Vortical Motion Research Articles

Spectral analysis of the evolution of energy-containing eddies

Energy-containing eddies (energy-eddies) are the elementary structures of wall turbulence that carry most of the kinetic energy and momentum. Despite the consensus that energy-eddies can self-sustain at each relevant length scale, their precise origin and spatial evolution are currently not well understood. In this study, we examine the spatial evolution of energy-eddies by quenching them at the inflow of a turbulent channel flow. Our study shows that the eddies involved in the energy cascade cannot be sustained without the energy-eddies. The streamwise velocity spectra of the evolving flow start to recover at a spanwise wavelength of $\lambda _z^+ \simeq 100$ , equal to the near-wall spacing of streaks in the buffer layer located at $y^+ \simeq 15$ , whereas there are no active vortical motions in the streamwise vorticity spectra until the energy at the streak location is re-established. Hence, the present study demonstrates that in a spatially evolving flow, the formation of near-wall streaks is the primary process necessary in the recovery of energy-eddies.

Flow characteristics and wake topology of two-seat convertibles

This study aims to clarify the flow characteristics and the wake structure of convertible vehicles. Numerical simulations are performed to obtain a preliminary visualization, and the potential vortical motion characteristics are investigated by examining the Q-criterion across multiple cross sections. Comparisons between numerical and experimental results validate the reasonableness of our numerical model. The predominant wake topology of a two-seat convertible is obtained in terms of the location, shape, and spin direction of the vortices. We observe a “nook” vortex that is triggered by the flow acceleration induced by the pressure gradient near the windshield step, provoking undesirable aeroacoustic noise and degrading the cabin comfort. Complicated A-pillar vortex dynamics are revealed, with small vortices that are shed into the cabin and impinge the seats, eventually forming a long tail structure above the back of the vehicle. Moreover, periodic fluctuations of the windshield vortex are induced by the Kelvin–Helmholtz instability, significant impacting the streamwise wake. Ultimately, the combined motion characteristics of the A-pillar and windshield vortices exert undesirable effects on the aeroacoustic noise and drag, suggesting fundamental mechanisms for achieving optimal energy-saving and acoustic convertibles in the future. Based on the wake topology and the vortical generating mechanism, some approaches are proposed to reduce the drag and aeroacoustic noise by impeding the flow over the door into the cabin, modifying the shape of windshield step, and lengthening the windshield in stream direction.

Observational Signatures of Coronal Heating in Magnetohydrodynamic Simulations without Radiation or a Lower Atmosphere

It is extremely difficult to simulate the details of coronal heating and also make meaningful predictions of the emitted radiation. Thus, testing realistic models with observations is a major challenge. Observational signatures of coronal heating depend crucially on radiation, thermal conduction, and the exchange of mass and energy with the transition region and chromosphere below. Many magnetohydrodynamic simulation studies do not include these effects, opting instead to devote computational resources to the magnetic aspects of the problem. We have developed a simple method of accounting approximately for the missing effects. It is applied to the simulation output ex post facto and therefore may be a valuable tool for many studies. We have used it to predict the emission from a model corona that is driven by vortical boundary motions meant to represent photospheric convection. We find that individual magnetic strands experience short-term brightenings, both scattered throughout the computational volume and in localized clusters. The former may explain the diffuse component of the observed corona, while the latter may explain bright coronal loops. Several observed properties of loops are reproduced reasonably well: width, lifetime, and quasi-circular cross section (aspect ratio not high). Our results lend support to the idea that loops are multistranded structures heated by “storms” of nanoflares.

