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Dhawal Buaria

Publications and source records attributed to Dhawal Buaria.

At least 19 recordsLinked to original sources
arXiv2026

Scalar dissipation anomaly and scalar-gradient scaling in turbulence: A joint velocity-scalar multifractal view

We revisit the problem of scalar dissipation anomaly and scaling of scalar gradients in passive scalar turbulence using theory and data from well-resolved direct numerical simulations (DNS) on grid sizes of up to $8192^3$, spanning Taylor-scale Reynolds numbers $Re_λ=140-1000$ and Schmidt numbers $Sc = 1-512$. The theory is based on a joint multifractal description of longitudinal velocity increments and scalar increments, constrained by Yaglom's law and extended to gradients via a fluctuating Batchelor cutoff scale. The DNS data show that the normalized mean scalar dissipation approaches a single asymptotic value as both $Re_λ$ and $Sc$ increase, although larger $Sc$ requires larger $Re_λ$ to reach this state. In the multifractal framework, this corresponds to an effective scalar Hölder exponent tending to zero, associated with sharp cliff-like scalar fronts, and saturation of inertial-range scaling scalar structure-function exponents. The joint velocity-scalar fractal dimension of the dissipative structures is inferred to approach $7/3$, indicating a non-space-filling support. The framework further predicts that for fixed $Re_λ$, higher-order central moments of scalar gradients are independent of $Sc$. This prediction is confirmed by DNS data and by the collapse of standardized probability distributions of scalar-gradient across Schmidt numbers. These results suggest that the $Sc$-scaling of scalar gradients is dictated solely by scalar dissipation anomaly. In contrast, their $Re_λ$-dependence reflects strong intermittency, which can be directly related to mixed velocity-scalar structure function exponents.

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arXiv2026

Scalar gradient structure and dynamics in turbulent mixing at high Reynolds and Schmidt numbers

How well turbulence mixes a scalar $θ$ is governed by the scalar dissipation rate $χ= 2D |\nablaθ|^2$, making scalar gradients central to turbulent mixing. We study the structure and amplification of these gradients for passive scalars driven by a uniform mean-gradient in isotropic turbulence, using DNS at grid resolutions up to $8192^3$. The $Re_λ$ spans $140-1000$, and $Sc\equivν/D$ spans $1-512$. We analyze joint statistical correlations of velocity and scalar gradients that underlie scalar-gradient amplification. Unconditional statistics reaffirm earlier observations that production of $χ$ is dominated by nonlinear amplification of scalar gradients by strain-rate. Scalar gradients preferentially align with the most compressive strain eigenvector and remain orthogonal to vorticity, with both trends virtually independent of $Re_λ$ and $Sc$. Conditional statistics reveal that this organization becomes dramatically enhanced in regions of intense scalar dissipation: scalar gradient becomes near-perfectly aligned with the most compressive eigendirection and orthogonal to other eigendirections and vorticity. This and visualizations suggest that intense scalar dissipation is organized in sheet-like structures formed in shear layers between vortex tubes, where intense strain also generally resides. However, the effective strain acting along intense scalar gradients is comparatively much weaker, indicating intense scalar dissipation arises primarily from optimal alignments rather than intense strain alone. Molecular diffusion arrests intense scalar-gradient events primarily by redistributing scalar-gradient variance away from intense structures. The contribution from imposed mean-gradient is negligible,but still imprints anisotropy directly onto smallest scales via the strain field. The statistics broadly become universal as $Sc$ and $Re_λ$ increases

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arXiv2026

Unified multifractal description of longitudinal and transverse intermittency in fully developed turbulence

Small-scale intermittency is a defining feature of fully developed fluid turbulence, marked by rare and extreme fluctuations of velocity increments and gradients that defy mean-field descriptions. Existing multifractal descriptions of intermittency focus primarily on longitudinal increments and gradients, despite mounting evidence that transverse components exhibit distinct and stronger intermittency. Here, we develop a unified multifractal framework that jointly prescribes longitudinal and transverse velocity increments, and extends to gradients. We derive explicit relations linking inertial-range scaling exponents of structure functions to moments of velocity gradients in dissipation range. Our results reveal that longitudinal gradient scaling is solely prescribed by longitudinal structure functions, as traditionally expected; however, transverse gradient scaling is prescribed by mixed longitudinal-transverse structure functions. Validation with high-resolution direct numerical simulations of isotropic turbulence, at Taylor-scale Reynolds number up to $1300$ demonstrates excellent agreement, paving way for a more complete and predictive description of intermittency faithful to the underlying turbulence dynamics.

