Vorticity Production Research Articles

Richtmyer-Meshkov instability in dilute gas-particle mixtures with re-shock

The Richtmyer-Meshkov instability (RMI) is investigated in a dilute gas-particle mixture using three-dimensional numerical simulations. This work extends an earlier two-dimensional study [S. Ukai, K. Balakrishnan, and S. Menon, “On Richtmyer-Meshkov instability in dilute gas-particle mixtures,” Phys. Fluids 22, 104103 (2010)] to a larger parameter space consisting of variations in the mass loading and the particle size as well as considering both single-mode and multi-mode interface initializations. In addition, the effect of the presence of particles on re-shock RMI is also investigated. Single-phase numerical predictions of the mixing layer growth-rate are shown to compare well to both experimental and theoretical results. In a dilute gas-particle mixture, the initial growth-rate of RMI shows similar trends compared to previous work; however, the current numerical predictions show that there is an observable increase, not previously predicted, in the growth of the mixing layer at higher mass loadings. For the range of cases considered, an increase as much as 56% is observed. This increase is attributed to additional vorticity production in the mixing layer resulting from inter-phase momentum coupling. Moreover, the presence of particles introduces a continuous drag on the gas-phase resulting in a delay in the time at which re-shock occurs. This delay, which is observed to be as much as 6%, is largest for higher initial mass loadings and smaller particle radii and has a corresponding effect on both the growth-rate of the mixing-layer after re-shock and the final width of the mixing layer. A new semi-analytical correlation is developed and verified against the numerical data to predict the re-shocked RMI growth-rate in dilute gas-particle flows. The correlation shows that the re-shock RMI growth-rate is linearly proportional to the velocity jump at re-shock, the molecular mixing fraction, and the multi-phase Atwood number. Depending on the initial mass loading and particle radii, the re-shock RMI growth-rates were observed to be reduced by as much as 48% in some cases with variations of around 26% in the width of the mixing layer after re-shock.

Interaction Between Swirl Number Fluctuations and Vortex Shedding in a Single-Nozzle Turbulent Swirling Fully-Premixed Combustor

Flame response to imposed velocity fluctuations is experimentally measured in a single-nozzle turbulent swirling fully-premixed combustor. The flame transfer function is used to quantify the flame's response to imposed velocity fluctuations. Both the gain and phase of the flame transfer function are qualitatively similar for all operating conditions tested. The flame transfer function gain exhibits alternating regions of decreasing gain with increasing forcing frequency followed by regions of increasing gain with increasing forcing frequency. This alternating behavior gives rise to gain extrema. The flame transfer function phase magnitude increases quasi-linearly with increasing forcing frequency. Deviations from the linear behavior occur in the form of inflection points. Within the field, the current understanding is that the flame transfer function gain extrema are caused by the constructive/destructive interference of swirl number fluctuations and vortex shedding. Phase-synchronized images of forced flames are acquired to investigate the presence/importance of swirl number fluctuations, which manifest as fluctuations in the mean flame position and vortex shedding in this combustor. An analysis of phase-synchronized flame images reveals that mean flame position fluctuations are present at forcing frequencies corresponding to flame transfer function gain minima but not at forcing frequencies corresponding to flame transfer function gain maxima. This observation contradicts the understanding that flame transfer function gain maxima are caused by the constructive interference of mean flame position fluctuations and vortex shedding, since mean flame position fluctuations are shown not to exist at flame transfer function gain maxima. Further analysis of phase-synchronized flame images shows that the variation of the mean flame position fluctuation magnitude with forcing frequency follows an inverse trend to the variation of flame transfer function gain with forcing frequency, i.e., when the mean flame position fluctuation magnitude increases, the flame transfer function gain decreases and vice versa. Based on these observations it is concluded that mean flame position fluctuations are a subtractive effect. The physical mechanism through which mean flame position fluctuations decrease flame response is through the interaction of the flame with the Kelvin–Helmholtz instability of the mixing layer in the combustor. When mean flame position fluctuations are large the flame moves closer to the mixing layer and damps the Kelvin–Helmholtz instability due to the increased kinematic viscosity, fluid dilatation, and baroclinic production of vorticity with the opposite sign associated with the high temperature reaction zone.

