Radial Vorticity Research Articles

Inner-Core Humidification and Prelandfall Rapid Intensification of Typhoon Mekkhala (2020) in Strong Vertical Wind Shear

Abstract A numerical simulation was conducted in this study to investigate the physical processes governing the unusual rapid intensification (RI) of Typhoon Mekkhala (2020) under strong vertical wind shear. The vortex tilt exhibited a gradual decrease from approximately 70 km to below 10 km over a period of six hours prior to and following the onset of the RI. Nevertheless, due to substantial midlevel ventilation, the storm intensity exhibited only slight variations in the early phase of the vortex alignment, six hours prior to the RI onset. The RI occurred subsequent to the precipitation within the inner core becoming increasingly axisymmetric as the stratiform clouds developed cyclonically. The precipitation axisymmetrization was found to be closely associated with inner-core humidification in the left-of-shear and upshear quadrants, occurring three hours before the RI onset. As previously documented, horizontal vapor advection greatly influenced the moistening process. A new finding of this study was that the “showerhead effect”, namely, moistening due to sublimation from stratiform clouds and evaporation from stratiform rain, could be predominantly conducive to the humidification of the inner core compared to horizontal vapor advection. Another noteworthy finding in the tangential wind budget was that the eddy radial vorticity flux contributed negatively and positively during the pre-RI and RI of Mekkhala, respectively, in conjunction with the dominant positive contribution resulting from the mean radial vorticity flux.

The role of time-varying external factors in the intensification of tropical cyclones

Abstract. The role of time-varying external parameters in tropical cyclone (TC) dynamics is explored through a low-order conceptual box model. Specifically, we look at stable-to-stable state transitions which may be linked to tropical cyclone intensification, dissipation, or eyewall replacement cycles (ERCs). To this end, we identify two parameters of interest: the exponent of radial decline and sea-surface temperature. We examine how variations in these parameters affect the stable states of the model and consider the behaviour of the system under different time-dependent forcing profiles for the parameters. By externally forcing the exponent of radial decline and sea-surface temperature, we show the existence of rate-dependent behaviour in the model. These findings are brought together in a case study of Hurricane Irma (2017). The results highlight the role of the radial vorticity gradient in behaviour such as rate-induced tipping and overshoot recovery. They also show that a simple model can be used to explore relatively complex tropical cyclone dynamics.

Extended Field Interactions in Poisson’s Equation Revision

This investigation introduces a new variational approach to refining Poisson’s equation, enabling the inclusion of a broader spectrum of physical phenomena, particularly in the emerging fields of spintronics and the analysis of resonant structures. The innovative formulation extends the traditional capabilities of Poisson’s equation, offering a nonlocal extension to classical theories of gravitation and opening new directions for energy conversion and enhanced communication technologies. By introducing a novel geometric structure, ω˜, into the equation, a deeper understanding of electrostatic potentials is achieved, and the intricate dynamics of the gravitational potential in systems characterized by radial vorticity fluctuations are illuminated. Furthermore, the research elucidates the generation of longitudinal electromagnetic waves and resonant phenomena within dusty plasma media, thereby contributing to the methodological advances in the study of nonequilibrium systems. These theoretical advances have the potential to transform the understanding of complex physical systems and open up opportunities for significant technological achievements across a range of scientific sectors.

Numerical study of non-toroidal inertial modes withl=m+ 1 radial vorticity in the Sun’s convection zone

Various types of inertial modes have been observed and identified on the Sun, including the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. Recent observations have further reported the detection of equatorially antisymmetric radial vorticity modes that propagate in a retrograde direction about three times faster than those of the equatorial Rossby modes, when seen in the corotating frame with the Sun. Here, we study the properties of these equatorially antisymmetric vorticity modes using a realistic linear model of the Sun’s convection zone. We find that they are essentially non-toroidal, involving a substantial radial flow at the equator. Thus, the background density stratification plays a critical role in determining their dispersion relation. The solar differential rotation is also found to have a significant impact by introducing the viscous critical layers and confining the modes near the base of the convection zone. Furthermore, we find that their propagation frequencies are strikingly sensitive to the background superadiabaticity,δ, because the buoyancy force acts as an additional restoring force for these non-toroidal modes. The observed frequencies are compatible with the linear model only when the bulk of the convection zone is weakly subadiabatic (−5 × 10−7 ≲ δ ≲ −2.5 × 10−7). Our result is consistent with but tighter than the constraint independently derived in a previous study (δ < 2 × 10−7), employing the high-latitude inertial mode. It is implied that, below the strongly superadiabatic near-surface layer, the bulk of the Sun’s convection zone might be much closer to adiabatic than typically assumed or it may even be weakly subadiabatic.

