Rankine Combined Vortex Research Articles

A vortex-type solar updraft power-desalination integrated system

In this paper, the convection vortex theory is combined with the existing solar chimney power plant combined with desalination (SCPPCSD), and a solar vortex power desalination system (SVPDS) is proposed. In SVPDS, the strong cyclone column generated by the convection vortex is used to replace the solid chimney. The physical model and three-dimensional numerical model of SVPDS are built. The flow field distributions in the solar vortex power plant (SVPP) and SVPDS under no-load condition are compared and analyzed, and the distribution rules of each parameter along the radial and axial direction and output performance are obtained. The results show that the simulation field has strong rotation characteristics, and there is obviously a low pressure area in the center of SVPDS, which enables the system to continuously draw in surrounding air, thus forming a stable vortex flow field. The maximum negative pressure of vortex center in SVPDS is −126.98 Pa, and the hourly freshwater output is about 7.92136 ton/h. Due to the sucking effect of vortex, the radial distributions of temperature and negative pressure at different heights both decrease from the center to the surrounding. With the increase of height, the temperature of central airflow, the pressure difference between the vortex center and the external environment are both decreasing, and finally close to the external environment. The vortex core structure can be obviously seen in the center, and the tangential velocity distribution is more consistent with the distribution of the Rankine combined vortex. The tangential velocity slowly decreases with the increase of height and then transforms into axial velocity. The temperature, vortex center negative pressure and tangential velocity in SVPDS are all slightly smaller than those of SVPP. With the increase of solar irradiance, the freshwater output and the vortex center maximum negative pressure both increase significantly.

A Vortex-Based Doppler Velocity Dealiasing Algorithm for Tropical Cyclones

AbstractIn this study, a vortex-based Doppler velocity dealiasing (VDVD) algorithm for tropical cyclones (TCs) is proposed. The algorithm uses a Rankine combined vortex model as a reference field for dealiasing based on an inner–outer iterative procedure. The structure of the reference vortex is adjusted in an inner iterative procedure of VDVD that applies the ground-based velocity track display (GBVTD) technique. The outer loop of the VDVD based on the GBVTD-simplex algorithm is used for center correction. The VDVD is able to recover not only the aliased Doppler velocities from a simulated symmetric vortex but also those superimposed with wavenumber-1 asymmetry, radial wind, or mean flow. For real cases, the VDVD provides dealiased Doppler velocity with 99.4% accuracy for all pixels, based on 472 elevation sweeps from a typhoon without landfall. It is suggested that the VDVD algorithm can improve the quality of downstream applications such as Doppler wind retrievals and radar data assimilations of TCs and other storms, such as tornadoes and mesocyclones, with vortex signatures.

Exact solutions for unsteady axisymmetric vortex motions governing atmospheric vortices

In this paper, attempts have been made to provide non-steady generalisation to some of the existing solutions for azimuthal velocity of vortex motion representing different rotational motions occurring in the nature. The existing solutions, viz., Rankine combined vortex and Burgers-Rott vortex steady models are extended to include non-steady effects. The derived expressions reduce to those available in the existing literature.It is concluded from the unsteady model extended from the Rankine combined model that when time tends to infinity, the core radius vanishes for inviscid flows. However, the unsteady viscous flow model, extended from the Burgers-Rott model, reveals that, when time tends to infinity, the core radius becomes infinitely large for zero axial pressure gradient but stabilises if the axial pressure gradient is non-zero. Thus, it is concluded that a vortex survives with time only when the flow is viscous and the axial pressure gradient is non-zero.

A two-dimensional IB-LBM framework combined with re-tailored RCVM for assessing the rotation intensity of a tornadic wind over a building configuration

A tornado is fundamentally a devastating airflow featuring simultaneous translation and rotation. This hybrid nature makes the simulations more interesting as well as challenging. Numerous laboratorial and computational simulations of tornadoes have been performed in the past few decades to study the tornado dynamics. This study concentrates on the tornado-structure interaction through numerical simulation. Establishing a set of physically-rational and meanwhile computationally-maneuverable boundary conditions for the tornado-building interaction scenario poses a challenge to numerical simulation developers. Inspired by the recent progress in the application of immersed-boundary (IB) lattice Boltzmann method (LBM) to the fluid-structure interaction simulations, this study presents an IB-LBM framework and, meanwhile, revises the renowned Rankine-Combined Vortex Model (RCVM) with the aid of the “relative motion” principle, such that the challenging boundary condition setup issue can be successfully resolved. The present IB-LBM simulations are aimed to investigate the tornado-like wind effects on a building configuration in different orientations and, particularly, seek the relation between the rotation intensity of a tornado and the tornadic wind loadings on the constructions. Through examinations at a series of rotation intensities, the extreme loading value is observed to be unrelated to Reynolds number once the rotation intensity exceeds a critical value. These simulation results reveal that it looks inappropriate to rely solely on the translational velocity component to characterize tornadoes, and call on additional attention towards the rotation intensity for a more comprehensive tornado dynamics study.