The Troposphere-to-Stratosphere Transport Caused by a Rossby Wave Breaking Event over the Tibetan Plateau in Mid-March 2006

Based on reanalysis data, satellite ozone concentration observations, and a Lagrangian trajectory simulation, a Rossby wave breaking (RWB) event and its effect on stratosphere–troposphere exchange (STE) over the Tibetan Plateau in mid-March 2006 were investigated. Results showed that the increased eddy heat flux from the subtropical westerly jet magnified the amplitude of the Rossby wave, which contributed to the occurrence of the cyclonic RWB event. The quasi-horizontal cyclonic motion of the isentropic potential vorticity in the RWB cut the tropical tropospheric air mass into the extratropical stratosphere, completing the stratosphere–troposphere mass exchange. Meanwhile, the tropopause folding zone extended polewards by 10° of latitude and the tropospheric air mass escaped from the tropical tropopause layer into the extratropical stratosphere through the tropopause folding zone. The particles in the troposphere-to-stratosphere transport (TST) pathway migrated both eastwards and polewards in the horizontal direction, and shifted upwards in the vertical direction. Eventually, the mass of the TST particles reached about 3.8 × 1014 kg, accounting for 42.2% of the particles near the tropopause in the RWB event. The rest of the particles remained in the troposphere, where they moved eastwards rapidly along the westerly jet and slid down in the downstream upper frontal zone.

Liutex-Represented Vortex Spectrum in Turbulence

The Liutex vector is new quantity introduced to represent the rigid-body rotation part of fluid motion and thus to define and identify vortices in various flows. In this work, the intermittency and power-law similarity of the Liutex vector in homogeneous, isotropic turbulence and a turbulent channel are explored. First, we found that the Liutex vector is more intermittent than the vorticity vector in the considered turbulent flows, which indicates that an iso-surface of a Liutex magnitude with an appropriate threshold could capture the major rotating motions or vortical motions of the flow. Second, the three-dimensional energy spectrums of velocity, vorticity (enstrophy spectrum) and the Liutex vector in homogeneous isotropic turbulence are shown to exhibit power laws of -5/3, 1/3 and 1/3 in the inertial subrange, respectively, whilst the Liutex energy spectrum particularly satisfies an additional -10/3 power law in the viscous subrange. This viscous similarity of the Liutex vector is the only power law that survived from the wall presence and is argued to originate from the fact that the Liutex vector represents the rigid part of fluid motion and is free from any shear contamination. The existence of such a viscous similarity law indicates a certain coherence of the small scales of turbulence and could possibly help understand and model turbulence.

Flame and heat transfer characteristics of a micro combustor with multihole baffle-induced inflows for a thermo-photovoltaic application

For an effective thermo-photovoltaic application, the inflow effects on the flame and heat transfer characteristics of micro power generators are numerically investigated in a multihole baffled micro combustor. The flow inside the baffle hole is considered as a circular pipe flow. Various inlet profiles of the micro combustor are obtained by varying the baffle thickness corresponding to the length of the baffle hole. The velocity distribution of the flow past the baffle plate attains an M-shaped (also called saddle-back), a parabolic, or a fully developed profile according to the baffle thickness. For a baffle thickness less than the fuel hole diameter, the inflow of the combustion chamber has an M-shaped velocity profile with two off-center peaks. Vortical motions and lobe-shaped flame are promoted by this type of inlet condition. Combustion characteristics, including flame length, combustion efficiency, heat loss ratio, and preheating effect, are comprehensively examined to evaluate the possibility as an thermo-photovoltaic device. The results indicate that a micro combustor with a thin baffle (bt ≤ 0.1Df ) increases the combustion efficiency and wall heat flux. This suggests that the current baffled combustor can be effectively applied in both micro power generation systems and micro thermal emitters.

Enhanced prediction of three-dimensional finite iced wing separated flow near stall

Icing on three-dimensional wings causes severe flow separation near stall. Standard improved delayed detached eddy simulation (IDDES) is unable to correctly predict the separating-reattaching flow due to its inability to accurately resolve the Kelvin-Helmholtz instability. In this study, a shear layer adapted subgrid length scale is applied to enhance the IDDES prediction of the flow around a finite NACA 0012 wing with leading edge horn ice. It shows that using the new length scale contributes to a more accurate prediction of the separated shear layer (SSL). The predicted reattachment occurs earlier as one moves towards either end of the wing, and the computed surface pressure distributions agree well with the experimental measurements. In contrast, standard IDDES severely elongates surface pressure plateaus. For instantaneous flow, the new length scale helps to correctly resolve the rollup and subsequent pairing of vortical structures due to its small values in the initial SSL. The vortical motion frequencies increase when moving towards the wing tip due to the downwash effect of the tip vortex. In comparison, the excessive eddy viscosity levels from the standard IDDES delay the rollup of spanwise structures and give rise to “overcoherent” structures.