Physical and numerical investigation of cavitating flows around a pitching hydrofoil

The objective of this paper is to investigate cavitating flows around a pitching hydrofoil via combined physical and numerical studies. The aims are to (1) improve the understanding of the interplay between unsteady cavitating flow, hydrofoil motion, and hydrodynamic performance, (2) quantify the influence of pitching rate on subcavitating and cavitating responses, and (3) quantify the influence of cavitation on the hydrodynamic load coefficients and surrounding flow structures. Results are presented for a NACA66 hydrofoil undergoing controlled, slow $(\dot \alpha = 6^\circ /{\rm s})$(α̇=6∘/s) and fast $(\dot \alpha = 63^\circ /{\rm s})$(α̇=63∘/s) pitching motions from α = 0° to α = 15° and back to α = 0° for both subcavitating and cavitating conditions at a moderate Reynolds number of Re = 750 000. The experimental studies were conducted in a cavitation tunnel at the French Naval Academy, France. The numerical simulations are performed by solving the incompressible, multiphase Unsteady Reynolds-Averaged Navier-Stokes Equations via the commercial code CFX using a transport equation-based cavitation model; a modified k-ω SST turbulence model is used to account for the effect of local compressibility on the turbulent eddy viscosity. The results showed that increases in the pitching rate suppressed laminar to turbulent transition, delayed stall, and significantly modified post-stall behavior. Cavitation inception at the leading edge modified the pressure distribution, which in turn significantly changed the interaction between leading edge and trailing edge vortices, and hence the magnitude as well as the frequency of the load fluctuations. For a fixed cavitation number, increases in pitching rate lead to increase in cavitation volume, which in turn changed the cavity shedding frequencies and significantly modified the hydrodynamic loads. Inversely, the leading edge cavitation observed for the low pitching velocity case tends to stabilize the stall because of the decrease of the pressure gradient due to the formation of the cavity. The results showed strong correlation between the cavity and vorticity structures, which suggest that the inception, growth, collapse and shedding of sheet/cloud cavities are important mechanisms for vorticity production and modification.

Physical and numerical investigation on transient cavitating flows

The objective of this paper is to investigate transient cavitating flows around a hydrofoil via combined physical and numerical studies. The aims are to 1) investigate the periodic formation, breakup, shedding, and collapse of the sheet/cloud cavities, 2) provide a better insight in the physical mechanism that governs the dynamics and structures of the sheet/cloud cavitation, 3) quantify the influence of cavitation on the surrounding flow structures. Results are presented for a Clark-Y hydrofoil fixed at an angle of attack of α=8° at a moderate Reynolds number, Re=7×105, for sheet/cloud cavitating conditions. The experimental studies were conducted in a cavitation tunnel at Beijing Institute of Technology, China. The numerical simulations are performed by solving the incompressible, multiphase unsteady Reynolds-averaged Navier-Stokes (URANS) equations via the commercial code CFX using a transport equation-based cavitation model; a filter-based density corrected model (FBDCM) is used to regulate the turbulent eddy viscosity in both the cavitation regions near the foil and in the wake. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding in accordance with the quantitative features observed in the experiment. Regarding vapor shedding in the cavitating flow around the three-dimensional foil, it is primarily attributed to the effect of the re-entrant flow, which is formed due to the strong adverse pressure gradient. The results show strong correlation between the cavity and vorticity structures, demonstrating that the inception, growth, shedding, and collapse of sheet/cloud cavities are important mechanisms for vorticity production and modification.

Combined Experimental and Computational Investigation of Unsteady Structure of Sheet/Cloud Cavitation

