Helmholtz Vortices Research Articles

Flow structure and unsteady fluctuation with separation over a two-dimensional backward-facing step

The flow over a backward-facing step (BFS) is a typical separation and reattachment flow. Its flow structures and unsteady mechanisms are still not well explored. In this paper, the global velocity fields of a BFS are obtained by a synchronous particle image velocimetry (PIV) system with Reh = 5 345 (Reynolds number) and Er = 2 (expansion ratio). Flow structures are distinguished and defined by the fraction of the negative velocity (upn). The reattachment zone (Lr) is quantitatively defined as (u0.9, u0.1) on the bottom wall. Spatial distribution of the large-scale vortices couples well with the divided flow structures and their temporal evolution presenting four stages (forming, developing, shedding and redeveloping) when travel downstream. The unsteady motions with various low frequencies are well explained by the coherent vortices and flow structures. Among the unsteady low frequency motions, the Kelvin Helmholtz (KH) vortices and the oscillation of Xr (OX) come likely from the free shear layer. The KH vortices contribute to the unsteadiness of the temporal flow, and the OX is the primary response to the vortical fluctuations.

Simulation of a lock-release gravity current based on a non-hydrostatic model

Abstract Gravity currents are important in many fields, including the estuarine sciences, meteorology and hydraulic engineering. The NHWAVE (non-hydrostatic wave) model was applied to simulate the detailed interface structure between a lock-release gravity current and the ambient fluid. The simulated structures, including the front height, front position and velocity of the current, are consistent with the results of laboratory experiments. However, the internal structure of the current is different from that revealed by previous research. The Kelvin–Helmholtz phenomenon in the interface and the interface vortices were successfully captured by the NHWAVE model. The difference in velocity between the front and rear vortices leads to entrainment, further causing changes in the shapes and amount of vortices. Flow field results obtained by the NHWAVE model reveal the existence of a significant circular flow, as well as some small eddies within it. The significant circular flow supports the forward movement of the current, whereas the small eddies reflect interface vortices. In contrast, hydrostatic simulation with the same model settings fails to capture the vortices. This research shows that the NHWAVE model performs better than a hydrostatic model when simulating the Kelvin–Helmholtz instability phenomenon and vortex entrainment in a lock-release gravity current.

The inverse problem for homothetic polygonal central configurations

We prove that, for some potentials (including the Newtonian one and the potential of Helmholtz vortices in the plane), central configurations with nonzero total mass consisting of two homothetic polygons of arbitrary size can only occur if the masses at each polygon are equal. The same result is true for many polygons as long as the ratios between the radii of the polygons are sufficiently large.

Experimental and numerical studies of the vortex-induced vibration behavior of an asymmetrical composite beam bridge

The vortex-induced vibration behavior and mechanism of an asymmetrical composite beam cable-stayed bridge is investigated by means of aerodynamic sectional tests and computational fluid dynamics methods. Tests are performed for the bridge deck under five wind attack angles (0°, ±2.5°, and ±5°) and two wind directions (0° and 180°) during the completion and construction stages. The influence of damping ratios, wind barriers, and vehicles on the vortex-induced vibration behaviors of the bridge deck is examined. The test and simulation results show that the properties of the vortex-induced vibrations vary with the wind direction as a result of the asymmetry of the main girder. The vertical maximum vortex-induced vibration amplitude of the bridge deck was found to occur at the wind attack angle of −5° and wind direction of 180°, while the torsional maximum was found at the wind attack angle of −5° and wind direction of 0°. Both vehicles and wind barriers have amplification effects on the vortex-induced vibrations of the bridge deck when the wind direction is 180°. The vortex-induced vibration of the bridge deck can be effectively mitigated when the damping ratio increases from 0.5% to 1.5%. The vortex-induced vibration mechanism of the bridge deck under different wind directions can be attributed to the same vortex shedding mode (the Kelvin–Helmholtz vortex and the Kármán vortex street). While, the location of the vortex generation and direction of the vortex shedding at the wake are strongly influenced by the wind directions, resulting in the variation of the vortex-induced vibration properties of the bridge deck with the wind direction. This study provides a guideline for the design of bridges with asymmetrical main girders to suppress the VIV.

