arXiv subjects

Dhawal Buaria

Publications and source records attributed to Dhawal Buaria.

24 records · Page 2Linked to original sources

arXiv2020

Dissipation range of the energy spectrum in high Reynolds number turbulence

We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to $R_λ=650$, with excellent small-scale resolution of $k_{max}η\approx 6$ for all cases (and additionally at $R_λ=1300$ with $k_{max}η\approx3$), where $k_{max}$ is the maximum resolved wavenumber and $η$ is the Kolmogorov length scale. We find that, for a limited range of wavenumbers $k$ past the bottleneck in the range $0.1 \lesssim kη\lesssim0.5$, the spectra for all $R_λ$ display a universal stretched exponential behavior of the form $\exp(-k^{2/3})$, in rough accordance with recent theoretical predictions. The stretched exponential fit in the near dissipation range $1 \lesssim kη\lesssim 4$ does not possess a unique exponent, which decreases with increasing $R_λ$. This region can be regarded as a crossover between the stretched exponential behavior and the far dissipation range $kη> 6$, in which analytical arguments as well as DNS data with superfine resolution (S. Khurshid et al., Phys.~Rev.~Fluids 3, 082601, 2018) suggest a $\exp(-k)$ dependence. We remark on the connection to the multifractal model which hypothesizes a pseudo-algebraic law.

physics.flu-dyn↗

arXiv2020

Vortex stretching and enstrophy production in high Reynolds number turbulence

An essential ingredient of turbulent flows is the vortex stretching mechanism, which emanates from the non-linear interaction of vorticity and strain-rate tensor and leads to formation of extreme events. We analyze the statistical correlations between vorticity and strain rate by using a massive database generated from very well resolved direct numerical simulations of forced isotropic turbulence in periodic domains. The grid resolution is up to $12288^3$, and the Taylor-scale Reynolds number is in the range $140-1300$. In order to understand the formation and structure of extreme vorticity fluctuations, we obtain statistics conditioned on enstrophy (vorticity-squared). The magnitude of strain, as well as its eigenvalues, is approximately constant when conditioned on weak enstrophy; whereas they grow approximately as power laws for strong enstrophy, which become steeper with increasing $R_λ$. We find that the well-known preferential alignment between vorticity and the intermediate eigenvector of strain tensor is even stronger for large enstrophy, whereas vorticity shows a tendency to be weakly orthogonal to the most extensive eigenvector (for large enstrophy). Yet the dominant contribution to the production of large enstrophy events arises from the most extensive eigendirection, the more so as $R_λ$ increases. Nevertheless, the stretching in intense vorticity regions is significantly depleted, consistent with the kinematic properties of weakly-curved tubes in which they are organized. Further analysis reveals that intense enstrophy is primarily depleted via viscous diffusion, though viscous dissipation is also significant. Implications for modeling are nominally addressed as appropriate.

physics.flu-dyn↗

arXiv2020

Self-attenuation of extreme events in Navier-Stokes turbulence

Turbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations (INSE). A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of INSE, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and in establishing regularity of INSE. Here, we unveil a novel aspect of this interaction, by separating strain into local and non-local contributions utilizing the Biot-Savart integral of vorticity in a sphere of radius R. Analyzing highly-resolved numerical turbulent solutions to INSE, we find that when vorticity becomes very large, the local strain over small R surprisingly counteracts further amplification. This uncovered self-attenuation mechanism is further shown to be connected to local Beltramization of the flow, and could provide a direction in establishing the regularity of INSE.

physics.flu-dyn↗

arXiv2020

A highly scalable particle tracking algorithm using partitioned global address space (PGAS) programming for extreme-scale turbulence simulations

