High-resolution Direct Numerical Simulations Research Articles

Buoyancy-Driven Flow through a Bed of Solid Particles Produces a New Form of Rayleigh-Taylor Turbulence

Rayleigh-Taylor (RT) fluid turbulence through a bed of rigid, finite-size spheres is investigated by means of high-resolution direct numerical simulations, fully coupling the fluid and the solid phase via a state-of-the-art immersed boundary method. The porous character of the medium reveals a totally different physics for the mixing process when compared to the well-known phenomenology of classical RT mixing. For sufficiently small porosity, the growth rate of the mixing layer is linear in time (instead of quadratical) and the velocity fluctuations tend to saturate to a constant value (instead of linearly growing). We propose an effective continuum model to fully explain these results where porosity originated by the finite-size spheres is parametrized by a friction coefficient.

Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence.

The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At a sufficiently large magnetic Reynolds number (R_{m}=10^{6}), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The disruption of current sheet structures facilitates the energy cascade towards small scales, leading to the breaking and steepening of the energy spectrum. In the plasmoid-mediated regime, the energy spectrum displays a scaling that is close to the spectral index -2.2 as proposed by recent analytic theories. We also demonstrate that the scale-dependent dynamic alignment exists in 2D MHD turbulence and the corresponding slope of the alignment angle is close to 0.25.

Pore-scale statistics of flow and transport through porous media.

Flow in porous media is known to be largely affected by pore morphology. In this work, we investigate the effects of pore geometry on the transport and spatial correlations of flow through porous media in two distinct pore structures arising from three-dimensional assemblies of overlapping and nonoverlapping spheres. Using high-resolution direct numerical simulations (DNS), we perform Eulerian and Lagrangian analysis of the flow and transport characteristics in porous media. We show that the Eulerian velocity distributions change from nearly exponential to Gaussian distributions as porosity increases. A stretched exponential distribution can be used to represent this behavior for a wide range of porosities. Evolution of Lagrangian velocities is studied for the uniform injection rule. Evaluation of tortuosity and trajectory length distributions of each porous medium shows that the model of overlapping spheres results in higher tortuosity and more skewed trajectory length distributions compared to the model of nonoverlapping spheres. Wider velocity distribution and higher tortuosity for overlapping spheres model give rise to non-Fickian transport while transport in nonoverlapping spheres model is found to be Fickian. Particularly, for overlapping spheres model our analysis of first-passage time distribution shows that the transport is very similar to those observed for sandstone. Finally, using three-dimensional (3D) velocity field obtained by DNS at the pore-scale, we quantitatively show that despite the randomness of pore-space, the spatially fluctuating velocity field and the 3D pore-space distribution are strongly correlated for a range of porous media from relatively homogeneous monodisperse sphere packs to Castlegate sandstone.

Towards simulating natural transition in hypersonic boundary layers via random inflow disturbances

A random forcing approach was implemented into a high-order accurate finite-difference code in order to investigate ‘natural’ laminar–turbulent transition in hypersonic boundary layers. In hypersonic transition wind-tunnel experiments, transition is caused ‘naturally’, by free-stream disturbances even when so-called quiet tunnels are employed such as the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The nature and composition of the free-stream disturbance environment in high-speed transition experiments is difficult to assess and therefore largely unknown. Consequently, in the direct numerical simulations (DNS) presented here, the free-stream disturbance environment is simply modelled by random pressure (acoustic) disturbances with a broad spectrum of frequencies and a wide range of azimuthal wavenumbers. Results of a high-resolution DNS for a flared cone at Mach 6, using the random forcing approach, are presented and compared to a fundamental breakdown simulation using a ‘controlled’ disturbance input (with a specified frequency and azimuthal wavenumber). The DNS results with random forcing clearly exhibit the ‘primary’ and ‘secondary’ streak pattern, which has previously been observed in our ‘controlled’ breakdown simulations and the experiments in the BAM6QT. In particular, the spanwise spacing of the ‘primary’ streaks for the random forcing case is identical to the spacing obtained from the ‘controlled’ fundamental breakdown simulation. A comparison of the wall pressure disturbance signals between the random forcing DNS and experimental data shows remarkable agreement. The random forcing approach seems to be a promising strategy to investigate nonlinear breakdown in hypersonic boundary layers without introducing any bias towards a distinct nonlinear breakdown mechanism and/or the selection of specific frequencies or wavenumbers that is required in the ‘controlled’ breakdown simulations.