The Evolution of Magnetic Rayleigh–Taylor Unstable Plumes and Hybrid KH-RT Instability into a Loop-like Eruptive Prominence

Abstract MRT-unstable plumes are observed in a loop-like eruptive prominence using Solar Dynamic Observatory/Atmospheric Imaging Assembly observations. The small-scale cavities are developed within the prominence, where perturbations trigger dark plumes (P1 and P2) propagating with speeds of 35–46 km s−1. The self-similar plume formation initially shows the growth of a linear MRT-unstable plume (P1), and thereafter the evolution of a nonlinear single-mode MRT-unstable second plume (P2). A differential emission measure analysis shows that plumes are less dense and hotter than the prominence. We have estimated the observational growth rate for both plumes as 1.32 ± 0.29 × 10−3 s−1 and 1.48 ± 0.29 × 10−3 s−1, respectively, which are comparable to the estimated theoretical growth rate (1.95 × 10−3 s−1). The nonlinear phase of an MRT-unstable plume (P2) may collapse via a Kelvin–Helmholtz vortex formation in the downfalling plasma. Later, a plasma thread is evident in the rising segment of this prominence. It may be associated with the tangled field and Rayleigh–Taylor instability. The tangled field initiates shearing at the prominence–cavity boundary. Due to this shear motion, the plasma downfall occurred at the right part of the prominence–cavity boundary. It triggers the characteristic KH unstable vortices and MRT-unstable plasma bubbles propagating at different speeds and merging with each other. The shear motion and lateral plasma downfall may initiate hybrid KH-RT instability there.

Rotating planar gravity currents at moderate Rossby numbers: fully resolved simulations and shallow-water modelling

The flow of a gravity current of finite volume and density $\unicode[STIX]{x1D70C}_{1}$ released from rest from a rectangular lock (of height $h_{0}$) into an ambient fluid of density $\unicode[STIX]{x1D70C}_{0}$ (${<}\unicode[STIX]{x1D70C}_{1}$) in a system rotating with $\unicode[STIX]{x1D6FA}$ about the vertical $z$ is investigated by means of fully resolved direct numerical simulations (DNS) and a theoretical model (based on shallow-water and Ekman layer spin-up theories, including mixing). The motion of the dense fluid includes several stages: propagation in the $x$-direction accompanied by Coriolis acceleration/deflection in the $-y$-direction, which produces a quasi-steady wedge-shaped structure with significant anticyclonic velocity $v$, followed by a spin-up reduction of $v$ accompanied by a slow $x$ drift, and oscillation. The theoretical model aims to provide useful insights and approximations concerning the formation time and shape of wedge, and the subsequent spin-up effect. The main parameter is the Coriolis number, ${\mathcal{C}}=\unicode[STIX]{x1D6FA}h_{0}/(g^{\prime }h_{0})^{1/2}$, where $g^{\prime }=(\unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{0}-1)g$ is the reduced gravity. The DNS results are focused on a range of relatively small Coriolis numbers, $0.1\leqslant {\mathcal{C}}\leqslant 0.25$ (i.e. Rossby number $Ro=1/(2{\mathcal{C}})$ in the range $2\leqslant Ro\leqslant 5$), and a large range of Schmidt numbers $1\leqslant Sc<\infty$; the Reynolds number is large in all cases. The current spreads out in the $x$ direction until it is arrested by the Coriolis effect (in ${\sim}1/4$ revolution of the system). A complex motion develops about this state. First, we record oscillations on the inertial time scale $1/\unicode[STIX]{x1D6FA}$ (which are a part of the geostrophic adjustment), accompanied by vortices at the interface. Second, we note the spread of the wedge on a significantly longer time scale; this is an indirect spin-up effect – mixing and entrainment reduce the lateral (angular) velocity, which in turn decreases the Coriolis support to the $\unicode[STIX]{x2202}h/\unicode[STIX]{x2202}x$ slope of the wedge shape. Contrary to non-rotating gravity currents, the front does not remain sharp as it is subject to (i) local stretching along the streamwise direction and (ii) convective mixing due to Kelvin–Helmholtz vortices generated by shear along the spanwise direction and stemming from Coriolis effects. The theoretical model predicts that the length of the wedge scales as ${\mathcal{C}}^{-2/3}$ (in contrast to the Rossby radius $\propto 1/{\mathcal{C}}$ which is relevant for large ${\mathcal{C}}$; and in contrast to ${\mathcal{C}}^{-1/2}$ for the axisymmetric lens).