A new parallel algorithm utilizing partitioned global address space (PGAS) programming model to achieve high scalability is reported for particle tracking in direct numerical simulations of turbulent flow. The work is motivated by the desire to obtain Lagrangian information necessary for the study of turbulent dispersion at the largest problem sizes feasible on current and next-generation multi-petaflop supercomputers. A large population of fluid particles is distributed among parallel processes dynamically, based on instantaneous particle positions such that all of the interpolation information needed for each particle is available either locally on its host process or neighboring processes holding adjacent sub-domains of the velocity field. With cubic splines as the preferred interpolation method, the new algorithm is designed to minimize the need for communication, by transferring between adjacent processes only those spline coefficients determined to be necessary for specific particles. This transfer is implemented very efficiently as a one-sided communication, using Co-Array Fortran (CAF) features which facilitate small data movements between different local partitions of a large global array. Detailed benchmarks are obtained on the Cray petascale supercomputer Blue Waters at the University of Illinois, Urbana-Champaign. For operations on the particles in a $8192^3$ simulation ($0.55$ trillion grid points) on $262,144$ Cray XE6 cores, the new algorithm is found to be orders of magnitude faster relative to a prior algorithm in which each particle is tracked by the same parallel process at all times. Improving support of PGAS models on major compilers suggests that this algorithm will be of wider applicability on most upcoming supercomputers.

physics.comp-ph↗

arXiv2020

Single-particle Lagrangian statistics from direct numerical simulations of rotating-stratified turbulence

Geophysical fluid flows are predominantly turbulent and often strongly affected by the Earth's rotation, as well as by stable density stratification. Using direct numerical simulations of forced Boussinesq equations, we study the influence of these effects on the motion of fluid particles, focusing on cases where the frequencies associated with rotation and stratification (RaS), $N$ and $f$ respectively, are held at a fixed ratio $N/f=5$. As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which can also be seemingly described by simply comparing the time scale $1/N$ and $τ_η$ (the Kolmogorov time scale). We perform a detailed study of Lagrangian statistics of acceleration, velocity and related quantities in the two regimes. The flow anisotropy induces a clear difference between particle motion in the horizontal and vertical directions. In the regime $Nτ_η<1$, acceleration statistics in both horizontal and vertical directions, exhibit well known characteristics of isotropic turbulence. In contrast for $Nτ_η>1$, they are directly influenced by imposed RaS. The Lagrangian velocity statistics exhibit visible anisotropy for all runs; nevertheless the degree of anisotropy becomes very strong in the regime $Nτ_η>1$. We find that in the regime $Nτ_η<1$, rotation enhances the mean displacement of particles in horizontal planes at short times, but inhibits them at longer times. This inhibition of horizontal displacement becomes stronger for $Nτ_η>1$, with no clear diffusive behavior. Displacements in the vertical direction are always inhibited. The inhibition becomes extremely strong when $Nτ_η>1$, with the particles almost being trapped horizontally.

physics.flu-dyn↗

arXiv2019

Extreme velocity gradients in turbulent flows

Fully turbulent flows are characterized by intermittent formation of very localized and intense velocity gradients. These gradients can be orders of magnitude larger than their typical value and lead to many unique properties of turbulence. Using direct numerical simulations of the Navier-Stokes equations with unprecedented small-scale resolution, we characterize such extreme events over a significant range of turbulence intensities, parameterized by the Taylor-scale Reynolds number ($R_λ$). Remarkably, we find the strongest velocity gradients to empirically scale as $τ_K^{-1} R_λ^β$, with $β\approx 0.775 \pm 0.025$, where $τ_K$ is the Kolmogorov time scale (with its inverse, $τ_K^{-1}$, being the {r.m.s.} of velocity gradient fluctuations). Additionally, we observe velocity increments across very small distances $r \le η$, where $η$ is the Kolmogorov length scale, to be as large as the {r.m.s.} of the velocity fluctuations. Both observations suggest that the smallest length scale in the flow behaves as $ηR_λ^{-α}$, with $α= β- \frac{1}{2}$, which is at odds with predictions from existing phenomenological theories. We find that extreme gradients are arranged in vortex tubes, such that strain conditioned on vorticity grows on average slower than vorticity, approximately as a power law with an exponent $γ< 1$, which weakly increases with $R_λ$. Using scaling arguments, we get $β=(2-γ)^{-1}$, which suggests that $β$ would also slowly increase with $R_λ$. We conjecture that approaching the limit of infinite $R_λ$, the flow is overall smooth, with intense velocity gradients over scale $ ηR_λ^{-1/2}$, corresponding to $β= 1$.

physics.flu-dyn↗