An IB-LBM investigation into the aerodynamic coefficients in relation to the rotation intensity of a tornado-like wind

A tornadic wind is essentially considered as an airflow that simultaneously translates and rotates. Numerical simulations of this kind of hybrid flow remain inadequate due to many numerical difficulties, one of the major challenges consisting in the establishment of a set of boundary conditions that are, for the tornado–obstacle interaction scenario, both rational in physics and simple in numerical implementation. Inspired by the success of immersed-boundary (IB) lattice Boltzmann method (LBM) for simulations of fluid–structure interaction problems, this study proposes a new outlet of the IB-LBM framework for investigation of tornadic wind effects, featuring a reformed interpretation of the Rankine-Combined Vortex Model (RCVM) that considerably facilitates the boundary condition setup. Moreover, the main purpose of this study is to examine the tornadic wind loadings in relation to the rotation intensity of a tornado, and presents a practical Newton’s bi-section-like method for determining the critical rotation intensity beyond which the aerodynamic coefficients no longer increase when Reynolds number rises. This critical rotation intensity serves to characterize tornadic winds, such that the tornado with a rotation density below its critical value can be considered as mainly dominated by the translation part and, otherwise, the dominance no longer belongs only to the translational component of the tornado. Since it has been rather conventional that, when studying tornadoes, Reynolds number is determined using only the translation velocity as characteristic velocity, the present tornado study intends to suggest, through a number of numerical test series, that more attention be paid to the insufficiently explored rotational component, which physically tends to play a more dominant role when an intensive rotation is present in a tornado scenario.

Rainband feature tracking for wind speeds around typhoon eyes using multiple sensors

In this article, five typhoon cases observed by quasi-concurrent satellite-based synthetic aperture radar (SAR) and Moderate Resolution Imaging Spectroradiometer (MODIS) were studied with a feature-tracking technique. The rainband features around typhoon eyes were first delineated using wavelet analysis, and then the wind speeds were estimated by feature tracking using quasi-concurrent multi-sensor images. It was found that the feature tracking-estimated wind speeds are reasonable compared with the maximum wind speed reported by the Joint Typhoon Warning Center (JTWC), which accounts for the radial dependence of wind speed using the Rankine combined vortex approximation. In a specific case, with the aid of Doppler radar observations near the northern coast of Taiwan, wind speed estimation based on the multi-sensor also shows consistent results. This study demonstrates that the local wind distribution of cyclonic winds around typhoon eyes at different radial distances from the typhoon centres may be derived from rainband feature tracking using quasi-concurrent multi-sensor images. This technique may offer useful wind information for typhoon simulations and forecasting.

Study on Prediction of Underwater Radiated Noise from Propeller Tip Vortex Cavitation

The method to predict underwater radiated noise from tip vortex cavitation was studied. The growth of a single cavitation bubble in tip vortex was estimated by substituting the tip vortex to Rankine combined vortex. The ideal spectrum function for the sound pressure generated by a single cavitation bubble was used, also the empirical factor for the number of collapsed bubbles per unit time was introduced. The estimated noise data were compared with measured ship's ones and it was found out that this method can estimate noise data within 3dB difference.

Rankine combined vortex interaction with a rectangular prism

Large eddy simulation is utilised to study the three-dimensional interaction between a travelling Rankine combined vortex and a rectangular prism. The study examines the strength and the topology of a vortex during the interaction with a prism that is much wider than the vortex core diameter. The physics of the interaction is revealed for the straight (β = 0°) and the oblique (β = 45°) impacts. For both cases, the low-level portion of the vortex undergoes displacements in the streamwise and the lateral directions. Also the vortex shape and the core vorticity are substantially disrupted. Behind the prism the full vortex circulation is recovered after a considerable distance. This created a low-velocity region. The sheltering effect of the prism is noticed for both straight and oblique impacts. The flow velocities in the sheltering region, right behind the prism, are reduced by more than 42% compared to the maximum flow speeds before the interaction.