Energy dissipation statistics along the Lagrangian trajectories in three-dimensional turbulent flows

Energy dissipation rate is relevant in the turbulent phenomenology theory, such as the classical Kolmogorov 1941 and 1962 refined similarity hypothesis. However, it is extremely difficult to retrieve experimentally or numerically. In this paper, the full energy dissipation, its proxy and the pseudo-energy dissipation rate along the Lagrangian trajectories in the three-dimensional turbulent flows are examined by using a state-of-art high resolution direct numerical simulation database with a Reynolds number Re λ = 400. It is found that the energy dissipation proxy e P is more correlated with the full energy dissipation rate e. The corresponding correlation coefficient ρ between the velocity gradient and e shows a Gaussian distribution. Furthermore, the coarse-grained dissipation rate is considered. The cross correlation ρ is found to be increased with the increasing of the scale τ. Finally, the hierarchical structure is extracted for the full energy dissipation rate, its proxy and the pseudo one. The results show a power-law behavior in the inertial range 10 ≤τ/τ η ≤ 100. The experimental scaling exponent of the full energy dissipation rate is found to be h L =0.69, agrees very well with the one found for the Eulerian velocity. The experimental values for e P and e S are around h L = 0.78, implying a more intermittent Lagrangian turbulence. Therefore, the intermittency parameter provided by e P and e S will be biased.

On the interaction of short linear internal waves with internal solitary waves

Abstract. We study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent waves are short in comparison to the solitary wave width, the interaction leads to an almost complete destruction of the short waves. For mode-1 short waves in the packet, as the wavelength increases, a cutoff is reached, and for larger wavelengths the waves in the packet are able to maintain their structure after the interaction. This cutoff corresponds to the wavelength at which the phase speed of the short waves upstream of the solitary wave exceeds the maximum current induced by the solitary wave. For mode-2 waves in the packet, however, no corresponding cutoff is found. Analysis based on linear theory suggests that the destruction of short waves occurs primarily due to the velocity shear induced by the solitary wave, which alters the vertical structure of the waves so that significant wave activity is found only above (below) the deformed pycnocline for overtaking (head-on) collisions. The deformation of vertical structure is more significant for waves with a smaller wavelength. Consequently, it is more difficult for these waves to adjust to the new solitary-wave-induced background environment. These results suggest that through the interaction with relatively smaller length scale waves, internal solitary waves can provide a means to decrease the power observed in the short-wave band in the coastal ocean.

Helical vortices generated by flapping wings of bumblebees

High resolution direct numerical simulations of rotating and flapping bumblebee wings are presented and their aerodynamics is studied focusing on the role of leading edge vortices and the associated helicity production. We first study the flow generated by only one rotating bumblebee wing in circular motion with 45◦ angle of attack. We then consider a model bumblebee flying in a numerical wind tunnel, which is tethered and has rigid wings flapping with a prescribed generic motion. The inflow condition of the wind varies from laminar to strongly turbulent regimes. Massively parallel simulations show that inflow turbulence does not significantly alter the wings’ leading edge vortex, which enhances lift production. Finally, we focus on studying the helicity of the generated vortices and analyze their contribution at different scales using orthogonal wavelets.

Enhancement of Small-scale Turbulent Dynamo by Large-scale Shear

Abstract Small-scale dynamos (SSDs) are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology, and structure formation. Using high-resolution direct numerical simulations, we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports SSD action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate γ of the SSD and the turbulent rms velocity with shear rate S that are independent of the magnetic Prandtl number: and . For large fluid and magnetic Reynolds numbers, γ, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the SSD exhibits the scaling, , arising solely from the induction equation for a given velocity field.

