Direct Numerical Simulation Analysis Research Articles

Control of roughness-induced transition in supersonic flows by local wall heating strips

Isolated-roughness-induced transitions controlled by local wall heating strips are studied via direct numerical simulation and BiGlobal linear stability analysis. The transition mechanisms are studied first with different wall temperatures. The separated shear layer–counter-rotating vortex system is found to be the main source for transitions. Symmetric and antisymmetric modes are observed in the wake, and the former is dominant. The local wall heating strip can delay the transition, and this effect is enhanced with higher heating temperature, wider strip and a combination of upstream and downstream control strips. The upstream strip lifts up the inlet flow and weakens the wake system in an indirect manner. The antisymmetric mode gradually vanishes, while the symmetric mode always exists but becomes weaker. The downstream strip exhibits a more effective transition delay by directly weakening the separated shear layer and vortex system in the wake. Vorticity transport analysis suggests that the downstream strip increases dissipation for streamwise vorticity and transfers it into wall-normal and spanwise vorticity. BiGlobal analyses indicate that the downstream strip shows less influence on the peak growth rate of the symmetric mode but significantly shrinks its unstable region. Analyses of the disturbance energy production indicate that the upstream strip wakens the wall-normal and spanwise shear at the same time, but the downstream strip mainly wakens the wall-normal one. More simulations are performed with different roughness heights, point-source disturbance and different roughness shapes. The results show that the current method remains effective enough in delaying transitions at a wide range of conditions.

Particle-resolved direct numerical simulation and bottom-up statistical analysis on solid-phase pressure in particle–fluid systems

Solid-phase stress is a major factor shaping the complex behaviors of particle–fluid systems. However, uncertainties and inconsistencies can be found among the various models proposed. This work pays attention to the effect of mesoscale structures, that is, the heterogeneity of particle distribution at a scale of statistical meaning but no significant flow field variation, on the solid-phase normal stress, or pressure. Using a bottom-up statistical method, the solid-phase pressure in liquid- and gas–solid flows is investigated by particle-resolved direct numerical simulation (PR-DNS). It is found that, in almost uniform liquid–solid flows, the solid-phase pressure is not well predicted by classical kinetic theory of granular flow (KTGF) due to the presence of interphase force, although KTGF applies much better to single-phase granular flows. In gas–solid flows, with increasing heterogeneity described by structural functions, the statistical solid-phase pressure becomes significantly larger than that in corresponding homogeneous flows. It reveals that mesoscale structures strongly affect solid-phase pressure, and suggests the deviation from classical KTGF in heterogeneous gas–solid flows can be attributed to both the interphase forces (mainly drag) and mesoscale structures. The coefficients in the solid-phase pressure models in KTFG are modified, fitting the statistical results of both homogeneous and heterogeneous particle–fluid flows.

Instability and transition control by steady local blowing/suction in a hypersonic boundary layer

The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

SpiralDesigner: An AI-assisted design interface for efficient separation of neutrally buoyant and non-buoyant particles using spiral microfluidic devices

Spiral microfluidic-based devices play an important role in particle separation and concentration which is essential for many biomedical, chemical, and environmental purposes. Although many platforms were developed for the separation and purification of various microparticles, there is a lack of practical rules for designing these microfluidic platforms. Moreover, the physics of migration for non-naturally buoyant particles was overlooked in the previous studies. In this vein, here, we used direct numerical simulation (DNS) and particle tracing analysis to examine the physics of particle migration for both naturally buoyant and non-naturally buoyant particles. Later, by combining our simulation results with artificial intelligence (AI), we introduced a software, hereafter called SpiralDesigner, that can easily predict the final position of particles (naturally buoyant and non-naturally buoyant) in the outlet of the spiral microchannel with an accuracy of ∼98 %. SpiralDesigner just needs the particle size and density, length and radius of curvature of the spiral microchannel, and the total flow rate for prediction and after that, it provides the separation index that tells the user whether two particles are separable or not. This software can be very useful for designing a spiral microchannel for particle separation since it is very easy to use and also does not require any computational fluid dynamic simulations or fabrication. Hence, SpiralDesigner can potentially be used for a variety of purposes such as circulating tumor cell separation, stem cell harvesting, powder technology, environmental technology, and food science.