Modeling nonlinear acoustic damping due to flow separation

Nonlinear acoustic damping has been observed in many high-amplitude acoustic systems as a result of flow separation and shear layer vortical motion, eventually transforming some of the acoustical energy into heat. The amount of nonlinear acoustic damping helps determine the nonlinear limit cycle amplitude, e.g., damping caused by baffle blades in a liquid rocket engine to reduce combustion instabilities. The damping mechanism is dependent on both the location and phase of flow separation. Identifying the flow separation is a function of both the boundary layer growth and the acoustically imposed pressure gradient. When the acoustic pressure gradient is adverse, the boundary layer is more prone to separation. Using this as a basis, a model can be created that is applicable to general geometry, which will then be used to approximate the nonlinear acoustic damping in various situations. The constructed model will be compared to established cases, such as an orifice in a duct, to validate the model.

Measurements of Turbulence Generated by Wake Eddies Near a Steep Headland

AbstractTidal and low‐frequency flows interact with abrupt topographic features, giving rise to a variety of small‐scale phenomena including lee waves, vortical motions and turbulence. With the goal of identifying the processes that transfer momentum and energy between the larger‐scale and smaller‐scale flows, detailed tidally‐resolving shipboard surveys were conducted near a sharp and steep headland north of Velasco Reef, Palau, in the Western Pacific. We present velocity, microstructure and rapid‐cycling conductivity and temperature measurements, contextualized with a nearby 10‐month moored record, to examine wake and vortex structures. Observed flow near Velasco Reef was layered and multi‐directional in depth such that the “downstream” side of the headland depended on depth. Downstream of the headland, during a period where mean flow dominated over the tide in the top 100 m of the water column, turbulent kinetic energy dissipation rates were enhanced by up to three orders of magnitude relative to those upstream. During a period dominated by tides, the flow reversed periodically and wake eddies were associated with turbulent dissipation rates up to . Turbulent dissipation rates in the wake increased with inverse Richardson number for both tidal and mean flows past the headland, and were larger for stronger vorticity flows. Our analysis suggests that the eddies themselves lead to shear instabilities and subsequent turbulence, either through tilting or their limited vertical extent. We associate the enhanced downstream dissipation with a combination of breaking internal tides and either these eddy processes or a multi‐scaled turbulent wake.

Formation of Quiescent Prominence Magnetic Fields by Supergranulations

To understand the formation of quiescent solar prominences, the origin of their magnetic field structures, i.e., magnetic flux ropes (MFRs), must be revealed. We use three-dimensional magnetofriction simulations in a spherical subdomain to investigate the role of typical supergranular motions in the long-term formation of a prominence magnetic field. Time-dependent horizontal supergranular motions with and without the effect of Coriolis force are simulated on the solar surface via Voronoi tessellation. The vortical motions by the Coriolis effect at boundaries of supergranules inject magnetic helicity into the corona. The helicity is transferred and accumulated along the polarity inversion line (PIL) as a strongly sheared magnetic field via helicity condensation. The diverging motions of supergranules converge opposite magnetic polarities at the PIL and drive the magnetic reconnection between footpoints of the sheared magnetic arcades to form an MFR. The magnetic network, negative-helicity MFR in the northern hemisphere, and fragmented-to-continuous formation process of magnetic dip regions are in agreement with observations. Although diverging supergranulations, differential rotation, and meridional flows are included, the simulation without the Coriolis effect cannot produce an MFR or sheared arcades to host a prominence. Therefore, Coriolis force is a key factor for helicity injection and the formation of magnetic structures of quiescent solar prominences.