Exact solution of the compressible Euler–Helmholtz equation and the millennium prize problem generalization

SummaryFor the first time the exact strong solution of the three-dimensional (3D) compressible Euler–Helmholtz (EH) vortex equation in unbounded space is obtained. It corresponds to the general solution obtained in Euler variables for the 3D Riemann–Hopf (RH) equation and has a singularity in finite time. The exact closed description for the evolution of all one and multi point moments of the hydrodynamic fields and their spectra is now possible and thus, the mysterious turbulence problem has the exact solution for this case. As an example, for the first time the two-dimensional (2D) energy spectrum in the inertial scale interval is obtained directly from the exact solution of compressible 2D Navier–Stokes (NS) equation. For this purpose, a smooth continuation at all times for these exact solutions to the EH and RH equations is obtained by introducing a super-threshold homogeneous friction or any even extremely low effective viscosity. A new, smooth for all time, analytic solutions to the 1D, 2D and 3D NS equations is obtained. This solution coincides with the above-mentioned modified by viscosity solutions to the EH and RH equations, when also taking into account a linear relation between the pressure and the velocity field divergence, which is well known for the systems far from the equilibrium with relatively large second viscosity. This gives the positive answer to the generalization of the millennium prize problem (www.claymath.org) for the case of the compressible NS equation. Indeed, earlier only a negative answer to the problem of the existence of smooth solutions for any finite time has been a priori considered for the compressible case with the finite initial energy of the smooth velocity field in the unbounded space.

Curvature-induced deformations of the vortex rings generated at the exit of a rectangular duct

Rectangular air jets of aspect ratio$2$are studied at$Re=UD_{h}/\unicode[STIX]{x1D708}=17\,750$using particle image velocimetry and hot-wire anemometry as they develop naturally or under acoustic forcing. The velocity spectra and the spatial theory of linear stability characterize the fundamental ($f_{n}$) and subharmonic ($f_{n}/2$) modes corresponding to the Kelvin–Helmholtz roll-up and vortex pairing, respectively. The rectangular cross-section of the jet deforms into elliptic/circular shapes downstream due to axis switching. Despite the apparent rotation of the vortex rings or the jet cross-section, the axis-switching phenomenon occurs due to reshaping into rounder geometries. By enhancing the vortex pairing, excitation at$f_{n}/2$shortens the potential core, increases the jet spread rate and eliminates the overshoot typically observed in the centreline velocity fluctuations. Unlike circular jets, the skewness and kurtosis of the rectangular jets demonstrate elevated anisotropy/intermittency levels before the end of the potential core. The axis-switching location is found to be variable by the acoustic control of the relative expansion/contraction rates of the shear layers in the top (longer edge), side (shorter edge) and diagonal views. The self-induced vortex deformations are demonstrated by the spatio-temporal evolution of the phase-locked three-dimensional ring structures. The curvature-induced velocities are found to reshape the vortex ring by imposing nonlinear azimuthal perturbations occurring at shorter wavelengths with time/space evolution. Eventually, the multiple high-curvature/high-velocity regions merge into a single mode distribution. In the plane of the top view, the self-induced velocity distribution evolves symmetrically while the tilted ring results in the asymmetry of the azimuthal perturbations in the side view as the side closer to the acoustic source rolls up in more upstream locations.

Structure and dynamics of CH2O, OH, and the velocity field of a confined bluff-body premixed flame, using simultaneous PLIF and PIV at 10 kHz.

