Vorticity Profiles Research Articles

An Analysis of Tropical Cyclone Vortex and Convective Characteristics in Relation to Storm Intensity Using a Novel Airborne Doppler Radar Database

Abstract This analysis introduces a novel airborne Doppler radar database, referred to as the Tropical Cyclone Radar Archive of Doppler Analyses with Re-centering (TC-RADAR). TC-RADAR comprises over 900 analyses from 273 flights into TCs in the North Atlantic, eastern North Pacific, and central North Pacific basins between 1997 and 2020. This database contains abundant sampling across a wide range of TC intensities, which facilitated a comprehensive observational analysis on how the three-dimensional, kinematic TC inner-core structure is related to TC intensity. To examine the storm-relative TC structure, we implemented a novel TC center-finding algorithm. Here, we show that TCs below hurricane intensity tend to have monopolar radial profiles of vorticity and a wide range of vortex tilt magnitudes. As TC intensity increases, vorticity becomes maximized within an annulus inward of the peak wind, the vortex decays more slowly with height, and the vortex tends to be more aligned in the vertical. The TC secondary circulation is also strongly linked to TC intensity, as more intense storms have shallower and stronger lower-tropospheric inflow as well as larger azimuthally averaged ascent. The distribution of vertical velocity is found to vary with TC intensity, height, and radial domain. These results—and the capabilities of TC-RADAR—motivate multiple avenues for future work, which are discussed. Significance Statement Acquiring observations of the inner core of tropical cyclones (TCs) is a challenge due to the hazardous conditions inherent to the storm. A proven method of sampling the TC core region is the use of airborne radar. This study presents a novel database comprising over 900 airborne radar analyses collected in storms between 1997 and 2020, which is freely available to the research community. Here we demonstrate the utility of the database by examining how the three-dimensional structure of the TC core region changes depending upon the intensity of the storm. By identifying how the baseline TC vortex structure varies with TC intensity, this work provides the foundation for multiple future research avenues and model evaluation efforts.

Profile of a two-dimensional vortex condensate beyond the universal limit.

It is well known that an inverse turbulent cascade in a finite (2π×2π) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length l_{f}=2π/k_{f} with k_{f} ranging from 100 to 12.5. Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior Ω(r)=(3ε/α)^{1/2}r^{-1}, where r is the distance to the vortex center, α is the bottom friction coefficient, and ε is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite k_{f} the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behavior is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with r, and show that in this case the vorticity profile can be flatter than the asymptotic limit.

Two-phase bio-nanofluid flow through a bifurcated artery with magnetic field interaction

A modified multiphase flow model is applied for a better understanding of bio-nanofluid (blood containing 4% (w/v) Fe3O4 nanoparticles) flow regimes through a real bifurcated artery. The magnetic field with distinct current intensities (I = 0 – 300 A) was employed to induce the flow features when the wire's source is placed nearby the junction of the asymmetrical branched artery during numerical computation. The finite volume method was used to solve the coupled hemodynamics model. Results show that the pressure, and vorticity profiles increased and fallen gradually with the existence of the magnetic source and further obtained the maximum pressure for the strong current intensity (I = 300 A). The fluctuating vorticity distributions are found along the inner and outer vessel wall as well as the predicted lines created within the simulated domain for the increase of current intensity. The velocity outlines variates steadily, and the local peak velocities are obtained with the increase of the magnetic force. With the increment of the current intensity upto I = 300 A, the flow rate rises progressively for the asymmetric branched vessel, and the opposite scenario is found for the root vessel. The temperature profiles decrease steadily with the increment of the applied current intensity. With the manifestation of the magnetic source, the irregular flow behaviours are found within the asymmetrical bifurcated artery. This modeling investigation could be beneficial for the emergent therapy plan of ample vascular diseases as the magnetic drug targeting system.

