High-resolution Direct Numerical Simulations Research Articles

The statistical geometry of material loops in turbulence

Material elements – which are lines, surfaces, or volumes behaving as passive, non-diffusive markers – provide an inherently geometric window into the intricate dynamics of chaotic flows. Their stretching and folding dynamics has immediate implications for mixing in the oceans or the atmosphere, as well as the emergence of self-sustained dynamos in astrophysical settings. Here, we uncover robust statistical properties of an ensemble of material loops in a turbulent environment. Our approach combines high-resolution direct numerical simulations of Navier-Stokes turbulence, stochastic models, and dynamical systems techniques to reveal predictable, universal features of these complex objects. We show that the loop curvature statistics become stationary through a dynamical formation process of high-curvature folds, leading to distributions with power-law tails whose exponents are determined by the large-deviations statistics of finite-time Lyapunov exponents of the flow. This prediction applies to advected material lines in a broad range of chaotic flows. To complement this dynamical picture, we confirm our theory in the analytically tractable Kraichnan model with an exact Fokker-Planck approach.

The principal stage in wind-wave generation

The dynamics of wind-generated water waves in the principal stage of the Phillips theory (Phillips, J. Fluid Mech., vol. 2, 1957, pp. 417–445) is investigated by a combined numerical and analytical approach. We perform a number of high-resolution direct numerical simulation (DNS) of turbulent wind over initially calm water to capture the multistage generation of water waves. Detailed analyses are conducted to evaluate the Phillips theory in both physical space and wavenumber space. Numerical evidence is obtained for the existence of a principal stage when the surface elevation variance grows linearly with time. We further propose a random sweeping turbulence pressure–wave interaction model by introducing the random sweeping hypothesis of air pressure fluctuations to the Phillips theory, and obtain an asymptotic solution of the mean square of surface wave elevations over time. This asymptotic analysis captures the temporal oscillations of surface elevation variance in the principal stage, which is also confirmed by our DNS results. The wavenumber spectrum of surface wave elevations is analysed using a time-dependent norm to elucidate the role of the resonance mechanism on wave generation. In physical space, we use the random sweeping turbulence pressure–wave interaction model to obtain a quantitative prediction of the growth rate of surface elevation variance in the principal stage, which is found to agree with the DNS results better than the original Phillips model.

Connecting wall modes and boundary zonal flows in rotating Rayleigh-Bénard convection

Rotating thermal convection captures key properties of geophysical and astrophysical systems. By performing high-resolution direct numerical simulations we strongly connect the physics of wall-localized states of rotating convection with observations of a boundary zonal flow where turbulent convection has a strong boundary localized structure with similar properties. We show that as buoyancy increases at fixed rotation rate, spatial, temporal, and heat-transport properties of the localized state change smoothly and monotonically. Our results connect the physics of rotating convection in finite containers with similar geophysical/astrophysical phenomena at much larger spatial scales.

Role of barriers in the airborne spread of virus-containing droplets: A study based on high-resolution direct numerical simulations

State-of-the-art direct numerical simulations are exploited to study the role of barriers on the airborne spread of virus-containing droplets. Our study is motivated by recent findings pointing to the key role of turbulence in dictating the final fate of virus-containing droplets in violent human exhalations. Here, all active scales of motion have been explicitly taken into account, including their interplay with the droplet evaporation process occurring once droplets are emitted in a drier ambient air, and accounting for the time-varying droplet inertia due to the water loss via evaporation. We show that barriers commonly used to mitigate the airborne spread of the virus cause nontrivial dynamical effects influencing the final reach of the virus-containing droplets, not always being beneficial to this aim. These conclusions do depend on the relative humidity of the ambient condition, and in particular whether the ambient humidity is above or below the so-called efflorescence relative humidity. Our findings provide a physically based answer to the question on how effective barriers are to protect people from airborne virus transmission in indoor environments.

Hypersonic boundary layer transitions over a yawed, blunt cone

The boundary layer transition process for a straight circular cone with angle of attack (AoA) of 6° at Mach 6 was studied via high-resolution direct numerical simulations and stability analyses. A pair of strong streamwise vortices simultaneously induced a low-speed mushroom structure to emerge near the leeward plane. This structure was subject to low-frequency sinuous and high-frequency varicose instabilities. The transition between windward and leeward rays likely occurred due to the interactions between low-frequency traveling and stationary crossflow vortices. The lower-amplitude high-frequency secondary crossflow instability mode could be traced back to the upstream Mack mode. Although the axial and crossflow vortices were fundamentally different, there was a striking similarity between them since both high-frequency perturbations were driven by azimuthal shear and resulted in staggered positive and negative axial vortices along the streamwise direction.

Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

We study the connection between extreme events of thermal and kinetic energy dissipation rates in the bulk of three-dimensional Rayleigh-Bénard convection and the wall shear stress patterns at the top and the bottom plates that enclose the layer. Zero points of this two-dimensional vector field stand for detachments of strong thermal plumes. If their position at the opposite plates and a given time is close then they can be considered as precursors for high-amplitude bulk dissipation events triggered by plume collisions or close passings. This scenario requires a breaking of the synchronicity of the boundary layer dynamics at both plates which is found to be in line with a transition of the bulk derivative statistics from Gaussian to intermittent. Our studies are based on three-dimensional high-resolution direct numerical simulations for moderate Rayleigh numbers between and .

Direct numerical simulation of quasi-two-dimensional MHD turbulent shear flows

Abstract

Coagulation of inertial particles in supersonic turbulence

Coagulation driven by supersonic turbulence is primarily an astrophysical problem because coagulation processes on Earth are normally associated with incompressible fluid flows at low Mach numbers, while dust aggregation in the interstellar medium for instance is an example of the opposite regime. We study coagulation of inertial particles in compressible turbulence using high-resolution direct and shock-capturing numerical simulations with a wide range of Mach numbers from nearly incompressible to moderately supersonic. The particle dynamics is simulated by representative particles and the effects on the size distribution and coagulation rate due to increasing Mach number is explored. We show that the time evolution of particle size distribution mainly depends on the compressibility (Mach number). We find that the average coagulation kernel ⟨Cij⟩ scales linearly with the average Mach number ℳrms multiplied by the combined size of the colliding particles, that is, 〈Cij〉∼〈(ai+aj)3〉 ℳrmsτη−1, which is qualitatively consistent with expectations from analytical estimates. A quantitative correction 〈Cij〉∼〈(ai+aj)3〉(vp,rms/cs)τη−1 is proposed and can serve as a benchmark for future studies. We argue that the coagulation rate ⟨Rc⟩ is also enhanced by compressibility-induced compaction of particles.

How Alfvén waves energize the solar wind: heat vs work.

A growing body of evidence suggests that the solar wind is powered to a large extent by an Alfvén-wave (AW) energy flux. AWs energize the solar wind via two mechanisms: heating and work. We use high-resolution direct numerical simulations of reflection-driven AW turbulence (RDAWT) in a fast-solar-wind stream emanating from a coronal hole to investigate both mechanisms. In particular, we compute the fraction of the AW power at the coronal base (P AWb) that is transferred to solar-wind particles via heating between the coronal base and heliocentric distance r, which we denote χ H(r), and the fraction that is transferred via work, which we denote χ W(r). We find that χ W(r A) ranges from 0.15 to 0.3, where r A is the Alfvén critical point. This value is small compared to one because the Alfvén speed v A exceeds the outflow velocity U at r < r A, so the AWs race through the plasma without doing much work. At r > r A, where v A < U, the AWs are in an approximate sense "stuck to the plasma," which helps them do pressure work as the plasma expands. However, much of the AW power has dissipated by the time the AWs reach r = r A, so the total rate at which AWs do work on the plasma at r > r A is a modest fraction of P AWb. We find that heating is more effective than work at r < r A, with χ H(r A) ranging from 0.5 to 0.7. The reason that χ H ⩾ 0.5 in our simulations is that an appreciable fraction of the local AW power dissipates within each Alfvén-speed scale height in RDAWT, and there are a few Alfvén-speed scale heights between the coronal base and r A. A given amount of heating produces more magnetic moment in regions of weaker magnetic field. Thus, paradoxically, the average proton magnetic moment increases robustly with increasing r at r > r A, even though the total rate at which AW energy is transferred to particles at r > r A is a small fraction of P AWb.