Flow-induced vibration of two tandem square cylinders at low Reynolds number: transitions among vortex-induced vibration, biased oscillation and galloping

The flow-induced vibrations (FIVs) of two identical tandem square cylinders with mass ratio m* = 3.5 at Reynolds number Re = 150 are investigated through two-dimensional direct numerical simulation (DNS) and linear stability analysis over a parameter range of spacing ratio 1.5 ≤ L* ≤ 5 and reduced velocity 3 ≤ Ur ≤ 34. Three kinds of FIV responses, namely vortex-induced vibration (VIV), biased oscillation (BO) and galloping (GA), are identified. The FIVs are then further classified into the branches of initial VIV (IV), resonant VIV (RV and RV′), flutter-induced VIV (FV), desynchronized VIV (DV), VIV developing from GA (GV), transitional state between VIV and GA (TR), BO and GA based on the characteristics of the vibration responses. The transitions among different FIV branches are examined by combining the DNS with linear stability analysis, where the transition boundaries among the VIV, BO and GA branches over the concerned parameters are identified on the branch maps. The transition from IV to RV or RV′ is found to be related to the unstable wake mode, while the FV, transiting from RV or RV′, is induced by the unstable structural factor in the wake-structure mode. The structural instability is considered as the physical origin of GA, whereas the mode competition between unstable wake and structure leads to DV, GV and TR, and thus delays the appearance of GA. The transition from DV to BO with biased equilibrium position, accompanied by the even-order harmonic frequencies, is essentially induced by the symmetry breaking bifurcation.

Direct Numerical Simulation Analysis of the Closure of Turbulent Scalar Flux during Flame–Wall Interaction of Premixed Flames within Turbulent Boundary Layers

Direct Numerical Simulation Analysis of the Closure of Turbulent Scalar Flux during Flame–Wall Interaction of Premixed Flames within Turbulent Boundary Layers

Effects of liquid water injection on flame surface topology and propagation characteristics in spray flames: A direct numerical simulation analysis

The effects of water injection on flame surface topology and local flame propagation characteristics have been analyzed for statistically planar turbulent n-heptane spray flames with an overall (i.e., liquid + gaseous) equivalence ratio of unity using carrier-phase direct numerical simulations. Most fuel droplets have been found to evaporate as they approach the flame even though some droplets can survive until the burnt gas side is reached, whereas water droplets do not significantly evaporate ahead of the flame and the evaporation of water droplets starts to take place in the reaction zone and is completed within the burnt gas. However, the gaseous-phase combustion occurs predominantly in fuel–lean mode although the overall equivalence ratio remains equal to unity. The water injection has been found to suppress the fuel droplet-induced flame wrinkling of the progress variable isosurface under the laminar condition, and this effect is particularly strong for small water droplets. However, turbulence-induced flame wrinkling masks these effects, and thus, water injection does not have any significant impact on flame wrinkling for the turbulent cases considered here. The higher rate of evaporation and the associated high latent heat extraction for smaller water droplets induce stronger cooling effects, which weakens the effects of chemical reaction. This is reflected in the decrease in the mean values of density-weighted displacement speed with decreasing water droplet diameter. The weakening of flame wrinkling as a result of injection of small water droplets is explained through the curvature dependence of the density-weighted displacement speed. The combined influence of cooling induced by the latent heat extraction of water droplets and flame surface flattening leads to a decrease in volume-integrated burning rate with decreasing water droplet diameter in the laminar cases, whereas the cooling effects are primarily responsible for the drop in burning rate with decreasing water droplet diameter in the turbulent cases.