The objective of this paper is to apply combined experimental and computational modeling to investigate unsteady sheet/cloud cavitating flows. In the numerical simulations, a filter-based density corrected model (FBDCM) is introduced to regulate the turbulent eddy viscosity in both the cavitation regions on the foil and in the wake, which is shown to be critical in accurately capturing the unsteady cavity shedding process, and the corresponding velocity and vorticity dynamics. In the experiments, high-speed video and particle image velocimetry (PIV) technique are used to measure the flow velocity and vorticity fields, as well as cavitation patterns. Results are presented for a Clark-Y hydrofoil fixed at an angle of attack of α = 8 deg at a moderate Reynolds number, Re = 7 × 105, for both subcavitating and sheet/cloud cavitating conditions. The results show that for the unsteady sheet/cloud cavitating case, the formation, breakup, shedding, and collapse of the sheet/cloud cavity lead to substantial increase in turbulent velocity fluctuations in the cavitating region around the foil and in the wake, and significantly modified the wake patterns. The turbulent boundary layer thickness is found to be much thicker, and the turbulent intensities are much higher in the sheet/cloud cavitating case. Compared to the wetted case, the wake region becomes much broader and is directed toward the suction side instead of the pressure side for the sheet/cloud cavitation case. The periodic formation, breakup, shedding, and collapse of the sheet/cloud cavities, and the associated baroclinic and viscoclinic torques, are shown to be important mechanisms for vorticity production and modification.

Stability and Vorticity Production in Stratified Astrophysical Disks

We study local linear non-axisymmetric perturbations in fully stratified 3D astrophysical disks. Radial stratification is set to be described by power law, while vertical stratification is set to be exponential. We analyze the linear perturbations in local shearing sheet frame and derive WKB dispersion equation. We show that stratification laws of the disk matter define not only the thermal stability of the disk, but also the efficiency of the potential vorticity production by rotationg convective turbulence in astrophysical disks. Taken developed convective turbulence we assume nonlinear tendencies set by linear spectrum and show that vortices are unlikely to be generated in rigid rotation flows. In contrast, differential rotation yields much higher vortex production rate that depends on the disk thickness, distance from the central object and the spectral characteristics of the developed thermal turbulence. It seems that measurements of the temperature and density distribution in accretion disks may indicate the efficiency of the turbulence development and largely define the luminosity characteristic of accreting flows.

Influence of active control on STG-based generation of streamwise vortices in near-wall turbulence

AbstractNear-wall streamwise vortices are closely related to the generation of high skin friction in wall-bounded turbulent flows. A common feature of controlled, friction-reduced turbulent flows is weakened near-wall streamwise vortices. In the present study, the streak transient growth (STG) mechanism for generating near-wall streamwise vortices by Schoppa & Hussain (J. Fluid Mech., vol. 453, 2002, pp. 57–108) is employed, and the opposition control proposed by Choi, Moin & Kim (J. Fluid Mech., vol. 262, 1994, pp. 75–110) is imposed during the transient growth process of perturbations to determine how active control affects the generation of quasi-streamwise vortices. In the transient growth stage, when the detection plane is located near the wall (${ y}_{d}^{+ } = 15$), the control can suppress the production of streamwise vorticity by weakening the near-wall vertical velocity; when the detection plane moves away from the wall (${ y}_{d}^{+ } = 28$), the control has the opposite effect. In the vortex generation stage, the control cannot change the dominance of the stretching effect. Controls imposed at different stages reveal the importance of the STG stage in vortex generation. Strengthened out-of-phase control and lessened in-phase control are proposed as an extension of the original opposition-control scheme. Application in a fully developed turbulent channel flow shows that strengthened ${ y}_{d}^{+ } = 10$ control can yield an even higher drag reduction rate than the original ${ y}_{d}^{+ } = 15$ control. Moreover, lessened ${ y}_{d}^{+ } = 28$ control can also achieve drag reduction and turbulence suppression.

Vorticity and entropy production in tilted Szekeres spacetimes

We analyze the properties of the tilted Szekeres spacetime, i.e. the version of such spacetime as seen by a congruence of observers with respect to which the fluid is moving. The imperfect fluid and the kinematical variables associated to the four-velocity of the fluid assigned by tilted observers are studied in detail. As it happens for the case of the Lemaitre--Tolman--Bondi spacetime, the fluid evolves nonreversibly (with nonvanishing entropy production) and is nongeodesic. However unlike that later case, the tilted observer detects vorticity in the congruence of the fluid world lines. Also, as for the nontilted congruence the magnetic part of the Weyl tensor vanishes, reinforcing the nonradiative character of this kind of spacetime. Possible physical implications of these results are discussed.

Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube

Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and the development of treatment options imperative. The effect of motion of the coronary artery due to the motion of the myocardium is not extensively studied. In this work, we focus our investigation on the localized hemodynamic effects of dynamic changes in curvature and torsion. It is our objective to understand and reveal the mechanism by which changes in curvature and torsion contribute towards the observed wall shear stress distribution. Such adverse hemodynamic conditions could have an effect on circumferential intimal thickening. Three-dimensional spatiotemporally resolved computational fluid dynamics (CFD) simulations of pulsatile flow with moving wall boundaries were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with stationary walls is used as the baseline control case. In order to study the effect of curvature and torsion variation on local hemodynamics, this baseline model is compared to models where the curvature, torsion, and both curvature and torsion change. The simulations provided detailed information regarding the secondary flow dynamics. The results suggest that changes in curvature and torsion cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients and secondary flow patterns. The wall shear stress (WSS) varies by a maximum of 22% when the curvature changes, by 3% when the torsion changes, and by 26% when both the curvature and torsion change. The oscillatory shear stress (OSI) varies by a maximum of 24% when the curvature changes, by 4% when the torsion changes, and by 28% when both the curvature and torsion change. We demonstrate that these changes are attributed to the physical mechanism associating the secondary flow patterns to the production of vorticity (vorticity flux) due to the wall movement. The secondary flow patterns and augmented vorticity flux affect the wall shear stresses. As a result, this work reveals how changes in curvature and torsion act to modify the near wall hemodynamics of arteries.

Formation of columnar baroclinic vortices in thermally stratified nonlinear spin-up

AbstractWe investigate the mechanisms that affect the formation of columnar vortices for spin-up in a cylinder where the temperatures at the horizontal walls are prescribed. Numerical results from the three-dimensional Navier–Stokes equations show that a short-lived instability, suppressed by the combined effect of rotation and stratification, generates small temperature variations in the azimuthal direction. Temperature-gradient anomalies produce vorticity, and these vortices stir the fluid at the interface of the central vortex core thus reinforcing the temperature gradients. For sufficiently strong temperature gradients, the central vortex core breaks up into several columnar vortices. It is found, in particular, that small aspect ratios (height over radius of the cylindrical fluid layer) $\Gamma = 1, 2$ tend to inhibit the instability, while larger ones, $\Gamma = 3. 3$, have the opposite effect. The main source of instability is the baroclinic vorticity production and not the presence of a solid sidewall since, counter-intuitively, the flow is more unstable for a free-slip boundary than for a no-slip one. Finally the effect of the temperature boundary conditions (isothermal versus adiabatic) on the horizontal boundaries has been investigated. The adiabatic boundaries help to preserve for longer times the sloping density interfaces that feed, with their potential energy, the baroclinic vorticity production; this results in more unstable flows.

Suppression of the vorticity production by the unsteady rarefaction waves in the blast-bubble interactions

Interactions between a blast wave and an isolated density-inhomogeneity were investigated numerically. A blast wave that consisted of a leading-edge shock wave followed by rarefaction waves impinged on a spherical light-gas bubble that models the density-inhomogeneity. As a result, it was found that the baroclinically produced vorticity on the bubble/atmosphere interface was suppressed significantly by the presence of the rarefaction waves when the shock strength was weak. The rarefaction waves became less influential as the shock strength was increased.

The influence of large-scale structures on entrainment in a decelerating transient turbulent jet revealed by large eddy simulation

To provide a better understanding of the fluid mechanical mechanisms governing entrainment in decelerating jets, we performed a large eddy simulation (LES) of a transient air jet. The ensemble-averaged LES calculations agree well with the available measurements of centerline velocity, and they reveal a region of increased entrainment that grows as it propagates downstream during deceleration. Within the temporal and spatial domains of the simulation, entrainment during deceleration temporarily increases by roughly a factor of two over that of the quasi-steady jet, and thereafter decays to a level lower than the quasi-steady jet. The LES results also provide large-structure flow details that lend insight into the effects of deceleration on entrainment. The simulations show greater growth and separation of large vortical structures during deceleration. Ambient fluid is engulfed into the gaps between the large-scale structures, causing large-scale indentations in the scalar jet boundary. The changes in the growth and separation of large structures during deceleration are attributed to changes in the production and convection of vorticity. Both the absolute and normalized scalar dissipation rates decrease during deceleration, implying that changes in small-scale mixing during deceleration do not play an important role in the increased entrainment. Hence, the simulations predict that entrainment in combustion devices may be controlled by manipulating the fuel-jet boundary conditions, which affect structures at large scales much more than at small scales.