Intermittency of Velocity Circulation in Quantum Turbulence

The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in classical and quantum flows. It is indeed a Lagrangian invariant in inviscid classical fluids. In quantum flows, circulation is quantized, taking discrete values that are directly related to the number and the orientation of thin vortex filaments enclosed by the path. By varying the size of such closed loop, the circulation provides a measure of the dependence of the flow structure on the considered scale. Here we consider the scale dependence of circulation statistics in quantum turbulence, using high resolution direct numerical simulations of a generalized Gross-Pitaevskii model. Results are compared to the circulation statistics obtained from simulations of the incompressible Navier-Stokes equations. When the integration path is smaller than the mean inter-vortex distance, the statistics of circulation in quantum turbulence displays extreme intermittent behavior due to the quantization of circulation, in stark contrast with the viscous scales of classical flows. In contrast, at larger scales, circulation moments display striking similarities with the statistics probed in the inertial range of classical turbulence. This includes the emergence of the power law scalings predicted from Kolmogorov's 1941 theory, as well as intermittency deviations that closely follow the recently proposed bifractal model for circulation moments in classical flows. To date, this is the most convincing evidence of intermittency in the large scales of quantum turbulence. Moreover, our results strongly reinforce the resemblance between classical and quantum turbulence, highlighting the universality of inertial range dynamics, including intermittency, across these two a priori very different systems.

Properties of turbulent channel flow similarity solutions

Abstract

Logarithmic profile of temperature in sheared and unstably stratified atmospheric boundary layers

Wall-bounded turbulent flows are widely observed in natural and engineering systems, such as air flows near the Earth's surface, water flows in rivers, and flows around a car or a plane. The universal logarithmic velocity profile in wall-bounded turbulent flows proposed by von K\'arm\'an in 1930 is one of the few exact physical descriptions of turbulence. However, the mean velocity and temperature profiles cannot be adequately described by this universal log law when buoyancy effects are present. Monin-Obukhov similarity theory (MOST), proposed in 1954, has been the cornerstone theory to account for these buoyancy effects and to describe the atmospheric boundary layer. MOST has been used in almost all global weather, climate and hydrological models to describe the dependence of the mean velocity, temperature and scalar profiles on buoyancy. According to MOST, the logarithmic temperature profile breaks down as buoyancy effects become important. In contrast, here we show that this long-standing MOST theory does not apply for temperature. We propose a new theory for the logarithmic profile of near-wall temperature, which corrects MOST pitfalls and is supported by both high-resolution direct numerical simulations and field observations of the convective atmospheric boundary layer. Buoyancy effects do not modify the logarithmic nature but instead modulate the slope of the temperature profile compared to the universal von K\'arm\'an slope. The new formulation has widespread applications such as in climate models, where the proposed new temperature log law should lead to more realistic continental surface temperature, which are strongly impacted by buoyancy.

Coherent structures in the wake of a long wall-mounted rectangular prism at large incident angles

High-resolution direct numerical simulations are conducted to analyze the flow dynamics of a wall-mounted rectangular prism with a high depth-ratio at different incidence angles. The results demonstrated that changing the incidence angle leads to the creation of transient helical structures in the wake of the prism. The characteristic length and dominant frequencies associated with the unsteady flow are determined, and the origin of different peak frequencies are identified. Finally, a skeleton model is established for the unsteady wake of the prism.

High-resolution direct numerical simulations of flow structure and aerodynamic performance of wind turbine airfoil at wide range of Reynolds numbers

The objective of this study is to develop direct numerical simulations (DNS) to investigate the aerodynamic performance, transition to turbulence, and to capture the laminar separation bubble occurring on a wind turbine blade. Simulations are conducted with spectral/hp element method to investigate the details of flow separation bubble over wind turbine blades with NACA-4412 airfoil at wide range of design parameters. This airfoil is chosen because recent studies have shown that it is challenging to capture the details of the flow instabilities and pressure fluctuations in the separated shear layer of wind turbines by experimental methods. Furthermore, owing to more accurate development of DNS, the separated bubbles at high Reynolds numbers are captured. The results show that the vortex structures shed from the trailing edge of the airfoil by raising the angle of attack (α). Consequently, the fully turbulent flow develops downstream of the trailing edge (Karman vortex). Moreover, the pressure fluctuation significantly increased by raising α. However, some rolling up of the flow structures, similar to Kelvin–Helmholtz rolls, on the pressure surface near the trailing edge, are observed at α>12°. The separation point was delayed from Xsep/C = 0.19 to 0.58 by decreasing α from 16 to 0 at Re = 5 × 104.

Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow

Thermal hydraulics, in certain components of nuclear reactor systems, involve complex flow scenarios, such as flows assisted by free jets and stratified flows leading to turbulent mixing and thermal fluctuations. These complex flow patterns and thermal fluctuations can be extremely critical from a reactor safety standpoint. The component-level lumped approximations (0D) or one-dimensional approximations (1D) models for such components and subsystems in safety analysis codes cannot capture the physics accurately, and may introduce a large degree of modeling uncertainty. On the other hand, high-fidelity computational fluid dynamics codes, which provide numerical solutions to the Navier–Stokes equations, are accurate but computationally intensive, and thus cannot be used for system-wide analysis. An alternate way to improve reactor safety analysis is by building reduced-order emulators from computational fluid dynamics (CFD) codes to improve system scale models. One of the key challenges in developing a reduced-order emulator is to preserve turbulent mixing and thermal fluctuations across different-length scales or time-scales. This paper presents the development of a reduced-order, non-linear, “Markovian” statistical surrogate for turbulent mixing and scalar transport. The method and its implementation are demonstrated on a canonical problem of differentially heated channel flow, and high-resolution direct numerical simulations (DNS) data are used for emulator or surrogate development. This statistical surrogate model relies on Kramers–Moyal expansion and emulates the turbulent velocity signal with a high degree of accuracy.

Turbulence role in the fate of virus-containing droplets in violent expiratory events

Violent expiratory events, such as coughing and sneezing, are highly nontrivial examples of a two-phase mixture of liquid droplets dispersed into an unsteady turbulent airflow. Understanding the physical mechanisms determining the dispersion and evaporation process of respiratory droplets has recently become a priority given the global emergency caused by the SARS-CoV-2 infection. By means of high-resolution direct numerical simulations (DNS) of the expiratory airflow and a comprehensive Lagrangian model for the droplet dynamics, we identify the key role of turbulence on the fate of exhaled droplets. Due to the considerable spread in the initial droplet size, we show that the droplet evaporation time is controlled by the combined effect of turbulence and droplet inertia. This mechanism is clearly highlighted when comparing the DNS results with those obtained using coarse-grained descriptions that are employed in the majority of the current state-of-the-art investigations, resulting in errors up to $100\%$ when the turbulent fluctuations are filtered or completely averaged out.

Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS

Abstract

Synchronizing subgrid scale models of turbulence to data

Large eddy simulations of turbulent flows are powerful tools used in many engineering and geophysical settings. Choosing the right value of the free parameters for their subgrid scale models is a crucial task for which the current methods present several shortcomings. Using a technique called nudging, we show that large eddy simulations can synchronize with data coming from a high-resolution direct numerical simulation of homogeneous and isotropic turbulence. Furthermore, we found that the degree of synchronization is dependent on the value of the parameters of the subgrid scale models utilized, suggesting that nudging can be used as a way to select the best parameters for a model. For example, we show that for the Smagorinsky model, synchronization is optimal when its constant takes the usual value of 0.16. Analyzing synchronization dynamics puts the focus on reconstructing trajectories in phase space, contrary to traditional a posteriori tests of large eddy simulations where the statistics of the flows are compared. These results open up the possibility of utilizing non-statistical analysis in a posteriori tests of large eddy simulations.

Second-order velocity structure functions in direct numerical simulations of turbulence with Rλ up to 2250

High-resolution direct numerical simulations of incompressible turbulence with Taylor-scale Reynolds number up to 2250 show that there exists a scaling-range (approximately $100&lt;r/\ensuremath{\eta}&lt;400$), in which the two-point second order velocity structure functions fit well to a simple power law scaling with respect to the distance $r$ between the two points, where $\ensuremath{\eta}$ is the Kolmogorov length scale. However, the prefactor of the power law depends on the Reynolds number.

Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh–Bénard convection

To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number (Nu) in a two-dimensional square Rayleigh–Bénard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between 107 and 109 and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged Nuvol, the wall-averaged Nuwall, the kinetic energy dissipation based Nukinetic, and the thermal energy dissipation based Nuthermal. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged Nuvol and the kinetic energy dissipation based Nukinetic can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged Nuwall and the thermal energy dissipation based Nuthermal, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of Nu during flow reversal shows that only the volume-averaged Nuvol can reproduce the overshoot phenomenon that is observed in the previous experimental study. Our results reveal that the proper choice of Nu is critical to obtain a meaningful interpretation.