Direct numerical simulation and mode analysis of turbulent transition flow in a compressor blade channel

The separation and turbulent transition of the flow in a compressor blade channel are investigated through direct numerical simulations (DNS) at a Reynolds number of 1.367 × 105. Based on the original DNS data, both time-averaged statistics and instantaneous vortex structures of the flow field are extensively analyzed. The vortices are visualized and studied by the Liutex method, and the streaming dynamic mode decomposition (SDMD), a low-storage variant of conventional DMD, is applied to the large datasets obtained on both pressure and suction sides. The physical quantity analyzed with SDMD is the Liutex magnitude R. The DNS results indicate that flow separation occurs on both sides of the blade. On the pressure surface, the separation is weak and the flow remains in a natural transition dominated by viscous Tollmien–Schlichting instabilities. In contrast, owing to the presence of a large laminar separation bubble, the flow experiences a separation transition governed by inviscid Kelvin–Helmholtz instabilities on the suction surface. The SDMD results suggest that a broad range of vortex frequencies exist in the transition flow, and the scale of the spatial structures is negatively correlated with the frequency of the mode. On the pressure surface, the extracted SDMD modes are primarily related to Kelvin–Helmholtz rolls, whereas on the suction side, influenced by the separated boundary layer, the modal structures exhibit greater diversity.

Modelling of the Flame Surface Density Transport During Flame-Wall Interaction of Premixed Flames within Turbulent Boundary Layers

ABSTRACT A priori Direct Numerical Simulation (DNS) analysis of the modelling of the generalised flame surface density (FSD) transport equation in the framework of Reynolds Averaged Navier-Stokes (RANS) simulations has been conducted with a focus on flame-wall interaction (FWI) within turbulent boundary layers. The analysis was performed using two different scenarios: one involving the unsteady head-on interaction of a statistically planar premixed flame as it propagates through a turbulent boundary layer, and the other addressing statistically stationary oblique-wall interaction of a V-shaped premixed flame within a turbulent channel flow. Flame-wall interaction has been observed to exert a significant influence on the statistical behavior of the terms in the FSD transport equation. Throughout all phases of flame-wall interaction in both configurations, the primary source and sink terms in the FSD transport equation are consistently associated with the tangential strain rate and curvature terms. The relative importance of the contributions of the propagation and turbulent transport terms in the FSD transport equation have been found to be influenced by the flame-wall interaction configuration. Existing models for the tangential strain rate term in the FSD transport equation have been identified as inadequate based on a priori DNS assessment. Hence, adjustments to these models have been proposed to address the impact of flame orientation and near-wall effects specifically in the context of flame-wall interaction within turbulent boundary layers. The alignment between the flame normal vector and the wall normal vector has been identified as a crucial factor in modelling the contributions of unresolved dilatation rate and unresolved normal strain rate to the FSD transport equation. New models for these terms have been demonstrated to exhibit satisfactory agreement with the corresponding terms extracted from DNS data.

Direct numerical simulation of a wall source dispersion in a turbulent channel flow

A comprehensive direct numerical simulation (DNS) is conducted to analyze the turbulent mixing process of a surface source dispersion emitting from the bottom wall in a turbulent channel flow. A comparative analysis of ten test cases has been conducted to examine the turbulent mixing process and its relationship with the source strength. The study involves an examination of the dispersion process in both physical and spectral spaces, which includes an evaluation of statistical moments of the concentration field, pre-multiplied spatial spectra of the velocity and concentration fields, as well as an analysis of the coherent turbulent structures in the flow. Upon normalization by friction concentration, the DNS analysis reveals that the first- and second-order statistical moments of the concentration field remain unaffected by variations in the source strength. Conversely, the relative intensity of concentration fluctuations and the thickness of the concentration boundary layer exhibit significant susceptibility to variations in the source strength. It has been observed that the dispersion process within the channel is significantly influenced by the small-scale eddies in cases where the source strength is not particularly intense. When confronted with high source strength scenarios, analysis of the simulation results establishes that both small- and large-scale eddies are crucial players in the dispersion phenomena, as evinced by a comparison of the pre-multiplied spectra of concentration and velocity fields. Furthermore, hairpin vortices have been recognized as the primary source of turbulence in the dispersal of substances from regions of high shear to the center of the channel.

