Baroclinic Vorticity Research Articles

Numerical studies of hydrodynamic relativistic astrophysical jet: The modification of vorticity transport equation

In this Letter, we have carried out the two-dimensional numerical simulation of axisymmetric relativistic jet in cylindrical coordinates by employing higher order finite volume method in PLUTO [Mignone et al., “PLUTO: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. 170, 228 (2007)] solver. The modified vorticity transport equation has been proposed for relativistic flow by taking the curl of the momentum equation, which shows significant change in the baroclinic vorticity production term due to relativistic effect. Both mathematical analysis and numerical results show that the vorticity production term due to baroclinic torque is heavily influenced due to the presence of specific enthalpy gradient and square of Lorentz factor gradient in a relativistic fluid flow.

The Similarity of Quasi-geostrophic Vortices Against the Background of Large-Scale Barotropic Currents

The paper proposes a theory of similarity of quasi-geostrophic vortices against the background of large-scale flows. This information is useful when planning laboratory and numerical experiments to study mesoscale and submesoscale vortex dynamics of vortices interacting with currents. Special attention is paid to the study of geometric similarity of phenomena. It is revealed that the complete set of dimensionless similarity numbers of baroclinic vortices includes four dimensionless parameters: the dimensionless intensity of the vortex, the geometric similarity of the background flow (the ratio of relative vorticity to the deformation coefficient of the background flow), the coefficient of horizontal elongation of the vortex core and the coefficient of vertical oblateness of the vortex core coinciding with the Burger number. To describe the similarity of barotropic vortices against the background of barotropic flows, the number of necessary dimensionless parameters is reduced by one number — the coefficient of vertical oblateness of the vortex core is eliminated from consideration. When studying axisymmetric vortices or vortex structures close to axisymmetric, another geometric parameter of the vortex is eliminated from consideration — the coefficient of horizontal elongation of the vortex core. As a result, the maximum possible set of similarity parameters includes four dimensionless numbers, and the minimum is two.

Influence of thermal buoyancy on the wake dynamics of a heated square cylinder

Direct numerical simulation of the three-dimensional (3-D) wake transition of a heated square cylinder subjected to horizontal cross-flow is performed in the presence of buoyancy. In order to capture the effects of large-scale heating, a non-Oberbeck–Boussinesq model is utilized, which includes the governing equations for compressible gas flow. All computations are performed at low free stream Mach number $M=0.1$ using air (free stream Prandtl number, $Pr=0.71$ ) as the working fluid. The 3-D instability modes A and B, which correspond to free stream Reynolds numbers of 180 and 250, are observed with longer and shorter spanwise wavelengths, respectively, and the onset of three-dimensionality is triggered at a Reynolds number of 173. In the presence of buoyancy, baroclinic vorticity production in the near-wake plays an important role for streamwise vorticity generation. The chaotic wake of the Mode-A instability bifurcates into periodic and quasiperiodic wakes at various heating levels, expressed by the overheat ratio, $\varepsilon =(T_w-T_\infty )/T_\infty$ , where $T_w$ and $T_\infty$ are the temperature of the cylinder surface and the ambient air, respectively. At low heating ( $\varepsilon =0.2$ ), the 3-D Mode-A instability is suppressed leading to a two-dimensional wake flow. Further increase in heating, again brings back the three-dimensionality in the wake through Mode-E instability. The variation of thermophysical properties and the effective Reynolds number with increase in heating level around the cylinder is examined. It is shown that the effect of thermophysical properties competes with the baroclinic streamwise vorticity generation at higher levels of heating ( $\varepsilon \geqslant 0.4$ ) to control the 3-D modes and wake dynamics.

Mesoscale and Large-Eddy Simulation of the Boundary-Layer Process of Cumulus Development over Naqu, Tibetan Plateau Part B: The Low-level Baroclinic Vortex and its Contribution to Cumulus Clouds Formation

Mesoscale and Large-Eddy Simulation of the Boundary-Layer Process of Cumulus Development over Naqu, Tibetan Plateau Part B: The Low-level Baroclinic Vortex and its Contribution to Cumulus Clouds Formation

Baroclinic vortex pulsars in unstable westward flows

We present a computational modeling study of geophysical coherent vortices embedded in horizontally homogeneous, baroclinically unstable, westward background flows with vertical shear. Within an idealized two-layer quasigeostrophic beta-plane model, we discovered two types of robust vortex-wave structures with distinct properties, which remain asymmetric and nonstationary in statistically-equilibrated turbulent flow regimes. The corresponding vortices, referred to as baroclinic vortex pulsars, are characterized by intense vorticity core coupled to the Rossby wave wake. The main conclusion — on the top of various analyses discussed in the paper — are that the vortex pulsars are fundamentally non-isolated coherent vortices, because they extract energy from the background circulation and expel excess potential vorticity, accumulating due to down-gradient material propagation, back into the environment. Both types may coexist as multiple statistically equilibrated states in some range of physical parameters, complicating any parameterization of eddy effects in climate-type models.