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arXiv2024

Universality of extreme events in turbulent flows

The universality of small scales, a cornerstone of turbulence, has been nominally confirmed for low-order mean-field statistics, such as the energy spectrum. However, small scales exhibit strong intermittency, exemplified by formation of extreme events which deviate anomalously from a mean-field description. Here, we investigate the universality of small scales by analyzing extreme events of velocity gradients in different turbulent flows, viz. direct numerical simulations (DNS) of homogeneous isotropic turbulence, inhomogeneous channel flow, and laboratory measurements in a von Karman mixing tank. We demonstrate that the scaling exponents of velocity gradient moments, as function of Reynolds number ($Re$), are universal, in agreement with previous studies at lower $Re$, and further show that even proportionality constants are universal when considering one moment order as a function of another. Additionally, by comparing various unconditional and conditional statistics across different flows, we demonstrate that the structure of the velocity gradient tensor is also universal. Overall, our findings provide compelling evidence that even extreme events are universal, with profound implications for turbulence theory and modeling.

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arXiv2024

Twisting vortex lines regularize Navier-Stokes turbulence

Fluid flows are intrinsically characterized via the topology and dynamics of underlying vortex lines. Turbulence in common fluids like water and air, mathematically described by the incompressible Navier-Stokes equations (INSE), engenders spontaneous self-stretching and twisting of vortex lines, generating a complex hierarchy of structures. While the INSE are routinely used to describe turbulence, their regularity remains unproven; the implicit assumption being that the self-stretching is ultimately regularized by viscosity, preventing any singularities. Here, we uncover an inviscid regularizing mechanism stemming from self-stretching itself, by analyzing the flow topology as perceived by an observer aligned with the vorticity vector undergoing amplification. While, initially, vorticity amplification occurs via increasing twisting of vortex lines, a regularizing anti-twist spontaneously emerges to prevent unbounded growth. By isolating a vortex, we additionally demonstrate the genericity of this self-regularizing anti-twist. Our work, directly linking dynamics of vortices to turbulence statistics, reveals how the Navier-Stokes dynamics avoids the development of singularities even without the aid of viscosity.

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arXiv2024

Saturation and multifractality of Lagrangian and Eulerian scaling exponents in 3D isotropic turbulence

Inertial range scaling exponents for both Lagrangian and Eulerian structure functions are obtained from direct numerical simulations of isotropic turbulence in triply periodic domains at Taylor-scale Reynolds number up to 1300. We reaffirm that transverse Eulerian scaling exponents saturate at $\approx 2.1$ for moment orders $p \ge 10$, significantly differing from the longitudinal exponents (which are predicted to saturate at $\approx 7.3$ for $p \ge 30$ from a recent theory). The Lagrangian scaling exponents likewise saturate at $\approx 2$ for $p \ge 8$. The saturation of Lagrangian exponents and transverse Eulerian exponents is related by the same multifractal spectrum by utilizing the well known frozen hypothesis to relate spatial and temporal scales. Furthermore, this spectrum is different from the known spectra for Eulerian longitudinal exponents, suggesting that that Lagrangian intermittency is characterized solely by transverse Eulerian intermittency. We discuss possible implication of this outlook when extending multifractal predictions to the dissipation range, especially for Lagrangian acceleration.

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arXiv2023

Role of pressure in generation of intense velocity gradients in turbulent flows

We investigate the role of pressure, via its Hessian tensor $\mathbf{H}$, on amplification of vorticity and strain-rate and contrast it with other inviscid nonlinear mechanisms. Results are obtained from direct numerical simulations of isotropic turbulence with Taylor-scale Reynolds number in the range $140-1300$. Decomposing $\mathbf{H}$ into local isotropic ($\mathbf{H}^{\rm I}$) and nonlocal deviatoric ($\mathbf{H}^{\rm D}$) components reveals that $\mathbf{H}^{\rm I}$ depletes vortex stretching (VS), whereas $\mathbf{H}^{\rm D}$ enables it, with the former slightly stronger. The resulting inhibition is significantly weaker than the nonlinear mechanism which always enables VS. However, in regions of intense vorticity, identified using conditional statistics, contribution from $\mathbf{H}$ dominates over nonlinearity, leading to overall depletion of VS. We also observe near-perfect alignment between vorticity and the eigenvector of $\mathbf{H}$ corresponding to the smallest eigenvalue, which conforms with well-known vortex-tubes. We discuss the connection between this depletion, essentially due to (local) $\mathbf{H}^{\rm I}$, and recently identified self-attenuation mechanism [Buaria et al. {\em Nat. Commun.} 11:5852 (2020)], whereby intense vorticity is locally attenuated through inviscid effects. In contrast, the influence of $\mathbf{H}$ on strain-amplification is weak. It opposes strain self-amplification, together with VS, but its effect is much weaker than VS. Correspondingly, the eigenvectors of strain and $\mathbf{H}$ do not exhibit any strong alignments. For all results, the dependence on Reynolds number is very weak. In addition to the fundamental insights, our work provides useful data and validation benchmarks for future modeling endeavors, for instance in Lagrangian modeling of velocity gradient dynamics, where conditional $\mathbf{H}$ is explicitly modeled.