Analysis of Floating Offshore Wind Platform Hydrodynamics Using Underwater SPIV: A Review

There is a need for new numerical tools to capture the physics of floating offshore wind turbines (FOWTs) more accurately to refine engineering designs and reduce costs. The conventional measurement apparatuses in tank tests, including wave probes, velocity and current profilers, and Doppler sensors, are unable to provide a full 3D picture of velocity, pressure, turbulence, and vorticity profile. In tank tests, use of the underwater stereoscopic particle image velocimetry (SPIV) method to fully characterise the 3D flow field around floating wind platforms can overcome some of the limitations associated with classical measurement techniques and provide a rich source of validation data to advance high-fidelity numerical tools. The underwater SPIV method has been widely used for marine and offshore applications, including ship and propeller wakes, wave dynamics, and tidal stream turbines; however, to date, this technology has not seen widespread use for the hydrodynamic study of FOWTs. This paper provides a critical review of the suitability of underwater SPIV for analysing the hydrodynamics of FOWTs, reviews the challenges of using the method for FOWT tank test applications, and discusses the contributions the method can make to mitigating current research gaps in FOWT tank tests.

Inviscid damping of an elliptical vortex subject to an external strain flow

Inviscid spatial Landau damping is studied experimentally for the case of oscillatory motion of a two-dimensional vortex about its elliptical equilibrium in the presence of an applied strain flow. The experiments are performed using electron plasmas in a Penning–Malmberg trap. They exploit the isomorphism between the two-dimensional Euler equations for an ideal fluid and the drift-Poisson equations for the plasma, where plasma density is the analog of vorticity. Perturbed elliptical vortex states are created using E×B strain flows, which are generated by applying voltages to electrodes surrounding the plasma. Measurements of spatial Landau damping (also called critical-layer damping) are in agreement with previous studies in the absence of an applied strain, where the damping is due to a resonance between the local fluid motion and the vortex oscillations. Interestingly, the damping rate does not change significantly over a wide range of applied strain rates. This can be accurately predicted from the initial vorticity profile, even though the resonant frequency is reduced substantially due to the applied strain. For higher amplitude perturbations, nonlinear trapping oscillations also exhibit behavior similar to the strain-free case. In principle, higher-order effects of the applied strain, such as separatrix crossing of peripheral vorticity and interactions with harmonics of the fundamental resonance, are expected to change the damping rate. However, this occurs only for conditions that are not realized in the experiments described here. Vortex-in-cell simulations are used to investigate the possible roles of these effects.

Явное представление сокращенных в размерности уравнений Эйлера и Навье – Стокса несжимаемой жидкости в интегральной форме

In this paper, we have obtained “stationary” systems of integraldifferential equations, which are consequences of the non-stationary Euler and Navier - Stokes equations of an incompressible fluid, and for which there are no time derivatives. If we set a correct problem for them, then we can determine the entire non-stationary flow in the volume without solving the nonstationary problem. It is enough to specify time-varying data only on some surface of this stream. The method of reduction of overdetermined systems of differential equations, proposed earlier by the authors, is used. In this method, in the case of a successful choice of the additional constraint equation, the overdetermined systems of differential equations are reduced to PDE systems of dimension less than that of the original PDE systems. The Euler and Navier-Stokes equations themselves act as the constraint equations, and the dimension is reduced for the integral equations, which are obtained using the Helmholtz theorem on the expansion of an arbitrary vector field into vortex and potential components. The peculiarity of this work lies in the fact that all the equations reduced in dimension are obtained in an explicit form, in contrast to the previous works of the authors, where up to 200–300 equations with reduced dimensions were proposed. In reduced systems of integral-differential equations, there is integration over space, therefore, reduction over spatial variables by given method is impossible. If this method is generalized a little, then we can obtain a reduced system of integral equations, where the unknowns have no derivatives with respect to space, but integration over space remains. Non-stationary new integral equations are also obtained, which determine the evolution of the flow. In Appendices A and B, sufficient conditions for the correctness of the reduced system of integral-differential equations are derived. Conditions are found under which the Euler equations follow directly from these reduced equations. It is shown how the time-varying data on some surface of this stream should be related. The change of variables, which is used in the reduction of the Navier - Stokes equations, is also investigated he resulting integral equations can be used to study complex vortices in the atmosphere. For example, if devices measuring data on its surface are installed on a flying object, then, knowing the vorticity profile ω0(r) at a certain moment in time, it is possible, by solving these equations, to track vortex activity at a distance from this object in real time.