Unfolding of shocked hydrodynamic instability at SF[formula omitted] elliptical interface: Physical insights from numerical simulations

The Richtmyer–Meshkov (RM) instability widely exists in variety of industrial and scientific applications, such as in inertial confinement fusion, astrophysics explosions, supersonic combustion, bubble dynamics and cavitation. This study investigates the unfolding physical phenomena of RM instability at SF6 elliptical bubbles using numerical simulations. In contrast to cylindrical bubble, both shocked horizontal/vertical-aligned elliptical bubbles with different aspect ratios are considered, emphasizing the aspect ratio effects on flow morphology, complex wave patterns, interface deformation, vorticity generation, and interface features. For this purpose, a two-dimensional system of compressible Navier–Stokes-Fourier equations for multicomponent flows are solved using by a mixed modal discontinuous Galerkin method. Numerical simulations illustrate that the aspect ratio of elliptical bubbles have a significant influence on the vortex dynamics and the associated RM instability flows in contrast to the cylindrical bubble. In horizontal-aligned elliptical bubbles, some additional complex waves pattern, including inward jet and secondary vortex rings are observed. While, in vertical-aligned elliptical bubbles, the interface between two primary vortex rings is always vertical and has a “hippocampus” appearance due to the enhancement of downstream velocity. The baroclinic vorticity due to misalignment of density and pressure gradients at interface affects the bubble deformation and induces the Kelvin–Helmholtz instability, which leads to turbulent mixing. It is observed that the complexity of the vorticity fields is enhanced with increasing aspect ratios. Further, these aspect ratio effects result in integral diagnostic of important spatially integrated fields, and various interface features.

Large-scale vortex formation in three-dimensional rotating Rayleigh-Bénard convection

Numerical experiments are performed on three-dimensional thermal convection between parallel plates in a rotating system with a larger horizontal region than in previous studies. It is confirmed that a large-scale vortex (LSV) with positive vorticity (cyclonic) is formed over a significant part of the region and its horizontal size increases if the horizontal region is extended. The correlation analysis in the vertical direction shows that the small-scale motion has a typical structure of the baroclinic vortex of thermal convection in the rotating system, whereas the large-scale motion is a barotropic vortex that is not associated with thermal convection. A horizontal spectral analysis of the individual terms in the kinetic energy equation reveals that the nonlinear effect of the small-scale vortex motion caused by the buoyancy force induces a large-scale toroidal component, and that the LSV is maintained by the balance between the nonlinear effect and the viscous dissipation of the large-scale motion. The results of this analysis indicate the importance of kinetic energy damping mechanism for the appearance of LSVs. When weak damping operates at larger scales, it is expected that the maximum extent of the vortex appears even if the horizontal region is extended further. On the other hand, the emergence of LSVs will be prevented when strong enough damping is effective at larger scales.

The nonlinear evolution of two surface quasi-geostrophic vortices

We investigate numerically the evolution of a baroclinic vortex in a two-level surface quasi-geostrophic model. The vortex is composed of two circular patches of uniform buoyancy, one located at each level. We vary the vortex radii, the magnitude of buoyancy, and the vertical distance between the two levels. We also study different radial profiles of buoyancy for each vortex. This article considers two main situations: firstly, initially columnar vortices with like-signed buoyancies. These vortices are contra-rotating, are linearly unstable and may break. Secondly, we consider initially tilted vortices with opposite-signed buoyancies, which may align vertically. Numerical experiments show that (1) identical contra-rotating vortices break into hetons when initially perturbed by low azimuthal modes; (2) unstable, vertically asymmetric, contra-rotating vortices can stabilise nonlinearly more often than vertically symmetric ones, and can form quasi-steady baroclinic tripoles; (3) co-rotating vortices can align when the two levels are close to each other vertically, and when the vortices are initially horizontally distant from each other by less than three radii; (4) for initially more distant vortices, two such vortices rotate around the plane center; and(5) in all cases, the vortex boundaries are disturbed by Rossby waves. These results compare favorably to earlier results with internal quasi-geostrophic vortices. Further modelling efforts may extend the present study to fully three-dimensional ocean dynamics.