Visualization of tornado-like vortex interacting with wide tornado-break wall

A three-dimensional CFD model, based on large eddy simulation, is utilized to numerically simulate a perpendicular interaction between a traveling tornado-like vortex and a wide rigid wall. The tornado-like flow is modeled by the Rankine-Combined Vortex Model. The case, where the wall width is much larger than the tornado vortex core diameter is examined. The main goal of the paper is to improve the understanding of the dynamics of the tornado–wall interaction. The conclusions drawn in this study are supported by various visualizations. During the tornado impact, the structure of the tornado-like vortex is substantially mitigated by the wide wall. The low-level portion of the vortex is disturbed both in front of the wall and behind the wall. When the vortex is approaching the wall, the vortex-induced velocities cause a boundary layer separation from the leading face of the wall. The ejected, from the wall, vorticity patches wrap around the tornado-like vortex causing its weakening. Behind the wall the tornado vortex is subjected to the turbulent flow that further disrupts the tornado vortex structure. The tornado-like vortex mitigation results in a low wind speed region behind the tornado-break wall, where the wind velocities are reduced by more than 50 %.

Thermoconvective vortices in a cylindrical annulus with varying inner radius.

This paper shows the influence of the inner radius on the stability and intensity of vertical vortices, qualitatively similar to dust devils and cyclones, generated in a cylindrical annulus non-homogeneously heated from below. Little relation is found between the intensity of the vortex and the magnitude of the inner radius. Strong stable vortices can be found for both small and large values of the inner radius. The Rankine combined vortex structure, that characterizes the tangential velocity in dust devils, is clearly observed when small values of the inner radius and large values of the ratio between the horizontal and vertical temperature differences are considered. A contraction on the radius of maximum azimuthal velocity is observed when the vortex is intensified by thermal mechanisms. This radius becomes then nearly stationary when frictional force balances the radial inflow generated by the pressure drop in the center, despite the vortex keeps intensifying. These results connect with the behavior of the radius of the maximum tangential wind associated with a hurricane.

The Improvement to the Environmental Wind and Tropical Cyclone Circulation Retrievals with the Modified GBVTD (MGBVTD) Technique

AbstractThe ground-based velocity track display (GBVTD) was developed to deduce a three-dimensional primary circulation of landfalling tropical cyclones from single-Doppler radar data. However, the cross-beam component of the mean wind cannot be resolved and is consequently aliased into the retrieved axisymmetric tangential wind . Recently, the development of the hurricane volume velocity processing method (HVVP) enabled the independent estimation of ; however, HVVP is potentially limited by the unknown accuracy of empirical assumptions used to deduce the modified Rankine-combined vortex exponent . By combing the GBVTD with HVVP techniques, this study proposes a modified GBVTD method (MGBVTD) to objectively deduce from the GBVTD technique and provide a more accurate estimation of and via an iterative procedure to reach converged and cross-beam component of solutions. MGBVTD retains the strength of both algorithms but avoids their weaknesses. The results from idealized experiments demonstrate that the MGBVTD-retrieved cross-beam component of is within 2 m s−1 of reality. MGBVTD was applied to Hurricane Bret (1999) whose inner core was captured simultaneously by two Weather Surveillance Radar-1988 Doppler (WSR-88D) instruments. The MGBVTD-retrieved cross-beam component of from single-Doppler radar data is very close to that from dual-Doppler radar synthesis using extended GBVTD (EGBVTD); their difference is less than 2 m s−1. The mean difference in the MGBVTD-retrieved from the two radars is ~2 m s−1, which is significantly smaller than that resolved in GBVTD retrievals (~5 m s−1).

Infrasonic ray tracing applied to mesoscale atmospheric structures: Refraction by hurricanes

A ray-tracing program is used to estimate the refraction of infrasound by the temperature structure of the atmosphere and by hurricanes represented by a Rankine-combined vortex wind plus a temperature perturbation. Refraction by the hurricane winds is significant, giving rise to regions of focusing, defocusing, and virtual sources. The refraction of infrasound by the temperature anomaly associated with a hurricane is small, probably no larger than that from uncertainties in the wind field. The results are pertinent to interpreting ocean wave generated infrasound in the vicinities of tropical cyclones.

Physical simulation of a single-celled tornado-like vortex, Part A: Flow field characterization

Tornado vortex simulation is described and a new simulator is presented. Radial, tangential, and vertical velocity measurements together with surface static pressure measurements are presented and compared with available data from the Manchester and Spencer, South Dakota tornadoes of May 30, 1998, and June 24, 2003, respectively. Comparisons of the surface pressure profile and tangential velocity decay showed good agreement with the TTU simulation. Analytically, the simulated velocity decay is found to be similar to that of a modified Rankine combined vortex with a variable exponent that changed with height. The simulator is demonstrated as a viable device for determining wind loading on building models in tornado-like vortex flows, and such results are presented in Part B.