Investigation on energy conversion instability of pump mode in hydro-pneumatic energy storage system

The pump mode of hydro-pneumatic energy storage (HPES) system often experiences off-design conditions due to the boundary pressure rises, and the resultant energy conversion instability has an adverse effect on the system operation. However, the evolutionary process of this instability and the corresponding flow events are still not fully understood. Experimental and numerical simulation studies of a centrifugal pump with vaned diffuser were conducted in a wide operating range, and the following notable results were obtained. The energy conversion of pump mode shows three typical stages as the pump head increases, stable work→stumbled work→shaky work, corresponding to the inner flow pattern development of stall-free→stall inception→stall deepening. In this evolutionary process, the attenuation of rotor blade loading gradually spreads from the inlet shroud side to the entire blade. This strengthens the natural adverse potential rothalpy gradient and induces the energetic vortical structures including leading backflow vortices, dynamic stall cells and trailing helical vortices. A strong coupling between large-scale vortical motions and energy conversion is observed and this yields a Logistic growth of the shaft power and pump head fluctuations. The critical condition for the energy conversion instability is the diagnostic function SI = 1, and this is recommended for determining the stability limit of the pump mode.

Simulating Solar Near-surface Rossby Waves by Inverse Cascade from Supergranule Energy

Rossby waves are found at several levels in the Sun, most recently in its supergranule layer. We show that Rossby waves in the supergranule layer can be excited by an inverse cascade of kinetic energy from the nearly horizontal motions in supergranules. We illustrate how this excitation occurs using a hydrodynamic shallow-water model for a 3D thin rotating spherical shell. We find that initial kinetic energy at small spatial scales inverse cascades quickly to global scales, exciting Rossby waves whose phase velocities are similar to linear Rossby waves on the sphere originally derived by Haurwitz. Modest departures from the Haurwitz formula originate from nonlinear finite amplitude effects and/or the presence of differential rotation. Like supergranules, the initial small-scale motions in our model contain very little vorticity compared to their horizontal divergence, but the resulting Rossby waves are almost all vortical motions. Supergranule kinetic energy could have mainly gone into gravity waves, but we find that most energy inverse cascades to global Rossby waves. Since kinetic energy in supergranules is three or four orders of magnitude larger than that of the observed Rossby waves in the supergranule layer, there is plenty of energy available to drive the inverse-cascade mechanism. Tachocline Rossby waves have previously been shown to play crucial roles in causing seasons of space weather through their nonlinear interactions with global flows and magnetic fields. We briefly discuss how various Rossby waves in the tachocline, convection zone, supergranule layer, and corona can be reconciled in a unified framework.

Dynamo effect in unstirred self-gravitating turbulence

ABSTRACT In many astrophysical environments, self-gravity can generate kinetic energy, which, in principle, is available for driving dynamo action. Using direct numerical simulations, we show that in unstirred self-gravitating subsonic turbulence with helicity and a magnetic Prandtl number of unity, there is a critical magnetic Reynolds number of about 25 above which the work done against the Lorentz force exceeds the Ohmic dissipation. The collapse itself drives predominantly irrotational motions that cannot be responsible for dynamo action. We find that, with a weak magnetic field, one-third of the work done by the gravitational force goes into compressional heating and the remaining two-thirds go first into kinetic energy of the turbulence before a fraction of it is converted further into magnetic and finally thermal energies. Close to the collapse, however, these fractions change toward 1/4 and 3/4 for compressional heating and kinetic energy, respectively. When the magnetic field is strong, the compressional heating fraction is unchanged. Out of the remaining kinetic energy, one quarter goes directly into magnetic energy via work against the Lorentz force. The fraction of vortical motions diminishes in favour of compressive motions that are almost exclusively driven by the Jeans instability. For an initially uniform magnetic field, field amplification at scales larger than those of the initial turbulence are driven by tangling.