Analysis of single-mode Richtmyer–Meshkov instability using high-order incompressible vorticity—streamfunction and shock-capturing simulations

Two- and three-dimensional simulation results obtained using a new high-order incompressible, variable-density vorticity–streamfunction (VS) method and data from previous ninth-order weighted essentially nonoscillatory (WENO) shock-capturing simulations [M. Latini and O. Schilling, “A comparison of two- and three-dimensional single-mode reshocked Richtmyer-Meshkov instability growth,” Physica D 401, 132201 (2020)] are used to investigate the nonlinear dynamics of single-mode Richtmyer–Meshkov instability using a model of a Mach 1.3 air(acetone)/SF6 shock tube experiment [J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005)]. A comparison of the density fields from both simulations with the experimental images demonstrates very good agreement in the large-scale structure with both methods but differences in the small-scale structure. The WENO method captures the small-scale disordered structure observed in the experiment, while the VS method partially captures such structure and yields a strong rotating core. The perturbation amplitude growth from the simulations generally agrees well with the experiment. The simulation bubble and spike amplitudes agree well at early times. At later times, the WENO bubble amplitude is smaller than the VS amplitude and vice versa for the spike amplitude. The predictions of nonlinear single-mode instability growth models are shown to agree with the simulation amplitudes at early-to-intermediate times but underpredict the amplitudes at later times in the nonlinear regime. Visualizations of the mass fraction and enstrophy isosurfaces, velocity and vorticity fields, and baroclinic vorticity production and vortex stretching terms from the three-dimensional simulations indicate that, with the exception of the small-scale structure within the rollups, the VS and WENO results are in good agreement.

Unsteady wave drag reduction in hypersonic flows: Correlations and influences of pulsed energy magnitude and deposition location

This paper presents a numerical study on the unsteady wave drag reduction realized through single pulse energy addition in a hypersonic stream. A single energy pulse of sufficient magnitude added to the stagnation line ahead of a 600 apex angle sphere-cone model placed in a Mach 5.75 stream is analyzed. An in-house developed Finite Volume compressible flow solver is tuned to analyze the flow features and time-dependent drag reduction offered by the pulse energy deposition. Two different flow features are found to be responsible for the drag reduction, one is the lens effect induced by the low-density core of blast wave and the second one is the baroclinic vortex created due to the blast wave-shock wave interaction. Propulsive energy savings associated with different combinations of energy addition parameters is quantified. Based on the 30 data sets generated from the current numerical study, scaling laws are proposed. The proposed scaling laws and mathematical framework derived are found to be suitable to judge the energy demand to realize drag reduction in varied flow and geometric conditions. For the sphere-cone model chosen for the current study, a maximum of 5.2% saving in propulsive energy demand is obtained with a single energy pulse 0.5 J added 50 mm upstream of the blunt body.

Attenuation of perturbation growth of single-mode SF6–air interface through reflected rarefaction waves

Attenuation and even freeze-out (amplitude growth stagnation) of the perturbation amplitude growth of a shocked SF $_6$ –air interface are first realized in shock-tube experiments through reflected rarefaction waves, which produce reverse baroclinic vorticity offsetting the vorticity deposited by the shock. A theoretical model is constructed to predict the perturbation growth after the impact of rarefaction waves, and seven possibilities of amplitude growth are analysed. Experimentally, a planar air–helium interface is used to produce reflected rarefaction waves. Through changing the perturbation wavelength and the time interval of two impacts, five experiments with specific initial conditions are carried out, and three different possibilities of perturbation growth attenuation are realized.

Two-Way Nesting in a Split-Implicit Ocean Model: NCOM

Abstract Presented is the approach, implementation, and evaluation of two-way nesting in a split-implicit ocean model, the Navy Coastal Ocean Model (NCOM). Emphasis is on the strategies applied to feed back fields from the fine-mesh nest (child grid) to the coarse mesh (parent grid). On an appropriate separation of dynamic and feedback interfaces, attention is especially needed for the feedback interface of surface elevation. One particular issue addressed is the inconsistency between the 3D baroclinic velocities and 2D barotropic transports in the feedback. The discrepancy is inherently associated with bathymetry, depth integration, and the need to average over spatial grid points. A simple remedy is proposed and proven to be effective and necessary in realistic coastal applications. In addition to the full two-way nesting, a simplified two-way nesting approach is provided in which only the temperature and salinity are fed back from the nest, and the velocity fields are assumed to self-adjust according to the geostrophic balance. The performance of both approaches is evaluated using the idealized benchmark, propagation of a baroclinic vortex, and an application to the Mississippi River outflow in the northeast Gulf of Mexico, including a comparison with available observations. Discussions are also made on the computational efficiency of the two-way nesting and its sensitivity to the open boundary conditions in regard to noise suppression. Significance Statement The two-way nesting approach reported here can be adapted to other structured-grid ocean models, in particular those using the split-implicit technique. The treatment of the feedback interface for surface elevation is especially important for suppressing the noise production and improving the feedback consistency. An effective procedure is given to amend the inconsistency in the velocity field feedback that is inherently due to bathymetry.