A numerical study of ice-drift divergence by cyclonic wind with a Lagrangian ice model

In polar regions low-pressure systems drive sea ice divergence, which can accelerate summer sea ice melt through energy absorption at resulting open water areas. This paper examines the mechanisms that cause the ice divergence and its seasonal change with a Lagrangian ice model. We focus on the effects of initial ice concentration, ice strength and ocean stratification. A series of idealized simulations (initially at 5 km resolution) are carried out with a Rankine combined vortex as external wind forcing. We have found a characteristic length scale r *1 in free drift, based on the influence of the Coriolis term. The results show that ice concentration decreases most greatly within the range of r *1. In addition, ice divergence becomes small in the inner region for high concentrations (i.e. over 0.95), due to inward internal force blocking divergent deformations. The effects of ocean stratification on ice-drift divergence are also examined. Numerical results show that as the density stratification increases divergent Ekman flows beneath ice further promote the ice-drift divergence and lead to more reduction in the ice concentration through thinning of surface Ekman layer.

A numerical study of ice-drift divergence by cyclonic wind with a Lagrangian ice model

In polar regions low-pressure systems drive sea ice divergence, which can accelerate summer sea ice melt through energy absorption at resulting open water areas. This paper examines the mechanisms that cause the ice divergence and its seasonal change with a Lagrangian ice model. We focus on the effects of initial ice concentration, ice strength and ocean stratification. A series of idealized simulations (initially at 5 km resolution) are carried out with a Rankine combined vortex as external wind forcing. We have found a characteristic length scale r*1 in free drift, based on the influence of the Coriolis term. The results show that ice concentration decreases most greatly within the range of r*1. In addition, ice divergence becomes small in the inner region for high concentrations (i.e. over 0.95), due to inward internal force blocking divergent deformations. The effects of ocean stratification on ice-drift divergence are also examined. Numerical results show that as the density stratification increases divergent Ekman flows beneath ice further promote the ice-drift divergence and lead to more reduction in the ice concentration through thinning of surface Ekman layer.

DEVELOPMENT OF A METHOD OF PREDICTETING TYPHOON-RELATED RAINFALL WITH RADAR AND GPV INFORMATION INTRODUCING OROGRAPHIC RAINFALL

This paper shows modification of the short-term rainfall prediction method based on the translation model so that it could become suitable for predicting typhoon-related rainfall. Firstly, we defined a new field of translation vector that can express movement of both typhoon-related spiral rainbands and other general rain area. Here, the rotation of the spiral rainbands around the eye is expressed by Rankine's combined vortex. Second, orographic rainfall, which is dominated in case of typhoon, is introduced based on the Tatehira's model. As a result, when the target domain is the whole Japanese archipelago and both typhoon related and front related rain areas are coexist, three-hours ahead prediction of location of both rain areas was much improved. Also when typhoon passed over the Kinki district, orgraphic rainfall over Kii mountains, Yohro and Hira mountain chains were well predicted.

Simulated Doppler Velocity Signatures of Evolving Tornado-Like Vortices

Abstract Exact solutions of the Navier–Stokes or Euler equations of motion and the continuity equation in cylindrical coordinates for 3D, axisymmetric, inviscid, or laminar flows are utilized to represent evolving vortices that roughly model tornado cyclones or misocyclones contracting to tornadoes. These solutions are unsteady versions of the diffusive Burgers–Rott vortex and the inviscid Rankine-combined vortex. They satisfy the free-slip condition at the ground. Different vortices are obtained by choosing different values of the constant eddy viscosity and uniform horizontal convergence while holding the circulation at infinity constant. A simulated Weather Surveillance Radar-1988 Doppler (WSR-88D) is employed to generate time-varying Doppler velocity signatures in uniform reflectivity of these analytical vortices at ranges of 25 and 50 km from the radar. Mean Doppler velocities are determined by computing 3D integrals over effective resolution volumes. Magnitudes of Doppler vortex signatures at different times in the evolution of the stationary vortices are computed for effective beamwidths of 1.02° and 1.39°, which correspond to azimuthal sampling intervals of 0.5° and 1.0°, respectively. Four tornado predictors—rotational velocity, shear, excess rotational kinetic energy, and circulation—are examined. Results of the simulations show that for smaller effective beamwidths, Doppler vortex signatures are stronger and exceed fixed threshold values of rotational velocity and shear earlier. With finer azimuthal resolution, tornado cyclone, misocyclone, or tornado signatures switch to tornadic vortex signatures later. Circulations of the vortex signatures give good estimates of the circulations of the simulated tornadoes and tornado cyclones with relative insensitivity to range, effective beamwidth, and stage of evolution. High circulation and convergence values of a rotation signature reveal the potential for a tornado earlier than all the other predictors, which increase significantly during tornadogenesis.