Abstract This study characterizes the structure and dynamics of a confined, bluff-body-stabilized turbulent premixed flame by simultaneously employing formaldehyde (CH2O) and hydroxyl (OH) planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV), at a rate of 10 kHz. The large field-of-view (>170 cm2) CH2O-PLIF is enabled by use of a burst-mode laser delivering 10-kHz pulse trains of 355-nm at 350 mJ/pulse, resulting in a CH2O signal-to-noise of 47:1 during PIV seed flow. Two cases illustrative of the CH2O dynamics are presented. A statistically stationary turbulent combustion case highlights the development of the CH2O layers in space and time. Notably, presumed CH2O-vortex dynamic interactions are observed where the CH2O accumulates broadly near the Kelvin–Helmholtz vortex core and remains thin near the vortex braid, contributing to a distribution of CH2O preheat zone thickness from 1 to 10 times of the calculated laminar value. The second case highlights the CH2O dynamics during a self-excited combustion instability. Two short-duration increases in CH2O are produced during the elevated velocity portion of the acoustic cycle. The first CH2O increase is caused by the reactant mass flux impulse as the velocity starts to increase. The second CH2O increase is the result of the upper and lower shear layers merging downstream and entraining fresh reactants that burn in intense, distributed regions inside the wake. Estimating the time delay between the CH2O and the heat release, it is suggested that the secondary CH2O increase may contribute to damping of the acoustic instability, because of its out-of-phase relationship with pressure, while the first CH2O increase appears to drive the instability.

Numerical Study of Iced Airfoils with Horn Features Using Large-Eddy Simulation

Separated flowfields around two iced airfoils with horn features near stall are numerically studied using wall-modeled large-eddy simulation. The iced airfoils are the GLC305 airfoil with rime ice 212 and the NLF0414 airfoil with glaze ice 623. A grid-quality-based hybrid central/upwind scheme is applied for numerical flux computation. The close agreement between the computed lift, drag, and surface pressure distribution and the experimental results illustrates the capability of the present method. In particular, the current method can accurately predict the Kelvin–Helmholtz instability of a free shear layer. The statistical results, instantaneous flowfields, pressure fluctuations, and characteristic frequencies are investigated. Both flowfields are dominated by separation bubbles. The bubble length increases with the angle of attack according to a quadratic relation. A strong-fluctuation region in the flowfield grows rapidly at high angles of attack, especially near stall. High- and low-frequency peaks are found in the initial and further downstream regions of the free shear layer, respectively. The high frequency is caused by the Kelvin–Helmholtz instability and vortex shedding. The low frequency might be caused by the vortex merging in the further downstream region of the free shear layer.

Data mining for vortices on the Earth's magnetosphere – algorithm application for detection and analysis

Abstract. Unsteady processes in the solar wind–magnetosphere interaction, such as vortices developed at the magnetopause boundary by the Kelvin–Helmholtz instability, may contribute to the process of mass, momentum and energy transfer into the Earth's magnetosphere. The research described in this paper validates an algorithm to automatically detect and characterize vortices based on velocity data from simulations. The vortex identification algorithm (VIA) systematically searches the 3-D velocity fields to identify critical points where the magnitude of the velocity vector vanishes. The velocity gradient tensor is computed and its invariants are used to assess vortex structure in the flow field. We use the Community Coordinated Modeling Center (CCMC) Runs on Request capability to create a series of model runs initialized from the conditions observed by the Cluster mission in the Hwang et al. (2011) analysis of Kelvin–Helmholtz vortices observed during southward interplanetary magnetic field (IMF) conditions. We analyze further the properties of the vortices found in the runs, including the velocity changes within their motion across the magnetosheath. We also demonstrate the potential of our tool to identify and characterize other transient features (e.g., flux transfer events, FTEs) with vortical internal structures. We find that the vortices are associated with flows on the magnetosheath side of the magnetopause that reach speeds greater than the solar wind speed at the bow shock. Keywords. Magnetospheric physics (MHD waves and instabilities; solar wind–magnetosphere interactions) – space plasma physics (numerical simulation studies)

Numerical study on the turbulent mixing of planar shock-accelerated triangular heavy gases interface

The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride ( $$\mathrm{SF_6}$$ ) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation reconstruction. The vortex dynamics of the Richtmyer–Meshkov instability and the turbulent mixing induced by the Kelvin–Helmholtz instability are discussed. A modified reconstruction model is proposed to predict the circulation for the shock triangular gas–cylinder interaction flow. Several typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are demonstrated. Both the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present case. The analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin–Helmholtz vortices can gain energy from the mean flow in total. Consequently, small scale flow structures are generated therein by means of nonlinear interactions. Furthermore, the occasional “pairing” between a vortex and its neighboring vortex will trigger the merging process of vortices and, finally, create a large turbulent mixing zone.