Exploring role of aspect ratio for compressible flow in a rectangular lid-driven cavity with a vertical temperature gradient

Numerical investigation of a compressible fluid in a two-dimensional rectangular lid-driven cavity (LDC) with a vertical temperature gradient is performed by solving the compressible Navier–Stokes equation. Here, we explore the role of aspect ratio (AR) (width/height) on the vorticity dynamics and redistribution by considering three ARs of 1:1, 2:1, and 3:1. The onset and propagation of the instability are explored via time-resolved and instantaneous distributions of vorticity, time-series of streamwise velocity, and its associated spectra. The flow physics reveal that the precessing vortical structures in certain square sub-cells of the rectangular LDC resemble that of orbital motion with a primary core eddy surrounded by gyrating satellite vortices, typical of a supercritical flow in a square LDC. Upon increasing the AR, there is a major shift in the vorticity transfer from the top right corner (acting as the source of maximum vorticity generation) toward the left square sub-cells in the domain. This is further aided by the convective motion due to the imposed destabilizing vertical thermal gradient. The spectra demonstrate that a multi-periodic, chaotic flow is the consistent flow feature for the rectangular LDC for Re = 5500, irrespective of the AR. The compressible enstrophy budget of the rectangular LDC with varying AR is computed for the first time. This shows the dominance of the baroclinic vorticity over the viscous diffusion terms, which was conceived of as the major contributor to the creation of rotational flow structures.

Evolution of the gas-liquid interface dominated by Richtmyer-Meshkov instability

As injection pressure for diesel spray increases, the Richtmyer-Meshkov (RM) instability increasingly impacts the interface, which dominates the deformation and breakup of the liquid interface together with the Rayleigh–Taylor (RT) instability, the Kelvin–Helmholtz (KH) instability, and turbulence, thus the breakup of sprays. Study on the gas-liquid instability dominated by RM instability is important to reveal the multiphase flow coupling in the nozzle and mechanism of the primary breakup. In this paper, a high-precision code for two-phase flow is proposed and its reliability is verified. Then the mechanism of interface evolution under high-speed airflow with the impact of RM instability is explored. The experimental and numerical methods were employed. It was found that the evolution of the gas-liquid interface can be divided into two stages according to the relative positional relationship between the shock wave and the droplet. In the first stage, the initial shock wave intersects with interface of droplet, and the reflected and refractive patterns of the shock wave change with the varying angle between the shock wave and the interface. The change of the pressure distribution and the accumulation of baroclinic vorticity at the interface play essential roles in the instability and deformation of the droplet after the initial shock wave separates from the droplet interface. In the second stage, the droplet surface gradually forms the structure of the spikes and bubbles, and the airflow with different velocities significantly influences the morphology of the droplets during the breakup, causing different breaking patterns.

Symmetric Stability of Vertical Baroclinic Vortices with a Warm Core

Symmetric Stability of Vertical Baroclinic Vortices with a Warm Core

Symmetric Stability of Vertical Baroclinic Vortices with a Warm Core

An attempt has been made to relate the morphological characteristics of intense convective vortices, such as waterspouts and dust devils, to their hydrodynamic stability. The symmetric stability of cyclostrophically balanced vertical baroclinic vortices, whose radius of maximum wind depends on height, is considered. It shows the stability of narrow vortices, nearly cylindrical at the bottom, with a radius that then increases with height at an increasing rate and becomes infinite at a finite level above the Earth’s surface. On the contrary, wider conical vortices satisfy the necessary condition of instability, and it is hypothesized that this partly explains the more diffuse, disorganized nature of this kind of dust devils. The possibility of taking into account the general rotation in the problem is considered.