Principal Component Analysis of Doppler Radar Data. Part I: Geometric Connections between Eigenvectors and the Core Region of Atmospheric Vortices

Abstract This is the first in a three-part series of papers that present the first applications of principal component analysis (PCA) to Doppler radar data. Although this novel approach has potential applications to many types of atmospheric phenomena, the specific goal of this series is to describe and verify a methodology that establishes the position and radial extent of the core region of atmospheric vortices. The underlying assumption in the current application is that the streamlines of the nondivergent component of the horizontal wind are predominantly circular, which is a characteristic often observed in intense vortices such as tropical cyclones. The method employs an S2-mode PCA on the Doppler velocity data taken from a single surveillance scan and arranged sequentially in a matrix according to the range and azimuth coordinates. Part I begins the series by examining the eigenvectors obtained from such a PCA applied to a Doppler velocity model for a modified, Rankine-combined vortex, where the ratio of the radius of maximum wind to the range from the radar to the circulation center is varied over a wide range of values typically encountered in the field. Results show that the first two eigenvectors within the eigenspace of range coordinates represent over 99% of the total variance in the data. It is also demonstrated that the coordinates of particular cusps in the curves of the eigenvector coefficients plotted against their indices are geometrically related to both the position of circulation center and the radius of maximum wind.

A review of ground-based, mobile, W-band Doppler-radar observations of tornadoes and dust devils

A ground-based, mobile, W-band Doppler-radar has been used in the U.S. during the last decade to obtain high-spatial resolution maps of the radar reflectivity and wind fields in tornadoes and dust devils. This radar is one of the best tools available for studying the substructure of intense, small-scale vortices in the boundary layer. The most significant findings to date are summarized. In one case, it was found that just prior to tornadogenesis in a supercell, a 100–200 m scale cyclonic vortex formed at the leading edge of a bulge in the rear–flank gust front. This vortex appeared to interact with a larger-scale (500 m to 1 km wide) cyclonic vortex, just as the tornado formed. Other small-scale cyclonic vortices were present along the rear–flank gust, but they did not develop into tornadoes. The mature tornado-vortex was dominated by quasi-stationary wavenumber-two disturbances, while the mean vortex resembled a two-celled, Rankine combined vortex. The diameter of the mean vortex narrowed as it intensified and widened as it weakened, even though the tornado condensation funnel narrowed as the tornado was dissipating. Evidence was also found of short-term, inertial-like oscillations in vortex diameter and intensity. Spiral bands and eyes were ubiquitous. The eye in one well-documented case was broader in the lowest few hundred meters than it was aloft. Multiple vortices and “umbilical” cords of very narrow bands of reflectivity have also been found. Both cyclonic and anticyclonic dust devils have been documented. Some dust devils resemble a relatively narrow, Rankine combined vortex, while others are wider and have a broad, calm eye and a narrow annulus of intense vorticity just within the radius of maximum wind (RMW), and rising motion just inside the RMW and sinking motion well inside the RMW. Multiple-vortex structure, Rossby-like wave motion, and the Fujiwhara effect have also been documented.

Large eddy simulation of the tornado-structure interaction to determine structural loadings

A tornado changes its wind speed and direction rapidly; therefore, it is difficult to study the effects of a tornado on buildings in a wind tunnel. The status of the tornado-structure interaction and various models of the tornado wind field found in literature are surveyed. Three dimensional computer modeling work using the turbulence model based on large eddy simulation is presented. The effect of a tornado on a cubic building is considered for this study. The Navier-Stokes (NS) equations are approximated by finite difference method, and solved by an semi-implicit procedure. The force coefficients are plotted in time to study the effect of the Rankine combined vortex model. The tornado is made to translate at a <TEX>$0^{\circ}$</TEX> and <TEX>$45^{\circ}$</TEX> angle, and the grid resolution is refined. Some flow visualizations are also reported to understand the flow behavior around the cube.