Bi-global stability of supersonic backward-facing step flow

Supersonic backward-facing step (BFS) flow is numerically studied using direct numerical simulation (DNS) and global stability analysis (GSA) with a free stream Mach number of 2.16 and a Reynolds number of 7.938 × 105 based on the flat-plate length L and free stream conditions. Two-dimensional BFS flow becomes unstable to three-dimensional perturbations as the step height h exceeds a certain value, while no two-dimensionally unstable mode is found. Global instability occurs with the fragmentation of the primary separation vortex downstream of the step. Two stationary modes and one oscillatory unstable mode are obtained at a supercritical ratio of L/h = 32.14, among which the two stationary modes originate from the coalescence of a pair of conjugate modes. The most unstable mode manifests itself as streamwise streaks in the reattached boundary layer, which is similar to that in shock-induced separated flow, although the flow separation mechanisms are different. Without introducing any external disturbances, the DNS captures the preferred perturbations and produces a growth rate in agreement with the GSA prediction in the linear growth stage. In the quasi-steady stage, the secondary separation vortex breaks up into several small bubbles, and the number of streamwise streaks is doubled. A low-frequency unsteadiness that may be associated with the oscillatory mode is also present.

Transition to fully developed turbulence in liquid-metal convection facilitated by spatial confinement

Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number $Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The $Ra_c$ and the transition to fully developed turbulence Rayleigh number $Ra_f$ depend on the aspect ratio $\varGamma$ with $Ra_c\sim \varGamma ^{-4.05}$ and $Ra_f\sim \varGamma ^{-3.01}$ , implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number $Ra/Ra_{c}$ ( $Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at $Ra\approx 200Ra_c$ in a $\varGamma =1$ cell, the same transition in a $\varGamma =1/20$ cell only requires $Ra\approx 3Ra_c$ . Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with $\varGamma <1$ , the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.

DNS analysis of the effect of control parameters on the heat transfer performance of intermittently controlled impinging jets

Impinging jets are used industrially in various applications such as heating and cooling. However, multiple impinging jets (MIJ) create a complex flow field due to interference between the individual jets, which hinders heat transfer. In order to solve the problem of heat transfer performance in MIJ, a new control method must be developed. This study introduces intermittent control to 13 hexagonally arranged circular jets to investigate the possibility of control. In the intermittent control, the 13 jets are divided into three groups, and each group is intermittently issued. The distance between jets and the issuing period are changed as control parameters, and the heat transfer characteristics are evaluated using direct numerical simulation (DNS). The time-averaged velocity field revealed the effects of the intermittent period and the distance between jets on the flow characteristics, and the Nusselt number distribution on the wall surface indicated that the proposed method improves the heat transfer characteristics.

Stability Analysis for High-Speed Boundary-Layer Flow with Cavities

This study uses direct numerical simulation and stability analysis methods to investigate the impact of wall cavity defects on the instability of boundary layers at Ma=5.92 and Ma=1.38. For flow at Ma=5.92, synchronization points with equal phase velocities in both fast and slow modes play a crucial role in controlling disturbance wave growth. When the inlet disturbance wave frequency (ω=0.98) approaches the synchronization point frequency, the impact of cavity size on the growth of the disturbance wave can be divided into three regions in the (L/δ99, D/δ99) plane, namely, region A, region B, and region C. Region A refers to small cavities with L/δ99<2, which have the weakest suppression effect. Region B includes large cavities with L/δ99>2 and D/δ99<1.5 and exhibits the best suppression effect. Finally, region C covers cavities with L/δ99>3 and D/δ99>1.5 and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at Ma=1.38, cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities (L/δ99>5, D/δ99<2) exhibit the most significant enhancement.