On the Two Types of Tropical Cyclone Eye Formation: Clearing Formation and Banding Formation

Abstract Two types of eye formation are proposed: “clearing formation (CF)” and “banding formation (BF)”. The objectives are to identify the tropical cyclone (TC) characteristics associated with these two types of eye formation and to clarify how the environment, pattern of synoptic systems and TC structure during initial and development stages affect the eye formation. The satellite imagery and best-track data are used to classify and analyze the TCs named in the western North Pacific from 2007 to 2020. The results show that TCs with CF have significantly higher intensity and intensification rate during the period of the first eye presence, smaller size after genesis and prior to eye formation, smaller eye size when the eye forms and a more westward track. It is noted that CF and BF TCs tend to occur in autumn and summer, respectively. Meanwhile, the composite results using reanalysis data show that the CF TCs are generally characterized by easterly-wave features with a dryer environment, smaller initial size and larger radial gradient of vorticity, while the BF TCs feature a monsoon-depression structure with a wetter environment, larger initial size and flatter vorticity profile. A conceptual hypothesis is thus proposed, as compared to BF TCs, the smaller size and weaker outer wind in CF storms associated with the easterly-wave disturbance are facilitated by inactive outer convection, leading to larger radial gradient of inertial stability. The low-level inflow can penetrate inward close to the center, resulting in more diabatic heating inside the radius of maximum wind with much higher heating efficiency, and also a higher intensification rate.

Inertio–elastic instability of a vortex column

We analyse the instability of a vortex column in a dilute polymer solution at large ${{Re}}$ and ${{De}}$ with ${{El}} = {{De}}/{{Re}}$ , the elasticity number, being finite. Here, ${{Re}} = \varOmega _0 a^2/\nu$ and ${{De}} = \varOmega _0 \tau$ are, respectively, the Reynolds and Deborah numbers based on the core angular velocity ( $\varOmega _0$ ), the radius of the column ( $a$ ), the total (solvent plus polymer) kinematic viscosity ( $\nu = (\mu _s +\mu _p)/\rho$ with $\mu _s$ and $\mu _p$ being the solvent and polymer contributions to the viscosity) and the polymeric relaxation time ( $\tau$ ). The stability of small-amplitude perturbations in this distinguished limit is governed by the elastic Rayleigh equation whose spectrum is parameterized by ${E} = {{El}}(1-\beta )$ , $\beta$ being the ratio of the solvent to the solution viscosity. The neglect of the relaxation terms, in the said limit, implies that the polymer solution supports undamped elastic shear waves propagating relative to the base-state flow. Unlike the neutrally stable inviscid case, an instability of the vortex column arises for finite ${E}$ due to a pair of elastic shear waves being driven into a resonant interaction under the differential convection by the irrotational shearing flow outside the core. An asymptotic analysis for the Rankine profile shows the absence of an elastic threshold for this instability. The growth rate is $O(\varOmega _0)$ for order unity $E$ , although it becomes transcendentally small for ${E} \ll 1$ , being $O(\varOmega _0 {E}^2{\rm e}^{-1/{E}^{{1}/{2}}})$ . An accompanying numerical investigation shows that the instability persists for smooth monotonically decreasing vorticity profiles, provided the radial extent of the transition region (from the rotational core to the irrotational exterior) is less than a certain ${E}$ -dependent threshold.

Vortex collapses for the Euler and Quasi-Geostrophic models

<p style='text-indent:20px;'>This article studies point-vortex models for the Euler and surface quasi-geostrophic equations. In the case of an inviscid fluid with planar motion, the point-vortex model gives account of dynamics where the vorticity profile is sharply concentrated around some points and approximated by Dirac masses. This article contains two main theorems and also smaller propositions with several links between each other. The first main result focuses on the Euler point-vortex model, and under the non-neutral cluster hypothesis we prove a convergence result. The second result is devoted to the generalization of a classical result by Marchioro and Pulvirenti concerning the improbability of collapses and the extension of this result to the quasi-geostrophic case.</p>

Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations

The instability of surface lenticular vortices is investigated using a comprehensive suite of laboratory experiments combined with numerical linear stability analysis as well as nonlinear numerical simulations in a two-layer Rotating Shallow Water model. The development of instabilities is discussed and compared between the different methods. The linear stability analysis allows for a clear description of the origin of the instability observed in both the laboratory experiments and numerical simulations. While global qualitative agreement is found, some discrepancies are observed and discussed. Our study highlights that the sensitivity of the instability outcome is related to the initial condition and the lower-layer flow. The inhibition or even suppression of some unstable modes may be explained in terms of the lower-layer potential vorticity profile.