Annular self-organization of the two-dimensional vorticity condensate

Self-organization of the vorticity condensate of forced two-dimensional turbulence is examined in analogy with the mixing of a background planetary vorticity gradient in geophysical flows. Starting from the theoretical vorticity profile of the condensate, different scenarios are illustrated by the construction of idealized angular momentum conserving rearrangements of vorticity into a staircase profile similar to the potential vorticity staircase of $\beta$ -plane turbulence. Two sets of numerical experiments are then presented that illustrate a similar self-organization of the background vorticity gradient in fully turbulent flows. In the first set of experiments, the flow is initialized with a laminar vortex dipole corresponding to the theoretical condensate vorticity profile. A fluctuation vorticity field is then induced by a stochastic forcing at smaller scales, which induces an azimuthally symmetric self-organization of the laminar flow into distinct annular bands. In the second set of experiments, the flow is initialized from rest with stochastic forcing generating a turbulent inverse energy cascade, out of which emerges the condensate in a self-consistent evolution as the turbulent energy accumulates at the domain scale. A self-organization of the condensate is again observed, giving a distinct annular structure on top of the theoretically predicted condensate profile. A major difference from the potential vorticity staircase of geophysical flows is the emergence in many cases of significantly non-monotonic radial vorticity profiles.

Dual-stage radial–tangential vortex tilting reverses radial vorticity and contributes to leading-edge vortex stability on revolving wings

The physics of leading-edge vortex (LEV) stability on flapping wings and autorotating seeds is still underexplored due to its complex dependency on Reynolds number ( $\textit {Re}$ ), aspect ratio (AR) and Rossby number (Ro). Our previous study observed an interesting dual-stage vortex tilting between radial and tangential components in a stable LEV. Here, the establishment of this novel mechanism, i.e. dual-stage radial–tangential vortex tilting (DS-VT $_{r-t}$ ), is investigated and explained in detail using numerical methods. The contributions of other tangential vorticity transport terms are also considered. It is shown that the stable LEV region coincides mostly with a constant ratio of tangential and radial vorticity components. The DS-VT $_{r-t}$ mechanism functions as a negative feedback loop for radial vorticity, thereby contributing to the LEV stability at $\textit {Re} > 500$ . Specifically, this mechanism involves a dual-stage vortex tilting starting from negative radial component to positive tangential component, and then back to positive radial component, thereby leading to a $180^{\circ }$ reversal of radial vorticity. The radial Coriolis acceleration can also assist the DS-VT $_{r-t}$ by enhancing the tangential vorticity component and the reduction of radial vorticity inside the LEV via the second stage of DS-VT $_{r-t}$ . The effects of $\textit {Re}$ , AR and Ro on the constant radial–tangential vorticity ratio and DS-VT $_{r-t}$ are then analysed. The coupled effects of AR and Ro are separated into rotational effects and those of tip and root vortices. Our results establish an evident relationship among the LEV stability, the constant radial–tangential vorticity ratio, and the DS-VT $_{r-t}$ , thereby deepening the understanding in the vorticity transport of LEV formation and stability.