On the thermo-acoustic Fant equation

A ‘reduced complexity’ equation is derived to investigate combustion instabilities of a Rijke burner. The equation is nonlinear and furnishes limit cycle solutions for finite amplitude burner modes. It is a generalisation to combustion flows of the Fant equation used to investigate the production of voiced speech by unsteady throttling of flow by the vocal folds [G. Fant, Acoustic Theory of Speech Production. Mouton, The Hague, 1960]. In the thermo-acoustic problem the throttling occurs at the flame holder. The Fant equation governs the unsteady volume flow past the flame holder which, in turn, determines the acoustics of the entire system. The equation includes a fully determinate part that depends on the geometry of the flame holder and the thermo-acoustic system, and terms defined by integrals involving thermo-aerodynamic sources, such as a flame and vortex sound sources. These integrals provide a clear indication of what must be known about the flow to obtain a proper understanding of the dynamics of the thermo-acoustic system. Illustrative numerical results are presented for the linearised equation. This governs the growth rates of the natural acoustic modes, determined by system geometry, boundary conditions and mean temperature distribution, which are excited into instability by unsteady heat release from the flame and damped by large scale vorticity production and radiation losses into the environment. In addition, the equation supplies information about the ‘combustion modes’ excited by the local time-delay feedback dynamics of the flame.

Vorticity production and survival in viscous and magnetized cosmologies

We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to the diluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length bellow which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay-rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated.

Numerical study on the evolution of the shock-accelerated SF6 interface: Influence of the interface shape

The early phases of the shock interaction process on two-dimensional interfaces with different shapes are numerically investigated in this study, which are closely related to the shock refraction and reflection, vorticity production and transport. The numerical method employs an adaptive unstructured quadrilateral mesh, which can capture the wave pattern and interface evolution very well. Simulations are carried out under the conditions of an incident shock Mach number of 1.2 and the light/heavy (air/SF6) interface. Five different shapes are considered in the simulations: rectangle, ellipse, diamond and two kinds of triangle. The results show that the interfacial shapes can influence the wave patterns particularly on the shape and evolution of refracted shock waves. The generation and the distribution of vorticity on the interfaces with five different shapes also have dissimilarities. The circulation deposition on five interfaces is quantitatively investigated and compared with theoretical model. A good agreement is found between the numerical results and the predictions by the theoretical model. Some characteristic scales of the interface are tracked. Under the influence of nonlinear-acoustic effect and vorticity effect, the interfaces present different evolution modes.

Computational study of shock‐wave interaction with solid obstacles using immersed boundary methods

SUMMARYIn this study, an immersed boundary (IB) method based on a direct forcing is coupled with a high‐order weighted‐essentially non‐oscillatory (WENO) scheme to simulate fluid–solid interaction (FSI) problems with complex geometries. The IB is a general simulation method for FSI, whereas the WENO is an efficient scheme for fluid flow simulations and shock waves, and both of them work on regular cartesian grids. The effectiveness and the accuracy of the coupled scheme are first analyzed on well‐documented supersonic test problems for a wide range of Mach numbers. The results are in good agreement with both analytical and experimental data. A comprehensive analysis of the interaction of the moving shock through an array of cylinder matrix is then conducted by varying the number of cylinders in the matrix block while keeping the same opening passage. The relaxation length between two adjacent columns of cylinders is kept identical to study uniquely the effect of surface‐to‐volume ratio of the obstacle matrix. It is shown that the configuration with higher surface‐to‐volume ratio produces more post‐shock flow instabilities downstream of the matrix block. The complex shock/shock and shock/vortex interactions are well resolved by the present computation. It is being observed that after the passage of the shock through the cylinder matrix, eddies of different length scales are generated, but the later stage of shock/vortex and shocklet/vortexlet interactions are different for the two cases. The analysis of the PSD of the total kinetic energy globally conforms to Richardson's inviscid cascade. An intermittent peaked PDF of downstream instantaneous vorticity field is obtained in the limit of Re → ∞ . The baroclinic production of vorticity is found to be feeble as previously founded by Sun and Takayama (J. Fluid Mech. 2003; 478:237–256). Copyright © 2011 John Wiley & Sons, Ltd.