Numerical Analysis of Airfoil Flow Control Using a Nanosecond Pulsed Plasma Actuator

The control mechanism of a nanosecond dielectric barrier discharge (NS-DBD) actuator for suppressing laminar separation on airfoils was investigated using two-dimensional scale-adaptive simulations. To model the control effect of the NS-DBD actuator, a surface heating approach based on the analytical solution for transient one-dimensional heat conduction has been used. The focus of the investigation lies in the study of vortex formation and evolution induced by the actuator. A NACA 0015 profile was simulated at 14° with 250,000 chord-based Reynolds number. Regarding energy deposition, a low-energy case and a high-energy case were simulated. Several actuation parameters were varied, including the electrode position and surface temperature. In addition, the influence of constant and temperature-dependent modeling of the kinematic viscosity was investigated. The results for the time-averaged pressure coefficients show excellent agreement with measurement results. High grid resolution in the boundary layer allowed a detailed investigation of the vortex formation process. The main finding is that vortices are generated by baroclinic torque and vortex dilatation and not by a Kelvin–Helmholtz instability. Initially, tiny vortices form at the beginning of the separation region. Subsequently, these vortices are carried downstream and grow in size, thus preventing full separation due to momentum transfer from the external flow.

Asymmetry of motion: vortex rings crossing a density gradient

Vortex rings are critical for thrust production underwater. In the ocean, self-propelled mesozooplankton generate vortices while swimming within a weakly stratified fluid. While large-scale biogenic transport has been observed during vertical migration in the wild and lab experiments, little focus has been given to the evolution of induced vortex rings as a function of their propagation direction relative to the density gradient. In this study, the evolution of an isolated vortex ring crossing the interface of a stable two-layer system is examined as a function of its translation direction with respect to gravity. The vortex ring size and position are visualized using planar laser-induced fluorescence (PLIF) and the induced vorticity field derived from particle image velocimetry (PIV) is examined. It is found that the production of baroclinic vorticity significantly affects the propagation of vortex rings crossing the density interface. As a result, any expected symmetry between vortex rings travelling from dense to light fluids and from light to dense fluids breaks down. In turn, the maximum penetration depth of the vortex ring occurs in the case in which the vortex propagates against the density gradient due to the misalignment of the pressure and density gradients. Our results have far-reaching implications for the characterization of local ecosystems in marine environments.

Numerical study of Richtmyer–Meshkov instability of a flat interface driven by perturbed and reflected shock waves

In this paper, the Richtmyer–Meshkov instability of a flat gas interface driven by perturbed and reflected shock waves is numerically investigated. The flat gas interface evolves into a “Λ”-shaped structure with a central N2 cavity and steps on both sides, due to the impaction of the perturbed shock wave. After the secondary collision of the reflected shock wave from the high-density region to the low-density region, the gas interface first undergoes phase inversion, and the “Λ” interface then evolves into a bubble and spike structure. Three cases of different Atwood numbers, N2/SF6, N2/Kr, and N2/CO2, are studied. The collision time and position of the reflected shock wave and the interface, the induced spikes, bubbles and gas mixing, are compared in detail. The formation of the spike and bubble is related to the RM instability developed by the collision of the reflected shock wave and the perturbed interface, in which the effect of baroclinic vorticity is highlighted. With the increase in the Atwood number, the density gradient and the baroclinic vorticity become larger, which induces more vortex along the interface. Kelvin Helmholtz unstable vortices are generated on the “legs” of the spikes due to shearing. The main spike structure is stretched and broken with the effect of the vortex, forming a turbulent mixing zone.

Suppression mechanism of Richtmyer–Meshkov instability by transverse magnetic field with different strengths

The Richtmyer–Meshkov instability (RMI) is caused by an incident planar shock wave impinging on the heavy-gas-density interface. We have numerically investigated the RMI controlled by different transverse magnetic-field strengths based on the ideal compressible magnetohydrodynamics (MHD) equations. The MHD equations are solved by the corner transport upwind + constrained transport algorithm, which guarantees a divergence-free constraint on the magnetic field. We discuss the flow characteristics and shock patterns in both classical hydrodynamic and MHD situations and verify our conclusions by comparing the experimental results with the numerical results. The results show that the magnetic field modifies the pressure-gradient distribution, and the baroclinic vorticity splits and attaches to the MHD shock waves. In addition, the results indicate that the interaction of shock wave and density interface changes the distribution of magnetic-field energy and distorts the magnetic induction line in the region of magnetic-field energy accumulation. The distortion of the magnetic induction lines alters the magnetic field gradient and creates a magnetic tension that produces a torque opposing that generated by the shear force on the vorticity layer, so the Kelvin–Helmholtz instability is effectively suppressed and no Kelvin–Helmholtz vortex appears on the vorticity layer. The result is that the interface instability is suppressed.