A new Eulerian-Eulerian-Lagrangian solver in OpenFOAM and its application in a three-phase bubble column

Gas-liquid-solid three-phase flows (GLSTPF) have important applications in nature and industries, but they are complex and numerical simulation is challenging. In this study, a new solver coupling Eulerian-Eulerian-Lagrangian approach with population balance model (PBM) was developed in OpenFOAM to simulate GLSTPF. In the new solver, the effects of solid particles on gas-phase or liquid-phase holdups were included. Moreover, interphase forces of gas-solid and liquid-solid were calculated separately, and all the forces exerted on a solid particle were added to calculate the particle movement. Furthermore, the new solver was successfully compared with the experimental results of bubble size distribution and phase velocities in a three-phase bubble column. The introduction of PBM significantly improved the predictions of bubble rise and solid velocities (by up to 20%) and phase holdups (by up to 30%). The gas phase oscillated in the bubble column due to flow turbulence, and both the liquid and solid phases tended to circulate in the bubble column. The liquid vorticity exhibited irregular distributions, and different scales of vortex structure were observed with higher maximum radial vorticity (10 s−1) than axial vorticity (4 s−1), demonstrating the existence of swirling and oscillating flow in the column.

Intensity fluctuations in Hurricane Irma (2017) during a period of rapid intensification

Abstract. This study aims to understand the fluctuations observed in Hurricane Irma (2017), which change the tangential wind speed and the size of the radius of maximum surface wind and therefore affect short-term destructive potential. Intensity fluctuations observed during a period of rapid intensification of Hurricane Irma between 4 and 6 September 2017 are investigated in a detailed modelling study using an ensemble of Met Office Unified Model (MetUM) convection-permitting forecasts. Although weakening and strengthening phases were defined using 10 m wind, structural changes in the storm were observed through the lower troposphere, with the most substantial changes just above the boundary layer (at around 1500 m). Isolated regions of rotating deep convection, coupled with outward propagating vortex Rossby waves, develop during the strengthening phases. Although these isolated convective structures initially contribute to the increase in azimuthally averaged tangential wind through positive radial eddy vorticity fluxes, the continued outward expansion of convection eventually leads to a negative radial eddy vorticity flux, which halts the strengthening of the tangential wind above the boundary layer at the start of the weakening phase. The outward expansion of the azimuthally averaged convection also enhances the outflow above the boundary layer in the eyewall region, as the convection is no longer strong enough to ventilate the mass inflow from the boundary layer in a process similar to one described in a recent idealised study.

Response of Extratropical Transitioning Tropical Cyclone Size to Ocean Warming: A Case Study for Typhoon Songda in 2016

This study attempts to investigate how future sea surface temperature increases will affect the size (radius of gale-force [17 m s−1] wind at 10 m height; i.e., R17) evolution of tropical cyclones that undergo extratropical transition (ET) through sensitivity experiments of sea surface temperature (SST) for Typhoon Songda (2016) in the northwestern Pacific. Two numerical experiments were carried out, including a control simulation (control) and a sensitivity experiment (SST4.5) with SST increased by 4.5 degrees in the entire domain. The results showed that Songda tended to be stronger and larger with projected higher SSTs. Moreover, the momentum equation for tangential wind was utilized to study the mechanism of R17 evolution in different SST scenarios, in which the radial absolute vorticity flux term played a dominant role in generating a positive tendency of tangential wind. The results indicate that before ET, higher SSTs in the entire domain led to more active rainbands in both inner-core and outer-core regions. As a result, stronger secondary circulation and low-level inflow extended outward, and the absolute angular momentum (AAM) importing from the outer region increased, which led to a larger R17 in SST4.5. During the ET, the peripheral baroclinically driven frontal convection induced extensive boundary layer inflow, which accelerated the tangential flow in the outer frontal region through strong inward AAM transport. However, due to the lower latitude of the cyclone and the strong frontolysis at the outer side of the cold pool in SST4.5, the peripheral frontal convection reached the location of R17 later; thus, the increase in the cyclone size lagged behind that in the control.

Giant vortex dynamics in confined bacterial turbulence.

We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.