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arXiv2023

Forecasting small scale dynamics of fluid turbulence using deep neural networks

Turbulent flows consist of a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality. In this work, using physics-informed deep learning methods, we present a modeling framework to capture and predict the small scale dynamics of turbulence, via the velocity gradient tensor. The model is based on obtaining functional closures for the pressure Hessian and viscous Laplacian contributions as functions of velocity gradient tensor. This task is accomplished using deep neural networks that are consistent with physical constraints and incorporate Reynolds number dependence explicitly to account for small-scale intermittency. We then utilize a massive direct numerical simulation database, spanning two orders of magnitude in the large-scale Reynolds number, for training and validation. The model learns from low to moderate Reynolds numbers, and successfully predicts velocity gradient statistics at both seen and higher (unseen) Reynolds numbers. The success of our present approach demonstrates the viability of deep learning over traditional modeling approaches in capturing and predicting small scale features of turbulence.

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arXiv2023

Comparing velocity and passive scalar statistics in fluid turbulence at high Schmidt numbers and Reynolds numbers

Recently, Shete et al. [Phys. Rev. Fluids 7, 024601 (2022)] explored the characteristics of passive scalars in the presence of a uniform mean gradient, mixed by stationary isotropic turbulence. They concluded that at high Reynolds and Schmidt numbers, the presence of both inertial-convective and viscous-convective ranges, renders the statistics of the scalar and velocity fluctuations to behave similarly. However, their data included Schmidt numbers of 0.1, 0.7, 1.0 and 7.0, only the last of which can (at best) be regarded as moderately high. Additionally, they do not consider already available data in the literature at substantially higher Schmidt number of up to 512. By including these data, we demonstrate here that the differences between velocity and scalar statistics show no vanishing trends with increasing Reynolds and Schmidt numbers, and essential differences remain in tact at all Reynolds and Schmidt numbers.

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arXiv2022

Lagrangian acceleration in fully developed turbulence and its Eulerian decompositions

We study the properties of various Eulerian contributions to fluid particle acceleration by using well-resolved direct numerical simulations of isotropic turbulence, with the grid resolution as high as $12288^3$ and the Taylor-scale Reynolds number $R_λ$ in the range between 140 and 1300. The variance of convective acceleration, when normalized by Kolmogorov scales, increases linearly with $R_λ$, consistent with simple theoretical arguments, but very strongly differing from phenomenological predictions of Kolmogorov's hypothesis as well as Eulerian multifractal models. The scaling of the local acceleration is also linear $R_λ$ to the leading order, but more complex in detail. The strong cancellation between the local and convective acceleration -- faithful to the random sweeping hypothesis -- results in the variance of the Lagrangian acceleration increasing only as $R_λ^{0.25}$, as recently shown by Buaria \& Sreenivasan [Phys. Rev. Lett. 128, 234502 (2022)]. The acceleration variance is dominated by irrotational pressure gradient contributions, whose variance also follows an $R_λ^{0.25}$ scaling; the solenoidal viscous contributions are relatively small and follow a $R_λ^{0.13}$, consistent with Eulerian multifractal predictions.

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arXiv2022

Scaling of acceleration statistics in high Reynolds number turbulence

The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range. The acceleration variance at higher Reynolds numbers departs from previous predictions based on multifractal models, which characterize Lagrangian intermittency as a naive extension of Eulerian intermittency. The disagreement is even more prominent for higher-order moments of the acceleration. Instead, starting from a known exact relation, we relate the scaling of acceleration variance to that of Eulerian fourth-order velocity gradient and velocity increment statistics. This prediction is in excellent agreement with the variance data. Our work highlights the need for models that consider Lagrangian intermittency independent of the Eulerian counterpart.

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arXiv2022

Intermittency of turbulent velocity and scalar fields using 3D local averaging

An efficient approach for extracting 3D local averages in spherical subdomains is proposed and applied to study the intermittency of small-scale velocity and scalar fields in direct numerical simulations of isotropic turbulence. We focus on the inertial-range scaling exponents of locally averaged energy dissipation rate, enstrophy and scalar dissipation rate corresponding to the mixing of a passive scalar $θ$ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number $R_λ$ goes up to $1300$, and the Schmidt number $Sc$ up to $512$ (albeit at smaller $R_λ$). The intermittency exponent of the energy dissipation rate is $μ\approx 0.23$, whereas that of enstrophy is slightly larger; trends with $R_λ$ suggest that this will be the case even at extremely large $R_λ$. The intermittency exponent of the scalar dissipation rate is $μ_θ\approx 0.35$ for $Sc=1$. These findings are in essential agreement with previously reported results in the literature. We further show that $μ_θ$ decreases monotonically with increasing $Sc$, either as $1/\log Sc$ or a weak power law, suggesting that $μ_θ\to 0$ as $Sc \to \infty$, reaffirming recent results on the breakdown of scalar dissipation anomaly in this limit.