Least-Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics: most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, called least-squares shadowing, avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of least-squares shadowing to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The least-squares shadowing sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current least-squares shadowing implementation is high.

On the evolution of the plume function and entrainment in the near-source region of lazy plumes

Plumes occur in many natural and industrial settings, such as chimney smoke, volcanic eruptions and deep water oil spills. A plume function, $\unicode[STIX]{x1D6E4}$, is used to characterize plumes and jets. The far-field behaviour of these flows has been studied in great detail while the near-field behaviour has not quite received the same attention. We examine near-field phenomena such as radial constriction, termed necking, and vortex structure formations with new high resolution direct numerical simulations. Four lazy plumes with increasing values of the source plume parameter, $\unicode[STIX]{x1D6E4}_{0}$, are simulated. We study the evolution of entrainment and the plume function. The original assumptions, that Reynolds stresses dominate viscous shear stresses, do not hold for lazy plumes in the near field. Due to this, a deviation from self-similarity occurs initially and is corrected by a large entrainment coefficient caused by vortex stretching and compression. After correcting for the virtual origin, comparison between theory and simulations shows a monotonic decay of $\unicode[STIX]{x1D6E4}$ towards pure plume behaviour. The entrainment coefficient asymptotes to a widely accepted constant value for plumes.

Reynolds and Prandtl number scaling of viscous heating in isotropic turbulence

Viscous heating is investigated using high-resolution direct numerical simulations. Scaling relations are derived and verified for different values of the Reynolds and Prandtl numbers. The scaling of the heat fluctuations is shown to depend on Lagrangian correlation times and on the scaling of dissipation-rate fluctuations. The convergence of the temperature spectrum to asymptotic scaling is observed to be slow, due to the broadband character of the temperature production spectrum and the slow convergence of the dissipation-rate spectrum to its asymptotic form.

Chaos and Predictability of Homogeneous-Isotropic Turbulence.

We study the chaoticity and the predictability of a turbulent flow on the basis of high-resolution direct numerical simulations at different Reynolds numbers. We find that the Lyapunov exponent of turbulence, which measures the exponential separation of two initially close solutions of the Navier-Stokes equations, grows with the Reynolds number of the flow, with an anomalous scaling exponent, larger than the one obtained on dimensional grounds. For large perturbations, the error is transferred to larger, slower scales, where it grows algebraically generating an "inverse cascade" of perturbations in the inertial range. In this regime, our simulations confirm the classical predictions based on closure models of turbulence. We show how to link chaoticity and predictability of a turbulent flow in terms of a finite size extension of the Lyapunov exponent.

Passive scalar mixing and decay at finite correlation times in the Batchelor regime

An elegant model for passive scalar mixing and decay was given by Kraichnan (Phys. Fluids, vol. 11, 1968, pp. 945–953) assuming the velocity to be delta correlated in time. For realistic random flows this assumption becomes invalid. We generalize the Kraichnan model to include the effects of a finite correlation time, $\unicode[STIX]{x1D70F}$, using renewing flows. The generalized evolution equation for the three-dimensional (3-D) passive scalar spectrum $\hat{M}(k,t)$ or its correlation function $M(r,t)$, gives the Kraichnan equation when $\unicode[STIX]{x1D70F}\rightarrow 0$, and extends it to the next order in $\unicode[STIX]{x1D70F}$. It involves third- and fourth-order derivatives of $M$ or $\hat{M}$ (in the high $k$ limit). For small-$\unicode[STIX]{x1D70F}$ (or small Kubo number), it can be recast using the Landau–Lifshitz approach to one with at most second derivatives of $\hat{M}$. We present both a scaling solution to this equation neglecting diffusion and a more exact solution including diffusive effects. To leading order in $\unicode[STIX]{x1D70F}$, we first show that the steady state 1-D passive scalar spectrum, preserves the Batchelor (J. Fluid Mech., vol. 5, 1959, pp. 113–133) form, $E_{\unicode[STIX]{x1D703}}(k)\propto k^{-1}$, in the viscous–convective limit, independent of $\unicode[STIX]{x1D70F}$. This result can also be obtained in a general manner using Lagrangian methods. Interestingly, in the absence of sources, when passive scalar fluctuations decay, we show that the spectrum in the Batchelor regime at late times is of the form $E_{\unicode[STIX]{x1D703}}(k)\propto k^{1/2}$ and also independent of $\unicode[STIX]{x1D70F}$. More generally, finite $\unicode[STIX]{x1D70F}$ does not qualitatively change the shape of the spectrum during decay. The decay rate is however reduced for finite $\unicode[STIX]{x1D70F}$. We also present results from high resolution ($1024^{3}$) direct numerical simulations of passive scalar mixing and decay. We find reasonable agreement with predictions of the Batchelor spectrum during steady state. The scalar spectrum during decay is however dependent on initial conditions. It agrees qualitatively with analytic predictions when power is dominantly in wavenumbers corresponding to the Batchelor regime, but is shallower when box-scale fluctuations dominate during decay.