A Laboratory Model for a Meandering Zonal Jet

AbstractThe meandering jet streams of the Northern Hemisphere influence the weather for more than half of Earth's population, so it is imperative that we improve our understanding of their behavior and how they respond to climate change. Here, we describe a novel laboratory model for a meandering zonal jet. This model comprises a large rotating annulus with a series of topographic ridges, and an imposed radial vorticity flux. Flow interactions with the topographic ridges operate to concentrate the zonal transport into a narrow jet, which supports the development and propagation of Rossby waves. We investigate the dynamics of the jet for a range of rotation rates, imposed radial vorticity fluxes, and topographic ridge configurations. The circulations are classified into two distinct regimes: predominantly zonal or predominantly meandering. The flow regime can be quantified by the ratio of the Ekman dissipation and jet advection timescales, which gives an indication of whether disturbances arising from the flow‐topography interaction are dissipated faster than the time taken to circuit the annulus; if not, these disturbances will reencounter the topography, and thus be reinforced and amplified. For predominantly zonal flows, the radial vorticity flux is split equally between the standing meanders and transient eddies. For predominantly meandering flows, standing meanders perform 79% of the radial vorticity flux, with 18% accommodated by the transient eddies. Our experiments indicate that the Arctic amplification associated with climate change will tend to favor predominantly zonal flow conditions, suggesting a reduced occurrence of atmospheric blocking events caused by the jet streams.

Imaging the Sun’s Near-surface Flows Using Mode-coupling Analysis

Abstract The technique of normal-mode coupling is a powerful tool with which to seismically image non-axisymmetric phenomena in the Sun. Here we apply mode coupling in the Cartesian approximation to probe steady, near-surface flows in the Sun. Using Doppler cubes obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we perform inversions on mode-coupling measurements to show that the resulting divergence and radial vorticity maps at supergranular length scales (∼30 Mm) near the surface compare extremely well with those obtained using the local correlation tracking method. We find that the Pearson correlation coefficient is ≥0.9 for divergence flows, while ≥0.8 is obtained for the radial vorticity.

Why does rapid contraction of the radius of maximum wind precede rapid intensification in tropical cyclones?

AbstractThe radius of maximum wind (RMW) has been found to contract rapidly well preceding rapid intensification in tropical cyclones (TCs) in recent literature but the understanding of the involved dynamics is incomplete. In this study, this phenomenon is revisited based on ensemble axisymmetric numerical simulations. Consistent with previous studies, because the absolute angular momentum (AAM) is not conserved following the RMW, the phenomenon can not be understood based on the AAM-based dynamics. Both budgets of tangential wind and the rate of change in the RMW are shown to provide dynamical insights into the simulated relationship between the rapid intensification and rapid RMW contraction. During the rapid RMW contraction stage, due to the weak TC intensity and large RMW, the moderate negative radial gradient of radial vorticity flux and small curvature of the radial distribution of tangential wind near the RMW favor rapid RMW contraction but weak diabatic heating far inside the RMW leads to weak low-level inflow and small radial absolute vorticity flux near the RMW and thus a relatively small intensification rate. As RMW contraction continues and TC intensity increases, diabatic heating inside the RMW and radial inflow near the RMW increase, leading to a substantial increase in radial absolute vorticity flux near the RMW and thus the rapid TC intensification. However, the RMW contraction rate decreases rapidly due to the rapid increase in the curvature of the radial distribution of tangential wind near the RMW as the TC intensifies rapidly and RMW decreases.

A minimal model for vertical shear instability in protoplanetary accretion disks

The vertical shear instability is an axisymmetric effect suggested to drive turbulence in the magnetically inactive zones of protoplanetary accretion disks. Here we examine its physical mechanism in analytically tractable “minimal models” in three settings that include a uniform density fluid, a stratified atmosphere, and a shearing-box section of a protoplanetary disk. Each of these analyses show that the vertical shear instability's essence is similar to the slantwise convective symmetric instability in the mid-latitude Earth atmosphere, in the presence of vertical shear of the baroclinic jet stream, as well as mixing in the top layers of the Gulf Stream. We show that in order to obtain instability, the fluid parcels' slope should exceed the slope of the mean absolute momentum in the disk radial-vertical plane. We provide a detailed and mutually self-consistent physical explanation from three perspectives: in terms of angular momentum conservation, as a dynamical interplay between a fluid's radial and azimuthal vorticity components, and from an energy perspective involving a generalised Solberg-Høiland Rayleigh condition. Furthermore, we explain why anelastic dynamics yields oscillatory unstable modes and isolate the oscillation mechanism from the instability one.