The intense vorticity structures near the turbulent/non-turbulent interface in a jet

AbstractThe characteristics of the intense vorticity structures (IVSs) near the turbulent/non-turbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about $5\eta $ from the T/NT interface, where $\eta $ is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are $R/ \eta \approx 4. 6$, ${u}_{0} / {u}^{\ensuremath{\prime} } \approx 0. 8$, and ${\mathit{Re}}_{\Gamma } / { \mathit{Re}}_{\lambda }^{1/ 2} \approx 28$, where ${u}_{0} $, and ${\mathit{Re}}_{\lambda } $ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius $R$, tangential velocity ${u}_{0} $ and circulation $\Gamma $ of the IVSs increase as the T/NT interface is approached, while the vorticity norm $\vert \omega \vert $ stays approximately constant. Specifically $R$, ${u}_{0} $ and $\Gamma $ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.

Navier–Stokes equations on a flat cylinder with vorticity production on the boundary

We study a singular version of the incompressible two-dimensional Navier–Stokes (NS) system on a flat cylinder , with Neumann conditions for the vorticity and a vorticity production term on the boundary to restore the no-slip boundary condition for the velocity . The problem is formulated as an infinite system of coupled ordinary differential equations (ODEs) for the Neumann Fourier modes. For a general class of initial data we prove existence and uniqueness of the solution, and equivalence to the usual NS system. The main tool in the proofs is a suitable decay of the modes, obtained by the explicit form of the ODEs. We finally show that the resulting expansions of the velocity u and of its first and second space derivatives converge and define continuous functions up to the boundary.

Photospheric magnetic vortex structures

Abstract. Using direct numerical magneto-hydrodynamic (MHD) simulations, we demonstrate the evidence of two physically different types of vortex motions in the solar photosphere. Baroclinic motions of plasma in non-magnetic granules are the primary source of vorticity in granular regions of the solar photosphere, however, there is a significantly more efficient mechanism of vorticity production in strongly magnetised intergranular lanes. These swirly motions of plasma in intergranular magnetic field concentrations could be responsible for the generation of different types of MHD wave modes, for example, kink, sausage and torsional Alfvén waves. These waves could transport a relevant amount of energy from the lower solar atmosphere and contribute to coronal plasma heating.

Unsteady wake dynamics and heat transfer in forced and mixed convection past a circular cylinder in cross flow for high Prandtl numbers

This paper investigates the combined effect of Prandtl number and Richardson number on the wake dynamics and heat transfer past a circular cylinder in crossflow using a SUPG based finite element method. The computations are carried out for 80 < Re < 180, 0.7 < Pr < 100 and 0 ⩽ Ri ⩽ 2 . The results have been presented for both forced and mixed convection flows. In the case of forced convection, crowding of temperature contours with reduced spatial spread is observed for increasing Prandtl numbers. The local and average Nusselt numbers are found to increase with increasing Reynolds number and Prandtl number. The average Nusselt number and Colburn factor are found to vary as Re 0.548 Pr 0.373 and Re −0.452, respectively. The extrapolated results of the average Nusselt number for low and high Reynolds numbers are found to match quite well with the available results in literature. Effect of Prandtl number shows various interesting phenomena for the mixed convective flows. Increasing the Prandtl numbers resulted in decreasing deflection and strength in the wake structures. The effect of baroclinic vorticity production during vortex shedding has been demonstrated at the vicinity of the cylinder and near wake. The Strouhal number is found to decrease with increasing Prandtl number, in the case of buoyancy induced flow. The effect of increasing Prandtl number is manifested as the stabilizing effect in the flow. This is, perhaps, the first time that such behavior for the Prandtl number is being reported. Additionally it is observed that the average Nusselt number decreases with increasing Richardson number.