Numerical analysis for the effects of heat transfer in modified square duct with heated obstacle inside it

This article deals with numerical analysis of two-dimensional viscous fluid in modified square duct. A rectangular obstacle with constant temperature at walls is placed inside it. Flow duct is depicted in Figs. 1 and 2. Influence of Prandtl number and geometry on heat transfer of working fluid is studied in two cases. Computation for the present model is made in commercial package ANSYS-Fluent. Calculations are carried at two different values of Reynolds numbers i.e., Re 40 and 200 for each of the cases. Liquid water (H20) and Liquid Aniline (C6H5NH2) are taken as working fluids. Stream functions, isotherms, vorticity, velocity and pressure profiles are examined. Graphical data for Cf and Nu is presented to analyze the effect of Reynolds number and Prandtl number on heat transfer. Thermal boundary layers are discussed in each of the cases. It is shown that heat transfer has high dependance on Reynolds number and Prandtl number. Geometry of the problem has noticeable effect on heat transfer.

Flow patterns of Jupiter's south polar region

Previous studies of Jupiter's wind patterns revealed the southernmost two prograde jets at 58°S and 64°S (planetocentric), which we designate as the S5 and S6 jets, respectively, but the jets and the wind patterns further poleward were not well defined. The Juno mission has provided the first opportunity to study the South Polar Region (SPR). Here we use images from Juno's camera, JunoCam, to characterize these jets and the wind patterns further south. We measure the main wind systems using JunoCam images taken up to two hours apart. The S5 jet coincides with a slightly sinuous boundary in methane-band images. The S6 jet is faster, broader and highly undulating in latitude, generally coinciding with the sinuous edge of the methane-bright South Polar Hood, whose wave pattern is often regular with a mean wavelength of 25.5° (±2.6°) longitude. Peak wind speeds along the S6 jet range from 42 (±12) to 49 (±11) m/s, faster than previously recognized. Poleward of the S6 jet, at ~65–70°S, there is an irregular belt of chaotic cyclonic regions termed folded filamentary regions (FFRs), with several small anticyclonic white ovals (AWOs) on or near its southern edge. Some of these FFRs appear to be extending northeast into the S6 jet. More FFRs are scattered from ~70 to 80°S. Wind speeds in the FFRs are generally ~20–60 m/s, comparable to lower-latitude cyclonic circulations. We also generate semi-quantitative maps of local vorticity, and thence, mean zonal vorticity profiles as a function of latitude. These confirm the S6 jet as sinuous and the southernmost belt of FFRs as a stable belt. Further south, there is usually a weak cyclonic vorticity maximum near 78°S, which probably represents irregular structures such as FFRs. Supplementary ground-based images, spaced by up to 4 days, show westward drifts for the ~65–70°S belt, with a mean of ~ + 0.9°/day in System III longitude. AWOs can also be tracked, for months or even years. They drift westward with a uniform speed of +0.8°/day between 69.5 and 72.4°S, but towards higher latitudes, up to 76°S, they show a steep latitudinal gradient to faster (eastward) speeds, comparable to those measured around the south polar pentagon of circumpolar cyclones at ~80°S. Overall, the ~65–70°S belt and associated AWOs show dynamical behaviour similar to lower latitudes. Further south, there are no rapid continuous jets, but the loose enhancement of cyclonic structures near 78°S suggests a trace of zonal structure extending almost as far as the polar pentagon.