New insights on the complex dynamics of two-phase flow in porous media under intermediate-wet conditions

Multiphase flow in porous media is important in a number of environmental and industrial applications such as soil remediation, CO2 sequestration, and enhanced oil recovery. Wetting properties control flow of immiscible fluids in porous media and fluids distribution in the pore space. In contrast to the strong and weak wet conditions, pore-scale physics of immiscible displacement under intermediate-wet conditions is less understood. This study reports the results of a series of two-dimensional high-resolution direct numerical simulations with the aim of understanding the pore-scale dynamics of two-phase immiscible fluid flow under intermediate-wet conditions. Our results show that for intermediate-wet porous media, pore geometry has a strong influence on interface dynamics, leading to co-existence of concave and convex interfaces. Intermediate wettability leads to various interfacial movements which are not identified under imbibition or drainage conditions. These pore-scale events significantly influence macro-scale flow behaviour causing the counter-intuitive decline in recovery of the defending fluid from weak imbibition to intermediate-wet conditions.

Laminar-turbulent transition in supersonic boundary layers with surface heat transfer: A numerical study

ABSTRACTThrough high-resolution direct numerical simulations, the present study aims to investigate several laminar-to-turbulent transition scenarios in the presence of wall heat transfer for supersonic boundary layers over strongly heated/cooled and adiabatic flat plates. The laminar boundary layer is tripped using a suction and blowing technique with a single-frequency, multiple-spanwise wavenumber excitation. The results are evaluated and compared with linear stability theory to isolate the effect of wall heat transfer, as well as forcing parameters, on the transition. It was found that increasing the disturbance amplitude as well as perturbation frequency moves the transition upstream. Also, the effect of wall heating was seen to stabilize the flow and to postpone the transition, contrary to the wall cooling.

Magnetically induced instabilities in duct flows

The occurrence of magnetically induced instability in magnetohydrodynamic duct flows is studied for Hunt flow, where one pair of walls parallel to the magnetic field is electrically insulating and the Hartmann walls perpendicular to the field are electrically conducting. The onset of time-dependent flow patterns and their intensity depends on the strength of the magnetic field and on the flow rate in terms of the Hartmann and Reynolds numbers, respectively. The problem is studied by a complementary approach using laboratory experiments, linear stability analysis and high-resolution direct numerical simulations.