Isolating effects of Darrieus–Landau instability on the morphology and propagation of turbulent premixed flames

The objective of this work is to provide physical insight into the mechanisms governing flame–turbulence interactions and explore the impact of the ubiquitous Darrieus–Landau instability on the propagation. It is based on the hydrodynamic theory of premixed flames that considers the flame thickness much smaller than all other fluidynamical length scales. In this asymptotic limit, the flame is thus confined to a surface whilst the diffusion and reaction processes occurring inside the flame zone are accounted for by two parameters: the unburned-to-burned density ratio and the Markstein length. The robust model, which is free of phenomenology and turbulence modelling assumptions, makes transparent the mutual interactions between the flame and the fluid flow, and permits examining trends in flame and flow characteristics while varying the turbulence intensity and mixture properties. It is used in this study to examine the morphological changes of the flame surface that result from the intertwined effects of the turbulence and instability, as demonstrated by the local displacement and curvature of the flame front, the extent of wrinkling and folding of the flame surface, and the overall flame brush thickness. It also provides a direct evaluation of the turbulent flame speed and its dependence on the mean flame curvature and on the hydrodynamic strain that it experiences. Also discussed are the effects of the flame on the flow by examining the various mechanisms of enstrophy and scalar gradient production/destruction, the degree of anisotropy created in the burned gas, and the restructuring of the vortical motion beyond the flame.

Modeling nonlinear acoustic damping due to flow separation

Nonlinear acoustic damping has been observed in many high-amplitude acoustic systems as a result of flow separation and shear layer vortical motion, eventually transforming some of the acoustical energy into heat. The amount of nonlinear acoustic damping helps to determine the nonlinear limit cycle amplitude, e.g., damping caused by baffle blades in a liquid rocket engine to reduce combustion instabilities. The damping mechanism is dependent on both the location and phase of flow separation. Identifying the flow separation is a function of both the boundary layer growth and the acoustically imposed pressure gradient. When the acoustic pressure gradient is adverse, the boundary layer is more prone to separation. Using this as a basis, a model can be created that is applicable to general geometry, which will then be used to approximate the nonlinear acoustic damping in various situations. The constructed model will be compared to established cases, such as an orifice in a duct, to validate the model.

A Fast Monotone Discretization of the Rotating Shallow Water Equations

AbstractThis paper presents a new discretization of the rotating shallow water equations and a set of decisions, ranging from a simplification of the continuous equations down to the implementation level, yielding a code that is fast and accurate. Accuracy is reached by using WENO reconstructions on the mass flux and on the nonlinear Coriolis term. The results show that the implicit mixing and dissipation, provided by the discretization, allow a very good material conservation of potential vorticity and a minimal energy dissipation. Numerical experiments are presented to assess the accuracy, which include a resolution convergence, a sensitivity on the free‐slip versus no‐slip boundary conditions, a study on the separation of waves from vortical motions. Speed is achieved by a series of choices rather than a single recipe. The main choice is to discretize the covariant form written in index coordinates. This form, rooted in the discrete differential geometry, removes most of the grid scale terms from the equations, and keeps them only where they should be. The model objects appearing in resulting continuous equations have a natural correspondence with the grid cell features. The other choices are guided by the maximization of the arithmetic intensity. Finally this paper also proves that a pure Python implementation can be very fast, thanks to the possibility of having compiled Python. As a result, the code performs 2 TFlops per second using thousand cores.

Supersonic turbulent channel flows over spanwise-oriented grooves

In the present study, we perform direct numerical simulations to study the influences of the spanwise-oriented grooves, which are emulated by the reasonably designed “relaxed” boundary conditions, on the kinetic and thermodynamic statistics in a supersonic turbulent channel flow at the Mach number of 1.5 and Reynolds number of 3000. The phase averaged flow fields show that the relaxed boundary induces compressive and expansive waves that travel across the whole channel and are reflected by the upper wall. These waves are isentropic in the average sense except in the viscous sublayer. In the near-wall region, vortices and streaks that constitute the self-sustaining cycles are less populated and less meandering, while in the outer region, especially near the channel center, the velocity divergence is as strong as the vorticity. The temperature, density, and pressure fluctuations are enhanced by these waves. The correlations between the velocity and temperature are altered, due to the counter effects caused by the vortical motions and isentropic waves.