Simulation of atmospheric dynamics during heavy rain events on Nias Island using WRF model and Himawari-8 satellite data

Nias is the largest island in the Indian Ocean west of Sumatra. The geographical condition of Nias Island which is a small island surrounded by waters causes strong weather dynamics and high intensity of rainfall. This study was conducted to determine changes in weather dynamics conditions during high rainfall on Nias Island, including the parameters of the vertical profile of air humidity, vorticity, divergence, vertical velocity, reflectivity; and cloud top temperatures. The simulation was carried out on 4 days of heavy rain in 2020, each representing each season period, namely 7 February 2020 for December-January-February (DJF), 30 April 2020 for March-April-May (MAM), 3 August 2020 for June-July-August (JJA), and 8 October 2020 for September-October-November (SON). The data used are Final Analysis Data (FNL) with a spatial resolution of 1°x1° as input data for the Weather Research and Forecast (WRF) model, IR1 data (band#13 – 10.4µm) Himawari-8 satellite, and observational rainfall data from the Binaka and Global Meteorological Stations. Precipitation Measurement – The Integrated Multi-Satellite Retrievals for GPM (GPM IMERG) with a spatial resolution of 0.1°x0.1°. The results showed that the presence of Cumulonimbus convective clouds caused heavy rain, with cloud top temperatures reaching -60°C to -80°C. The relatively humid atmosphere, accompanied by the convection mechanism that occurs, causes the convective activity on Nias Island to be quite intense.

Numerical investigation of the onset of three-dimensional characteristics in flow past a pair of square cylinders at various arrangements

An incompressible Navier–Stokes solver has been developed to analyze the three-dimensional viscous flow around a pair of square cylinders at a low Reynolds number (Re = 100) at various arrangements. A semi-implicit finite difference scheme was employed on a staggered grid, which facilitated the easier application of boundary conditions while achieving satisfactory accuracy and stability. A third-order upwind (Kawamura–Kuwahara) scheme was applied to discretize the convective terms and a second-order central difference scheme to discretize the diffusive terms. Time integration was performed using a second-order accurate Adams–Bashforth scheme. An iterative pressure–velocity correction was used to obtain a divergence-free velocity field. Aspects of the flow such as vorticity profiles, the time evolution of lift and drag coefficients, and three-dimensionality appearance were studied. Three-dimensional characteristics ceased to appear in a tandem arrangement, irrespective of the gap ratio. In contrast, the side by side arrangement showed a clear three-dimensional transition in the flow when analyzing the vortex structures. Further investigations carried out for staggered arrangement keeping the center to center distance constant and varying the stagger angle (α) reveal that the three-dimensional behavior starts at α = 30° and keeps progressing with the angle increase.

Mixing enhancement in T-junction microchannel with acoustic streaming induced by triangular structure.

The T-shaped microchannel system is used to mix similar or different fluids, and the laminar flow nature makes the mixing at the entrance junction region a challenging task. Acoustic streaming is a steady vortical flow phenomenon that can be produced in the microchannel by oscillating acoustic transducer around the sharp edge tip structure. In this study, the acoustic streaming is produced using a triangular structure with tip angles of 22.62°, 33.4°, and 61.91°, which is placed at the entrance junction region and mixes the inlets flow from two directions. The acoustic streaming flow patterns were investigated using micro-particle image velocimetry (μPIV) in various tip edge angles, flow rate, oscillation frequency, and amplitude. The velocity and vorticity profiles show that a pair of counter-rotating streaming vortices were created around the sharp triangle structure and raised the Z vorticity up to 10 times more than the case without acoustic streaming. The mixing experiments were performed by using fluorescent green dye solution and de-ionized water and evaluated its performance with the degree of mixing (M) at different amplitudes, flow rates, frequencies, and tip edge angles using the grayscale value of pixel intensity. The degree of mixing characterized was found significantly improved to 0.769 with acoustic streaming from 0.4017 without acoustic streaming, in the case of 0.008 μl/min flow rate and 38 V oscillation amplitude at y = 2.15 mm. The results suggested that the creation of acoustic streaming around the entrance junction region promotes the mixing of two fluids inside the microchannel, which is restricted by the laminar flow conditions.