Scaling the vorticity dynamics in the leading-edge vortices of revolving wings with two directional length scales

In revolving or flapping wings, radial planetary vorticity tilting (PVTr) is a mechanism that contributes to the removal of radial (spanwise) vorticity within the leading-edge vortex (LEV), while vorticity advection increases its strength. Dimensional analysis predicts that the PVTr and advection should scale with the wing aspect-ratio (AR) in identical fashion, assuming a uniform characteristic length is used. However, the authors’ previous work suggests that the vorticity advection decreases more rapidly than the PVTr as AR increases, indicating that separate normalizations should be applied. Here, we aim to develop a comprehensive scaling for the PVTr and vorticity advection based on simulation results using computational fluid dynamics. Two sets of simulations of revolving rectangular wings at an angle of attack of 45° were performed, the first set with the wing-tip velocity maintained constant, so that the Reynolds number (Re) defined at the radius of gyration equals 110, and the second set with the wing angular velocity maintained constant, so that Re defined at one chord length equals 63.5. We proposed two independent length scales based on LEV geometry, i.e., wing-span for the radial and tangential directions and wing chord for the vertical direction. The LEV size in the radial and tangential directions was limited by the wing-span, while the vertical depth remained invariant. The use of two length scales successfully predicted not only the scaling for the PVTr and the vorticity advection but also the relative magnitude of advection in three directions, i.e., tangential advection was strongest, followed by the vertical (downwash) and then the radial that was negligible.

Polygonal Eyewall Asymmetries During the Rapid Intensification of Hurricane Michael (2018)

AbstractPolygonal eyewall asymmetries of Hurricane Michael (2018) during rapid intensification (RI) are analyzed from ground‐based single Doppler radar. Here, we present the first observational evidence of the evolving wind field of a polygonal eyewall during RI to Category 5 intensity by deducing the axisymmetric and asymmetric winds at 5‐min intervals. Spectral time decomposition of the retrieved tangential wind structure shows quantitative evidence of low (1–4) azimuthal wavenumbers with propagation speeds that are consistent with linear wave theory on a radial vorticity gradient, suggesting the presence of rapidly evolving vortex Rossby waves. Dual‐Doppler winds from the NOAA P‐3 Hurricane Hunter airborne radar provide further evidence of the three‐dimensional vortex structure that supports growth of asymmetries during RI. Both reflectivity and tangential wind fields show polygonal structure and propagate at similar speeds, suggesting a close coupling of the dynamics and the convective organization during the intensification.

Vorticity transport in laminar steady rotating plumes

A steady laminar rotating thermal plume was investigated by the numerical solution of the 3D momentum and energy equations. The flow originated from a low momentum hot jet (Richardson number Ri = 173 and Grashof number Gr = 5000) issued from a small inlet in the bottom wall of a cylindrical domain with a permeable lateral surface that is rotating (Ekman number Ek = 12). Second order accurate calculations of the structure and dynamics of the buoyant vortex were investigated, with specific emphasis on the evolution of the vorticity distributions and their effects on the ensuing vortex. Budgets of the vorticity transport equations were investigated to analyze the genesis of the developed axial vorticity, explaining how the whirling flow was generated. Nonslip and slip bottom boundary conditions allowed the investigation of the impact of the boundary layer on the axial vorticity generation. The results showed that there is a conversion of radial vorticity into axial vorticity. The radial vorticity was found to be generated not only in the boundary layer but also by tilting of the tangential vorticity, which results from buoyancy. Additionally, the boundary layer was found to have a strong impact on the generation of axial vorticity, but not to be necessary to generate the whirl. In fact, a stronger whirl was originated without the effect of the boundary layer, since the axial vorticity was generated closer to the inlet, where additional stretching is provided by the acceleration of the flow.