Enhanced Prediction of Three-Dimensional Finite Iced Wing Separated Flow Near Stall

Icing on three-dimensional wings causes severe flow separation near stall. Standard improved delayed detached eddy simulation (IDDES) is unable to correctly predict the separating reattaching flow due to its inability to accurately resolve the Kelvin-Helmholtz instability. In this study, a shear layer adapted subgrid length scale is applied to enhance the IDDES prediction of the flow around a finite NACA (National Advisory Committee for Aeronautics) 0012 wing with leading edge horn ice. It is found that applying the new length scale contributes to a more accurate prediction of the separated shear layer (SSL). The reattachment occurs earlier as one moves towards either end of the wing due to the downwash effect of the wing tip vortex or the influence of end-wall flow. Consequently, the computed surface pressure distributions agree well with the experimental measurements. In contrast, standard IDDES severely elongates surface pressure plateaus. For instantaneous flow, the new length scale helps correctly resolve the rollup and subsequent pairing of vortical structures due to its small values in the initial SSL. The computed Strouhal numbers of vortical motions are approximately 0.2 in the initial SSL based on the vorticity thickness and 0.1 around the reattachment based on the separation bubble length. Both frequencies increase when moving towards the wing tip due to the downwash effect of the tip vortex. In comparison, the excessive eddy viscosity levels from the standard IDDES severely delay the rollup of spanwise structures and give rise to "overcoherent" structures.

Heat transfer enhancement in fin channels using aeroelastically fluttering reeds

AbstractForced convection heat transfer in rectangular channels is enhanced by aeroelastically fluttering thin reeds extending over the channel span. The resulting small‐scale vortical motions substantially increase local heat transfer at the channel walls and mixing between the wall thermal boundary layers and the channel's core flow. Mechanisms associated with evolution of these small‐scale motions and their thermal effects are experimentally studied in a channel of width W, span , and length . Reed effects on heat transfer are characterized at Reynolds numbers (Re) of 2000, 7000, and 12,000 using embedded thermocouple arrays, and related to small‐scale motions by particle image velocimetry and hot‐wire anemometry. Reed‐induced small‐scale motions increase turbulent kinetic energy, increasing the global Nusselt number (by up to 145% at Re = 7000), with enhancement being sustained even when the base flow becomes fully turbulent (Re = 12,000). Enhancement is also demonstrated for fin arrays. Single‐reed computations show the effect of reed length on enhancement. Computations with two reeds, one downstream of the trailing edge of the other, predict heat transfer enhancement significantly greater than twice the single‐reed result, and point the way to use of a streamwise array of reeds in long channels. A techno‐economic analysis for an air‐cooled condenser suggests that fluttering reeds can be economically justified for a range of operating conditions.

II. The effect of axisymmetric and spatially varying equilibria and flow on MHD wave modes: cylindrical geometry

ABSTRACT Magnetohydrodynamic (MHD) waves are routinely observed in the solar atmosphere. These waves are important in the context of solar physics as it is widely believed they can contribute to the energy budget of the solar atmosphere and are a prime candidate to contribute towards coronal heating. Realistic models of these waves are required representing observed configurations such that plasma properties can be determined more accurately, since they cannot be measured directly. This work utilizes a previously developed numerical technique to find permittable eigenvalues under different non-uniform equilibrium conditions in a Cartesian magnetic slab geometry. Here, we investigate the properties of magnetoacoustic waves under non-uniform equilibria in a cylindrical geometry. Previously obtained analytical results are retrieved to emphasize the power and applicability of this numerical technique. Further case studies investigate the effect that a radially non-uniform plasma density and non-uniform plasma flow, modelled as a series of Gaussian profiles, have on the properties of different MHD waves. For all cases the dispersion diagrams are obtained and spatial eigenfunctions calculated which display the effects of the equilibrium inhomogeneity. It is shown that as the equilibrium non-uniformity is increased, the radial spatial eigenfunctions are affected and extra nodes introduced, similar to the previous investigation of a magnetic slab. Furthermore, azimuthal perturbations are increased with increasing inhomogeneity introducing vortical motions inside the waveguide. Finally, 2D and 3D representations of the velocity fields are shown which may be useful for observers for wave mode identification under realistic magnetic waveguides with ever increasing instrument resolution.