Boundary layer transition due to distributed roughness: effect of roughness spacing

The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation and global stability analysis, and compared with isolated roughness elements at the same Reynolds number $Re_h=U_eh/\nu$ ( $U_e$ is the boundary layer edge velocity, h is roughness height and $\nu$ is the kinetic viscosity of the fluid). Small spanwise spacing ( $\lambda _z=2.5h$ ) inhibits the formation of counter-rotating vortex pairs (CVP) and, as a result, hairpin vortices are not generated and the downstream shear layer is steady. For $\lambda _z=5h$ , the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. The temporal periodicity of the primary hairpin vortices appears to be independent of the streamwise spacing. Distributed roughness leads to a lower critical roughness Reynolds number for instability to occur and a more significant breakdown of the boundary layer compared with isolated roughness. When the streamwise spacing is $\lambda _x=5h$ , the high-momentum fluid barely moves downward into the cavities and the wake flow has little impact on the following roughness elements. The leading unstable varicose mode is associated with the central low-speed streaks along the aligned roughness elements, and its frequency is close to the shedding frequency of hairpin vortices in the isolated case. For larger streamwise spacing ( $\lambda _x=10h$ ), two distinct modes are obtained from global stability analysis. The first mode shows varicose symmetry, corresponding to the primary hairpin vortex shedding induced by the first-row roughness. The high-speed streaks formed in the longitudinal grooves are also found to be unstable and interact with the varicose mode. The second mode is a sinuous mode with lower frequency, induced as the wake flow of the first-row roughness runs into the second row. It extracts most energy from the spanwise shear between the high- and low-speed streaks.

Sensitivity Analysis of Direct Numerical Simulation of a Spatially Developing Turbulent Mixing Layer to the Domain Dimensions

Abstract Understanding spatial development of a turbulent mixing layer is essential for many engineering applications. However, the flow development is difficult to replicate in physical or numerical experiments. For this reason, the most attractive method for the mixing layer analysis is the direct numerical simulation (DNS), with the most control over the simulation inputs and free from modeling assumptions. On the other hand, the DNS cost often prevents conducting the sensitivity analysis of the simulation results to variations in the numerical procedure and thus, separating numerical and physical effects. In this paper, effects of the computational domain dimensions on statistics collected from DNS of a spatially developing incompressible turbulent mixing layer are analyzed with the focus on determining the domain dimensions suitable for studying the flow asymptotic state. In the simulations, the mixing layer develops between two coflowing laminar boundary layers formed on two sides of a sharp-ended splitter plate of a finite thickness with characteristics close to those of the untripped boundary layers in the experiments by Bell and Mehta, AIAA J., 28(12), 2034 (1990). The simulations were conducted using the spectral-element code Nek5000.

Statistical Behaviour and Modelling of Variances of Reaction Progress Variable and Temperature During Flame-Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The statistical behaviour of the transport of reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} have been analysed using three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame-wall interaction with isothermal inert walls within turbulent boundary layers for (i) an unsteady head-on quenching of a statistically planar flame propagating across the boundary layer, and (ii) a statistically stationary oblique wall quenching of a V-flame. It has been found that the reaction rate contribution acts as a leading order source term to the transport of both reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} whereas the molecular dissipation term remains the leading order sink term for both configurations analysed here. With the progress of flame wall interaction, the magnitude of all the source terms for the transport equations of both reaction progress variable and non-dimensional temperature variances vanish in the near-wall region with the onset of flame quenching. However, the molecular dissipation term continues to act as a sink term. The performances of the existing models for turbulent scalar flux, reaction rate and scalar dissipation rate contributions have been assessed for both flame-wall interaction configurations based on a priori DNS analysis. The existing available models for scalar dissipation rate for temperature and the reaction rate contribution in the variance transport equations even with the previously proposed wall corrections do not adequately predict the behaviour in the near-wall region. Modifications have been suggested to the existing closure models for the scalar dissipation rate and the reaction rate contribution to the scalar variance transport equations to improve the predictions in the near-wall region. Furthermore, the recommended closures for the unclosed terms of both reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} are shown to accurately capture the corresponding variations obtained from DNS data for both near to and away from the wall.