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arXiv2022

Vorticity-strain rate dynamics and the smallest scales of turbulence

Building upon the intrinsic properties of Navier-Stokes dynamics, namely the prevalence of intense vortical structures and the interrelationship between vorticity and strain rate, we propose a simple framework to quantify the extreme events and the smallest scales of turbulence. We demonstrate that our approach is in excellent agreement with the best available data from direct numerical simulations of isotropic turbulence, with Taylor-scale Reynolds number up to 1300. We additionally highlight a shortcoming of prevailing intermittency models due to their disconnection from observed correlation between vorticity and strain. Our work accentuates the importance of this correlation as a crucial step in developing an accurate understanding of intermittency in turbulence.

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arXiv2021

Small-scale isotropy and ramp-cliff structures in scalar turbulence

Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to $8192^3$ at high Péclet numbers to understand this anomaly as the scalar diffusivity, $D$, diminishes, or as the Schmidt number, $Sc = ν/D$, increases; here $ν$ is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and $Sc$ varies from 1 to 512. A simple model for the ramp-cliff structures is shown to characterize the scalar derivative statistics extremely well. It accurately captures how the small-scale isotropy is restored in the large-$Sc$ limit, and additionally suggests a slight correction to the Batchelor length scale as the relevant smallest scale in the scalar field.

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arXiv2021

Turbulence is an ineffective mixer when Schmidt numbers are large

We solve the advection-diffusion equation for a stochastically stationary passive scalar $θ$, in conjunction with forced 3D Navier-Stokes equations, using direct numerical simulations in periodic domains of various sizes, the largest being $8192^3$. The Taylor-scale Reynolds number varies in the range $140-650$ and the Schmidt number $Sc \equiv ν/D$ in the range $1-512$, where $ν$ is the kinematic viscosity of the fluid and $D$ is the molecular diffusivity of $θ$. Our results show that turbulence becomes an ineffective mixer when $Sc$ is large. First, the mean scalar dissipation rate $\langle χ\rangle = 2D \langle |\nabla θ|^2\rangle$, when suitably non-dimensionalized, decreases as $1/\log Sc$. Second, 1D cuts through the scalar field indicate increasing density of sharp fronts on larger scales, oscillating with large excursions leading to reduced mixing, and additionally suggesting weakening of scalar variance flux across the scales. The scaling exponents of the scalar structure functions in the inertial-convective range appear to saturate with respect to the moment order and the saturation exponent approaches unity as $Sc$ increases, qualitatively consistent with 1D cuts of the scalar.

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arXiv2021

Non-local amplification of intense vorticity in turbulent flows

The nonlinear and nonlocal coupling of vorticity and strain-rate constitutes a major hindrance in understanding the self-amplification of velocity gradients in turbulent fluid flows. Utilizing highly-resolved direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds number $R_λ$ in the range $140-1300$, we investigate this non-locality by decomposing the strain-rate tensor into local and non-local contributions obtained through Biot-Savart integration of vorticity in a sphere of radius $R$. We find that vorticity is predominantly amplified by the non-local strain coming beyond a characteristic scale size, which varies as a simple power-law of vorticity magnitude. The underlying dynamics preferentially align vorticity with the most extensive eigenvector of non-local strain. The remaining local strain aligns vorticity with the intermediate eigenvector and does not contribute significantly to amplification; instead it surprisingly attenuates intense vorticity, leading to breakdown of the observed power-law and ultimately also the scale-invariance of vorticity amplification, with important implications for prevailing intermittency theories.

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arXiv2021

Generation of intense dissipation in high Reynolds number turbulence

Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and the pressure Hessian tensor, which we analyze here using direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds numbers in the range $140-1300$. We extract the statistics of various terms involved in amplification of strain and additionally condition them on the magnitude of strain. We find that strain is overall self-amplified by the quadratic nonlinearity, and depleted via vortex stretching; whereas pressure Hessian acts to redistribute strain fluctuations towards the mean-field and thus depleting intense strain. Analyzing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. In contrast, the self-amplification terms acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, both effects canceling each other almost perfectly. The effect of the pressure Hessian for each eigenvalue is qualitatively similar to that of vortex stretching, but significantly weaker in magnitude. Our results conform with the familiar notion that intense strain is organized in sheet-like structures, which are in the vicinity of, but never overlap with regions of intense vorticity due to fundamental differences in their amplifying mechanisms.

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