A boundary vorticity diagnosis of the flows in a model pump-turbine in turbine mode

In the present study, the internal flow field in a model pump-turbine operating in turbine mode was numerically studied. By recognizing that appearance of boundary vorticity flux (BVF)’s peaks might act as the precursors of flow separation in turbomachines, flow diagnosis based on the boundary vorticity dynamics was then performed. It was shown that the effect of the BVF distribution at the condition in design operating zone is to weaken the axial vorticity component ωz, as well as to enhance the radial and circumferential vorticity components ωr and ωθ. Thus, the peaks of the axial BVF component σz led to the strong weakening of ωz, which is responsible for the flow separations. Geometric optimization for the runner was then achieved by modifying the inlet angle of the blade from 14° to 16°. The optimization successfully suppressed the occurrence of the flow separations and improved the moment on the runner at design operating condition by 4%, which was achieved by the redistribution of the axial BVF component generated by pressure σpz on the pressure side. The fact that only an accurate steady simulation is required for the analysis indicates the great potential application of this method in engineering practice.

Solar Rossby waves observed in GONG++ ring-diagram flow maps

Context. Solar Rossby waves have only recently been unambiguously identified in Helioseimsic and Magnetic Imager (HMI) and Michelson Doppler Imager maps of flows near the solar surface. So far this has not been done with the Global Oscillation Network Group (GONG) ground-based observations, which have different noise properties. Aims. We use 17 years of GONG++ data to identify and characterize solar Rossby waves using ring-diagram helioseismology. We compare directly with HMI ring-diagram analysis. Methods. Maps of the radial vorticity were obtained for flows within the top 2 Mm of the surface for 17 years of GONG++ data. The data were corrected for systematic effects including the annual periodicity related to the B0 angle. We then computed the Fourier components of the radial vorticity of the flows in the co-rotating frame. We performed the same analysis on the HMI data that overlap in time. Results. We find that the solar Rossby waves have measurable amplitudes in the GONG++ sectoral power spectra for azimuthal orders between m = 3 and m = 15. The measured mode characteristics (frequencies, lifetimes, and amplitudes) from GONG++ are consistent with the HMI measurements in the overlap period from 2010 to 2018 for m ≤ 9. For higher-m modes the amplitudes and frequencies agree within two sigmas. The signal-to-noise ratio of modes in GONG++ power spectra is comparable to those of HMI for 8 ≤ m ≤ 11, but is lower by a factor of two for other modes. Conclusions. The GONG++ data provide a long and uniform data set that can be used to study solar global-scale Rossby waves from 2001.

Exploring the latitude and depth dependence of solar Rossby waves using ring-diagram analysis

Context. Global-scale equatorial Rossby waves have recently been unambiguously identified on the Sun. Like solar acoustic modes, Rossby waves are probes of the solar interior. Aims. We study the latitude and depth dependence of the Rossby wave eigenfunctions. Methods. By applying helioseismic ring-diagram analysis and granulation tracking to observations by HMI aboard SDO, we computed maps of the radial vorticity of flows in the upper solar convection zone (down to depths of more than 16 Mm). The horizontal sampling of the ring-diagram maps is approximately 90 Mm (∼7.5°) and the temporal sampling is roughly 27 hr. We used a Fourier transform in longitude to separate the different azimuthal orders m in the range 3 ≤ m ≤ 15. At each m we obtained the phase and amplitude of the Rossby waves as functions of depth using the helioseismic data. At each m we also measured the latitude dependence of the eigenfunctions by calculating the covariance between the equator and other latitudes. Results. We conducted a study of the horizontal and radial dependences of the radial vorticity eigenfunctions. The horizontal eigenfunctions are complex. As observed previously, the real part peaks at the equator and switches sign near ±30°, thus the eigenfunctions show significant non-sectoral contributions. The imaginary part is smaller than the real part. The phase of the radial eigenfunctions varies by only ±5° over the top 15 Mm. The amplitude of the radial eigenfunctions decreases by about 10% from the surface down to 8 Mm (the region in which ring-diagram analysis is most reliable, as seen by comparing with the rotation rate measured by global-mode seismology). Conclusions. The radial dependence of the radial vorticity eigenfunctions deduced from ring-diagram analysis is consistent with a power law down to 8 Mm and is unreliable at larger depths. However, the observations provide only weak constraints on the power-law exponents. For the real part, the latitude dependence of the eigenfunctions is consistent with previous work (using granulation tracking). The imaginary part is smaller than the real part but significantly nonzero.