Numerical analyses of wire-plate electrohydrodynamic flows

We present numerical analyses of two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid between a wire electrode and two plate electrodes with a Poiseuille flow, using direct numerical simulation and global stability analysis. Both conduction and injection mechanisms for charge generation are considered. In this work we focused on the intensity of the cross-flow and studied the EHD flows without a cross-flow, with a weak cross-flow and with a strong cross-flow. (1) In the case without a cross-flow, we investigated its nonlinear flow structures and linear dynamics. We found that the flow in the conduction regime is steady, whereas the flow in the injection regime is oscillatory, which can be explained by a global stability analysis. (2) The EHD flow with a weak cross-flow is closely related to the flow phenomena in an electrostatic precipitator (ESP). Our analyses indicate that increasing the cross-flow intensity or the electric Reynolds number leads to a less stable flow. Based on these results, we infer that one should adopt a relatively low voltage and weak cross-flow in the wire-plate EHD flow to avoid flow instability, which may hold practical implications for ESP. (3) The case of strong cross-flow is examined to study the EHD effect on the wake flow. By comparing the conventional cylindrical wake with the EHD wake in linear and nonlinear regimes, we found that the EHD effect brings forward the vortex shedding in wake flows. Besides, the EHD effect reduces the drag coefficient when the cross-flow is weak, but increases it when it is strong.

Kinematic Effects on Probability Density Functions of Energy Dissipation Rate and Enstrophy in Turbulence.

Direct numerical simulation and theoretical analyses showed that the probability density functions (PDFs) of the energy dissipation rate and enstrophy in turbulence are asymptotically stretched gamma distributions with the same stretching exponent, and both the left and right tails of the enstrophy PDF are longer than those of the energy dissipation rate regardless of the Reynolds number. The differences in PDF tails arise due to the kinematics, with differences in the number of terms contributing to the dissipation rate and enstrophy. Meanwhile, the stretching exponent is determined by the dynamics and likeliness of singularities.

Rossby waves past the breaking point in zonally dominated turbulence

The spontaneous emergence of structure is a ubiquitous process observed in fluid and plasma turbulence. These structures typically manifest as flows which remain coherent over a range of spatial and temporal scales, resisting statistically homogeneous description. This work conducts a computational and theoretical study of coherence in turbulent flows in the stochastically forced barotropic$\beta$-plane quasi-geostrophic equations. These equations serve as a prototypical two-dimensional model for turbulent flows in Jovian atmospheres, and can also be extended to study flows in magnetically confined fusion plasmas. First, analysis of direct numerical simulations demonstrates that a significant fraction of the flow energy is organized into coherent large-scale Rossby wave eigenmodes, comparable with the total energy in the zonal flows. A characterization is given for Rossby wave eigenmodes as nearly integrable perturbations to zonal flow Lagrangian trajectories, linking finite-dimensional deterministic Hamiltonian chaos in the plane to a laminar-to-turbulent flow transition. Poincaré section analysis reveals that Lagrangian flows induced by the zonal flows plus large-scale waves exhibit localized chaotic regions bounded by invariant tori, manifesting as Rossby wave breaking in the absence of critical layers. It is argued that the surviving invariant tori organize the large-scale flows into a single temporally and zonally varying laminar flow, suggesting a form of self-organization and wave stability that can account for the resilience of the observed large-amplitude Rossby waves.