Study of BPF pressure pulsations reduction in centrifugal bladed machines using splitters

Presence of intensive pressure pulsations and noise on blade passing frequencies is a characteristic feature of all types of centrifugal bladed machines including pumps. Under definite conditions pressure pulsations can reduce the pump reliability and life cycle. High level of tonal noise can be inappropriate due to ecological requirements. The paper is devoted to the study of application of splitters for reduction of pressure pulsations in centrifugal pumps. 2D and 3D numerical methods are used in the study. Initial computational tests were performed with a two-dimensional formulation for a centrifugal pump with a simple volute using 2D discreet vortex method for the impeller flow and 2D acoustic-vortex approach for pressure pulsations prediction. 3D unsteady flow computations of an air model of the centrifugal pump are undertaken with the impeller having splitters. Calculations of pressure pulsations show that the use of additional blades reduces the amplitude of the first harmonic of blade passing frequency by more than three times compared to the design without splitters. It correlates with flow parameters distribution along the impeller outlet diameter that has less nonuniformity and a more balanced vorticity profile. Application of splitters reduces the amplitude of pressure pulsations by a factor of 3.

Role of flow reversals in transition to turbulence and relaminarization of pulsatile flows

Abstract

Investigation of the flow, pressure drop characteristics, and augmentation of heat performance in a 3D flow pipe based on different inserts of twisted tape configurations

AbstractThe flow behavior, pressure drop, and heat performance rate in the three‐dimensional pipe with and without inserted tape are analyzed in his study. The enhancement of thermohydraulic performance is carried out by increasing the twisted tape configurations with different Re. The numerical simulation model is validated with experimental data, where the outcomes indicate a good agreement between both data. The results revealed that the pressure drop across the pipe using twisted tape insert was higher than in a smooth pipe. The increased drop in pressure along the pipe enhanced the performance of heat transfer. In addition, there was a rise in fluid velocity, but it was nonuniform. This happened due to the swirl created through the inserted tape in the pipe. The comparative study also specified that the profiles of dynamic pressure, static pressure, velocity magnitude, and vorticity are nonuniform, compared with the smooth tube type. Moreover, the results found that the best improvement of heat transfer is at a low value of mass flow with a twisted tape of 1 × 3 mm, which is equal to approximately 27.7%, 26.5%, 26.4%, and 22.9% respectively. Furthermore, this study provides numerical investigations for engineering design on flow field analysis and enhanced heat transfer performance with different insert tape configurations.

Asymmetric vortex sheet

We present a steady analytical solution of the incompressible Navier–Stokes equation for arbitrary viscosity in an arbitrary dimension d of space. It represents a d − 1 dimensional vortex “sheet” with an asymmetric profile of vorticity as a function of the normal coordinate z. This profile is related to the Hermite polynomials Hμ(z), which are analytically continued to the negative fractional index μ=−dd−1. In d = 2 dimensions, the solution degenerates to a constant vorticity flow. In d≥3 dimensions, the vorticity is confined to the thin layer around the hyperplane with Gaussian decay on one side of the hyperplane and the power decay on another side. One can adjust the common scale of velocity so that the dissipation will stay finite at vanishing viscosity. In this limit, the width w of the viscous lawyer will shrink to zero as ν35 for arbitrary dimension d >3. In d = 3 dimensions, this power law is also accompanied by powers of the logarithm.

Proppant transport in a planar fracture: Particle image velocimetry

Particle Image Velocimetry (PIV) is a well established technique used to measure displacements in fluids. Proppant transport and placement is a crucial phase in the process of well completion to stimulate production in gas and oil reservoirs. Proppant (a granular material) is injected along fluids during hydraulic stimulation to prop fractures open after hydrocarbon production is initiated. This work presents results on the use of PIV for the study of the transport of proppant in a large laboratory scale flat vertical fracture. Velocity and vorticity profiles were analyzed for different flow rates during the transport and settlement of the proppant inside the fracture. High flow rates, compatible with field operations are achieved in this setup. The results indicate that vortexes are present in a large portion of the system and that a non-linear interplay between the settling dune and the main vortex seems to determine the time at which a fast dune growth occurs in the fracture.