A comparative three-dimensional study of impulsive flow emanating from a shock tube for shock Mach number 1.6

A three-dimensional transient impulsive flow emanating from an open end of a 165-mm driver section shock tube is investigated numerically in the present study for a shock Mach number of 1.6. Here, the main objective was to find out an appropriate model to simulate the early evolution of the high Mach number transient flows by comparing the flow field obtained from two numerical models with both qualitative and quantitative experimental observations. The 3-D numerical simulations were performed by solving RANS equations using the shear stress transport K-ω model and large eddy simulation of the flow with the help of ANSYS CFX software. The experiments were performed with the simultaneous 2-D and 3-D particle image velocimetry systems and high-resolution smoke flow visualizations. The 2-D PIV results were used for comparing the numerical results obtained on a plane, and the 3-D PIV results were used to compare the azimuthal variations across the vortex ring. It is observed that the velocity field of the transient jet, Kelvin–Helmholtz (K–H) vortices at the trailing jet and the interaction of K–H vortices with the primary vortex ring were resolved well in LES quite similar to the experiments. However, the SST K-ω model resolved only the velocity field of the transient jet in the axial region similar to the experiments and dissipated the K–H vortices at the jet boundary. Though both models resolved the shear layer originated from the triple point, they did not predict the rollup and formation of vortices and their interactions observed in a 24 MP camera. This demands the use of a higher spatial resolution. It is also noticed that a substantial adverse pressure gradient experienced by the vortex ring and trailing jet during the early stage of evolution due to the presence of precursor/incident shock was responsible for the pairing up and merging of the shear layer vortices to form a stronger counter-rotating vortex ring. This adverse gradient also plays a dominant role in the azimuthal expansion (rapid increase in diameter) of the vortex ring.

Computational Fluid Dynamics for Modeling Gravity Currents in the Presence of Oscillatory Ambient Flow

Gravity currents generated by lock release are studied in the case of initially quiescent ambient fluid and oscillating ambient fluid (regular surface waves). In particular, the dynamics of the density currents are investigated by means of CFD numerical simulations. The aim is to evaluate the influence of the ambient fluid velocity field on the observed mixing and turbulent processes. Results of two different turbulence closure models, namely the standard k − ε turbulence model and the LES model, are analyzed. Model predictions are validated through comparison with laboratory measurements. Results show that the k − ε model is able to catch the main current propagation parameters (e.g., front velocity at the different phases of the evolution of the current, gravity current depth, etc.), but that a LES model provides more realistic insights into the turbulent processes (e.g., formation of interfacial Kelvin–Helmholtz billows, vortex stretching and eventual break up into 3D turbulence). The ambient fluid velocity field strongly influences the dynamics of the gravity currents. In particular, the presence of an oscillatory motion induces a relative increase of mixing at the front (up to 25%) in proximity of the bottom layer, and further upstream, an increase of the mixing process (up to 60%) is observed due to the mass transport generated by waves. The observed mixing phenomena observed are also affected by the ratio between the gravity current velocity v f and the horizontal orbital velocity induced by waves u w , which has a stronger impact in the wave dominated regime ( v f / u w < 1).