The role of Reynolds number in the fluid-elastic instability of tube arrays

The onset of fluid-elastic instability in tube arrays is thought to depend primarily on the mean flow velocity, the Scruton number and the natural frequencies of the tubes. However, evidence from experiments suggests that the Reynolds number is also an important parameter, although the available data are insufficient to understand or quantify this effect. We use high resolution direct numerical simulations to solve the penalized two-dimensional Navier–Stokes equations in order to accurately model turbulent flow through tube arrays with a pitch to diameter ratio P∕D=1.5. To investigate the Reynolds number effect we perform simulations that independently vary the mean flow velocity and the Reynolds number at fixed Scruton number. Parameters are chosen so that the simulations are well outside the lock-in regime of resonant vortex excitation. Increasing Reynolds number and mean flow velocity both have strong de-stabilizing effects for rotated arrays. For in-line arrays the effect is weaker and not monotonic with increasing Reynolds number and mean flow velocity. This study clarifies how the onset of fluid-elastic instability depends on Reynolds number (and hence turbulence intensity) and reduces uncertainties arising from the experimental data, which usually do not account for the effect of Reynolds number. It also demonstrates the usefulness of two-dimensional direct numerical simulations to investigate fluid-elastic instability at turbulent Reynolds numbers.

Multiscale anisotropic fluctuations in sheared turbulence with multiple states

We use high resolution direct numerical simulations to study the anisotropic contents of a turbulent, statistically homogeneous flow with random transitions among multiple energy containing states. We decompose the velocity correlation functions on different sectors of the three dimensional group of rotations, SO(3), using a high-precision quadrature. Scaling properties of anisotropic components of longitudinal and transverse velocity fluctuations are accurately measured at changing Reynolds numbers. We show that independently of the anisotropic content of the energy containing eddies, small-scale turbulent fluctuations recover isotropy and universality faster than previously reported in experimental and numerical studies. The discrepancies are ascribed to the presence of highly anisotropic contributions that have either been neglected or measured with less accuracy in the foregoing works. Furthermore, the anomalous anisotropic scaling exponents are devoid of any sign of saturation with increasing order. Our study paves the way to systematically assess persistence of anisotropy in high Reynolds number flows.

Hurricanes Ingrid and Manuel (2013) and their impact on the salinity of the Meteoric Water Mass, Quintana Roo, Mexico

We report on measurements of the salinity and temperature in the Yax Chen cave system on the Yuacatan peninsula. This paper is submitted together with Kovacs et al. (2017). Kovacs et al. focuses on the salinity levels of the meteoric lens, while this paper uses the observed results to elucidate the hydrodynamics. The cave passages have water depths on the order of 10m, with flow on the order of ten centimeters a second, and as such is a hydrodynamic, as opposed to a porous, system. The measurements reveal that episodes of significant mixing between the fresh meteoric lens and the underlying salty water are driven by meteorological events (e.g., Hurricane Rina in 2011, and the twin Hurricanes Ingrid and Manuel in 2013). We find evidence that after the hurricanes in 2013, the water column remains unstable for several months. Through wavelet analysis, we find that the marine Water Mass (WM) exhibits much less low period activity compared to the meteoric WM. We hypothesize that the open cenotes are locations of high mixing intensity, with turbulent fronts propagating away from the sites of direct mixing into the cave network. We perform laboratory experiments and numerical simulations to explore this phenomenon, and find that mixing preferentially occurs on the flanks of regions of strong, stable density stratification (i.e., on the periphery of pycnoclines), and leads to entrainment of fluid into the turbulent region. Using high resolution direct numerical simulation, we explore the detailed manner in which turbulent entrainment can drive flow toward the mixing region, and lead to mixing of passive tracers. Finally, we discuss the implications of these results for the mixing of passive tracers, such as suspended chemicals.

Role of thermal disequilibrium on natural convection in porous media: Insights from pore-scale study.

The present study investigates the role of thermal nonequilibrium on natural convection in a fluid-saturated porous medium heated from below. We conduct high-resolution direct numerical simulation at the pore scale in a two-dimensional regular porous structure by means of the thermal lattice-Boltzmann method (LBM). We perform a combination of linear stability analysis of continuum-scale heat transfer models, and pore-scale and continuum-scale simulations to study the role of thermal conductivity contrasts among phases on natural convection. The comparison of pore-scale lattice-Boltzmann simulations with linear stability analysis reveals that traditional continuum-scale models fail to capture the correct onset of convection, convection mode, and heat transfer when the thermal conductivity of the solid obstacles does not match that of the fluid.