 to 2 times larger than those widely used in other cloud models retain more power in short scales, but without an unwanted buildup of energy; with these optimum values, no numerical filters are required to avoid computational noise. These optimum constants do not depend significantly on grid spacings of O(1 km). Therefore, it is concluded that by using the eddy viscosity formulation appropriate for mesoscale cloud simulations, the use of artificial numerical filters is avoided, and the mixing processes are represented by more physically based turbulence-closure models.

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Yu Du
and
Richard Rotunno

Abstract

A simple analytical model including both diurnal thermal forcing over sloping terrain (the “Holton” mechanism) and diurnally varying boundary layer friction (the “Blackadar” mechanism) is developed to account for the observed amplitude and phase of the low-level jet (LLJ) over the Great Plains and to understand better the role of each mechanism. The present model indicates that, for the pure Holton mechanism (time-independent friction coefficient), the maximum southerly wind speed occurs (depending on the assumed friction coefficient) between sunset and midnight local standard time, which is earlier than the observed after-midnight maximum. For the pure Blackadar mechanism (time-independent thermal forcing), the present model shows that generally occurs later (closer to sunrise) than observed and has a strong latitudinal dependence. For both mechanisms combined, the present model indicates that occurs near to the observed time, which lies between the time obtained in the pure Holton mechanism and the time obtained in the pure Blackadar mechanism; furthermore, is larger (and closer to that observed) than in each one considered individually. The amplitude and phase of the LLJ as a function of latitude can be obtained by the combined model by allowing for the observed latitude-dependent mean and diurnally varying thermal forcing.

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Juerg Schmidli
and
Richard Rotunno

Abstract

In a recent study, the authors investigated the mechanisms leading to the formation of diurnal along-valley winds in a valley formed by two isolated mountain ridges on a horizontal plain. The main focus was on the relation between the valley heat budget and the valley–plain pressure difference. The present work investigates the influence of the valley surroundings on the evolution of the valley winds. Three valley–plain configurations with identical valley volumes are studied: a periodic valley, an isolated valley on a plain (the former case), and an isolated valley entrenched in an elevated plateau. According to the valley volume argument (topographic amplification factor), these three cases should develop identical temperature perturbations and thus similar along-valley winds. However, substantial differences are found between the three cases, in particular a much stronger daytime up-valley wind and nighttime down-valley wind for the plateau configuration. The analysis demonstrates the importance of the exchange of along-valley momentum between the valley atmosphere and its surroundings and of the upper-level pressure gradient in explaining the differences among the cases. Furthermore, differences in the upper-level pressure gradient are shown to be related to the heat exchange of the air above the valley atmosphere with the surroundings, which is related to larger-scale cross-valley circulations.

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Yu Du
and
Richard Rotunno

Abstract

The characteristics of thermally driven diurnally periodic wind signals off the east coast of China are studied using hourly model data for the period June 2006–11 simulated with a mesoscale model. Analysis of these model data indicates low-level diurnally periodic wind signals propagate eastward off the southeast coast, whereas diurnal wind variations off the northeast coast are nearly in phase. It is found that a simple 2D linear land–sea-breeze model with friction can capture this main difference in propagation character with respect to latitude. Idealized simulations using a simplified version of the mesoscale model that includes surface heating and terrain are found to explain certain features not captured by the present linear theory such as the absolute time phase and cross-coast location of the maximum amplitude of the diurnally periodic winds.

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