Mean turbulence statistics in boundary layers over high-porosity foams

This paper reports turbulent boundary layer measurements made over open-cell reticulated foams with varying pore size and thickness, but constant porosity ($\unicode[STIX]{x1D716}\approx 0.97$). The foams were flush-mounted into a cutout on a flat plate. A laser Doppler velocimeter (LDV) was used to measure mean streamwise velocity and turbulence intensity immediately upstream of the porous section, and at multiple measurement stations along the porous substrate. The friction Reynolds number upstream of the porous section was $Re_{\unicode[STIX]{x1D70F}}\approx 1690$. For all but the thickest foam tested, the internal boundary layer was fully developed by ${<}10\unicode[STIX]{x1D6FF}$ downstream from the porous transition, where $\unicode[STIX]{x1D6FF}$ is the boundary layer thickness. Fully developed mean velocity profiles showed the presence of a substantial slip velocity at the porous interface (${>}30\,\%$ of the free-stream velocity) and a mean velocity deficit relative to the canonical smooth-wall profile further from the wall. While the magnitude of the mean velocity deficit increased with average pore size, the slip velocity remained approximately constant. Fits to the mean velocity profile suggest that the logarithmic region is shifted relative to a smooth wall, and that this shift increases with pore size until it becomes comparable to substrate thickness $h$. For all foams, the turbulence intensity was found to be elevated further into the boundary layer to $y/\unicode[STIX]{x1D6FF}\approx 0.2$. An outer peak in intensity was also evident for the largest pore sizes. Velocity spectra indicate that this outer peak is associated with large-scale structures resembling Kelvin–Helmholtz vortices that have streamwise length scale $2\unicode[STIX]{x1D6FF}{-}4\unicode[STIX]{x1D6FF}$. Skewness profiles suggest that these large-scale structures may have an amplitude-modulating effect on the interfacial turbulence.

Frontal collision of internal solitary waves of first mode

The dynamics and energetics of a frontal collision of internal solitary waves (ISW) of first mode in a fluid with two homogeneous layers separated by a thin interfacial layer are studied numerically within the framework of the Navier–Stokes equations for stratified fluid. It was shown that the head-on collision of internal solitary waves of small and moderate amplitude results in a small phase shift and in the generation of dispersive wave train travelling behind the transmitted solitary wave. The phase shift grows as amplitudes of the interacting waves increase. The maximum run-up amplitude during the wave collision reaches a value larger than the sum of the amplitudes of the incident solitary waves. The excess of the maximum run-up amplitude over the sum of the amplitudes of the colliding waves grows with the increasing amplitude of interacting waves of small and moderate amplitudes whereas it decreases for colliding waves of large amplitude. Unlike the waves of small and moderate amplitudes collision of ISWs of large amplitude was accompanied by shear instability and the formation of Kelvin–Helmholtz (KH) vortices in the interface layer, however, subsequently waves again become stable. The loss of energy due to the KH instability does not exceed 5%–6%. An interaction of large amplitude ISW with even small amplitude ISW can trigger instability of larger wave and development of KH billows in larger wave. When smaller wave amplitude increases the wave interaction was accompanied by KH instability of both waves.

Effects of the stroke length and nozzle-to-plate distance on synthetic jet impingement heat transfer

This study focuses on the combined effect of the nozzle-to-plate distance and of the stroke length on the cooling performances of impinging synthetic jets. Infrared thermography is used as temperature transducer in conjunction with the heated thin foil heat transfer sensor to measure time- and phase-averaged convective heat transfer. All the experiments have been performed at a fixed Reynolds number equal to 5250, while different values of the dimensionless stroke length (L0/D equal to 5, 10 and 20) and nozzle-to-plate distance (H/D between 2 and 10) have been considered. At high L0/D, the heat transfer behaviour resembles that of a continuous impinging jet. It is characterized by a time-averaged stagnation Nusselt number maximum between H/D equal to 4 and 6 and inner and outer ring-shaped regions of Nusselt number maximum at short H/D. These two regions are replaced by a bell-shaped distribution at higher nozzle-to-plate distances. The existence of these regions is clearly observed through the phase-averaged heat transfer measurements. At short H/D, the heat transfer evolution reveals the simultaneous presence of two outer ring-shaped regions. The external outer region is ascribed to the strong coherence of the primary vortex ring, while the internal one is mainly due to the vortex rings generated by the Kelvin–Helmholtz instability along the trailing jet shear layer. At high H/D, the internal outer-ring shaped region disappears because of the weakening of the trailing jet Kelvin–Helmholtz vortex rings. In opposition, at short L0/D, the time-averaged stagnation point Nusselt number is found to have a maximum at lower values of H/D, and no inner ring-shaped region of heat transfer maximum is observed. This region is not present, at low dimensionless stroke lengths, because of the weakness and reduced extent of the trailing jet in the flow field. Indeed, the phase-averaged measurements mainly show the heat transfer caused by the impinging primary vortex ring. Despite the weakness of the trailing jet, the outer ring-shaped region of heat transfer maximum is observed at short H/D because of the presence of a strong primary vortex ring. In addition to that, the dimensionless stroke length and nozzle-to-plate distance also affect the heat transfer fluctuations, which decrease as L0/D decreases and/or H/D increases.

Magnetized Kelvin–Helmholtz instability: theory and simulations in the Earth’s magnetosphere context

The Kelvin–Helmholtz instability, proposed a long time ago for its role in and impact on the transport properties at magnetospheric flanks, has been widely investigated in the Earth’s magnetosphere context. This review covers more than fifty years of theoretical and numerical efforts in investigating the evolution of Kelvin–Helmholtz vortices and how the rich nonlinear dynamics they drive allow solar wind plasma bubbles to enter into the magnetosphere. Special care is devoted to pointing out the main advantages and weak points of the different plasma models that can be adopted for describing the collisionless magnetospheric medium and in underlying the important role of the three-dimensional geometry of the system.

SPH modelling of multi-fluid lock-exchange over and within porous media

Multi-fluid flow over and within porous media occurs frequently in nature and plays an important role in engineering applications. The modeling of these flows and validation against experimental or field observations have not been largely conducted in literature. An explicit numerical scheme for incompressible fluid using Smoothed Particle Hydrodynamics (EISPH) was employed and solved using two integration algorithms. To explore the capabilities and limitations of the model, case studies including percolation of a single fluid in a porous medium, gravity current of a single fluid over a porous medium, multi-fluid flow over an impermeable bed, and a porous medium were simulated and compared with experimental data. The EISPH method led to results overall similar to the observed experimental data. The model was able to reproduce the behaviour of the flow within media with different porosities. In addition, the model reproduced behaviour of multi-fluid flow at the interface between different fluids, such as reproducing Kelvin–Helmholtz vortices and diffusion of salt.

High-resolution simulations of cylindrical gravity currents in a rotating system

Cylindrical gravity currents, produced by a full-depth lock release, in a rotating system are investigated by means of three-dimensional high-resolution simulations of the incompressible variable-density Navier–Stokes equations with the Coriolis term and using the Boussinesq approximation for a small density difference. Here, the depth of the fluid is chosen to be the same as the radius of the cylindrical lock and the ambient fluid is non-stratified. Our attention is focused on the situation when the ratio of Coriolis to inertia forces is not large, namely $0.1\leqslant {\mathcal{C}}\leqslant 0.3$, and the non-rotating case, namely ${\mathcal{C}}=0$, is also briefly considered. The simulations reproduce the major features observed in the laboratory and provide more detailed flow information. After the heavy fluid contained in a cylindrical lock is released in a rotating system, the influence of the Coriolis effects is not significant during the initial one-tenth of a revolution of the system. During the initial one-tenth of a revolution of the system, Kelvin–Helmholtz vortices form and the rotating cylindrical gravity currents maintain nearly perfect axisymmetry. Afterwards, three-dimensionality of the flow quickly develops and the outer rim of the spreading heavy fluid breaks away from the body of the current, which gives rise to the maximum dissipation rate in the system during the entire adjustment process. The detached outer rim of heavy fluid then continues to propagate outward until a maximum radius of propagation is attained. The body of the current exhibits a complex contraction–relaxation motion and new outwardly propagating pulses form regularly in a period slightly less than half-revolution of the system. Depending on the ratio of Coriolis to inertia forces, such a contraction–relaxation motion may be initiated after or before the attainment of a maximum radius of propagation. In the contraction–relaxation motion of the heavy fluid, energy is transformed between potential energy and kinetic energy, while it is mainly the kinetic energy that is consumed by the dissipation. As a new pulse initially propagates outward, the potential energy in the system increases at the expense of decreasing kinetic energy, until a local maximum of potential energy is reached. During the latter part of the new pulse propagation, the kinetic energy in the system increases at the expense of decreasing potential energy, until a local minimum of potential energy is reached and another new pulse takes form. With the use of three-dimensional high-resolution simulations, the lobe-and-cleft structure at the advancing front can be clearly observed. The number of lobes is maintained only for a limited period of time before merger between existing lobes occurs when a maximum radius of propagation is approached. The high-resolution simulations complement the existing shallow-water formulation, which accurately predicts many important features and provides insights for rotating cylindrical gravity currents with good physical assumptions and simple mathematical models.