arXiv subjects

Mahendra K. Verma

Publications and source records attributed to Mahendra K. Verma.

At least 19 recordsLinked to original sources

arXiv2026

Quantum turbulence in the many-body regime

We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly-interacting superfluids, often modeled by a mean-field theory governed by the Gross-Pitaevskii equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We motivate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.

cond-mat.quant-gas↗

arXiv2026

Scaling in Supersonic Turbulence: Energy Spectra and Fluxes using High-Fidelity Direct Numerical Simulations

Supersonic turbulence is vital to astrophysical and high-speed engineering flows, yet its energy transfer mechanisms remain poorly understood. We present high-resolution ($1024^3$) direct numerical simulations (DNS) of forced compressible turbulence across a range of turbulent Mach numbers ($M_t = 0.2$ to $3.0$). Using the GPU-accelerated solver \texttt{DHARA} with a seventh-order, low-dissipation Targeted Essentially Non-Oscillatory (TENO) scheme, we resolve both fine-scale eddies and sharp shock fronts. Our results reveal a fundamental shift in the energy cascade in the supersonic regime. As $M_t$ increases, the rotational kinetic energy spectrum steepens from a Kolmogorov-like $k^{-5/3}$ scaling toward a Burgers-like $k^{-2}$ scaling. Conversely, the compressive energy spectrum becomes shallower, deviating from Burgers scaling. We show that these spectral modifications are driven by a dominant cross-scale transfer of energy from solenoidal to compressive modes within the inertial range, alongside significant contributions from pressure dilatation. Scaling laws for the root-mean-square compressive velocity ($U_C$) and compressive energy flux ($Π_C$) are found to mirror classical Burgers turbulence. Finally, we show that while energy injection rates depend on forcing type rather than Mach number, increased $M_t$ leads to decreased rotational dissipation and increased compressive dissipation and pressure dilatation. These findings elucidate intermodal energy cascade mechanisms, advancing our understanding of energy transfers in supersonic turbulence.

physics.flu-dyn↗

arXiv2026

Structure Functions and Intermittency for Coarsening Systems

In studies of turbulence, there has been extensive use of physical quantities such as {\it energy transfers} and {\it structure functions}. We examine whether these quantities can be useful in understanding problems of domain growth or coarsening, as modeled by the {\it time-dependent Ginzburg-Landau} (TDGL) equation and the {\it Cahn-Hilliard} (CH) equation. This paper has two major themes. First, we review our recent papers on energy transfers in domain growth. Second, we study structure functions and intermittency for coarsening systems. As a consequence of sharp interfaces, the structure functions scale as $S_q \sim r^{ζ_q}$, where $r$ is the distance between two points. For the TDGL and CH models, $ζ_q = 1$, indicating {\it anomalous scaling}

cond-mat.stat-mech↗

arXiv2026

Kolmogorov Scaling for Total Energy and Cross Helicity in Magnetohydrodynamic Turbulence

The problem of scaling in isotropic magnetohydrodynamic (MHD) turbulence has remained unresolved, with competing predictions of $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. In this paper, we address this long-standing controversy using high-resolution numerical simulations on $8192^2$ and $1536^3$ grids. We show that the total energy and cross helicity spectra are closer to $k^{-5/3}$ than $k^{-3/2}$. The fluxes and structure functions of the total energy and cross helicity also demonstrate robust support for Kolmogorov scaling. The magnetic energy shows $k^{-5/3}$ spectrum, but the kinetic energy exhibits $k^{-3/2}$ spectrum; the latter spectrum is due to the energy transfers from the magnetic field to the velocity field.

physics.plasm-ph↗

arXiv2025

Numerical Demonstration of Kolmogorov Scaling in Magnetohydrodynamic Turbulence

The two leading models of isotropic magnetohydrodynamic (MHD) turbulence have competing predictions: $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. This paper identifies the valid MHD turbulence model using high-resolution numerical and diagnostics-structure functions, intermittency exponents, and energy spectra and fluxes of imbalance MHD. The energy spectra of our forced MHD simulations on $8192^2$, $4096^2$, $1024^3$, and $512^3$ support Kolmogorov's k^{-5/3} spectrum over Iroshnikov-Kraichnan's k^{-3/2} spectrum, but the difference in the spectral exponents is small. However, the numerically computed third-order structure functions and intermittency exponents support Kolmogorov scaling in both two and three dimensions. Also, the energy fluxes of the imbalance MHD follow the predictions of Kolmogorov scaling. These results would help in better modelling of solar wind, solar corona, and dynamos.

physics.plasm-ph↗

arXiv2025

Bursting of columnar structures in forced rotating turbulence

In this study, we report intermittent bursting of cyclonic columnar structures in direct numerical simulations of forced rotating turbulence in a three-dimensional (3D) periodic box. Columnar structure formation is associated with dominant inverse cascade of energy in addition to the typical forward cascade at large wavenumbers. The forcing is random and isotropic, applied in two distinct wavenumber bands (kf = [3, 4] and [6, 7]). Notably, bursting is observed only for small forcing wavenumber, kf = [3, 4] and not at kf = [6, 7], for the same rotation rate and initial conditions. These bursting events are associated with forward cascade of energy in contrast to the inverse cascade of rotating turbulence, as confirmed from the ring spectrum and time-series of modal kinetic energy of modes with kz = 2, 3. Identifying some of the triads involved in the energy transfer from modal analysis, we also calculate the mode-to-mode energy transfer. We find that, before the event, the circular cyclonic vortex becomes elliptical due to cyclone-anticyclone interactions leading to elliptical instability. We argue that energy transfer preceding the bursting events to modes with higher kz triggers the Crow instability. These instabilities ultimately lead to bursting of the columnar vortex, which subsequently forms again due to the external rotation. Our results portray a tug-of-war between the destabilizing effect of elliptical instability and the stabilizing effect of external rotation.

physics.flu-dyn↗

arXiv2025

Mathematical formulation of mode-to-mode energy transfers and energy fluxes in compressible turbulence

Understanding compressible turbulence is critical for modeling atmospheric, astrophysical, and engineering flows. However, compressible turbulence poses a more significant challenge than incompressible turbulence. We present a novel mathematical framework to compute \textit{mode-to-mode energy transfer rates} and energy fluxes for compressible flows. The formalism captures detailed energy conservation within triads and allows decomposition of transfers into rotational, compressive, and mixed components, providing a clear picture of energy exchange among velocity and internal energy modes. We also establish analogies with incompressible hydrodynamic and magnetohydrodynamic flows, highlighting the framework's universality in studying energy transfers.

physics.flu-dyn↗

arXiv2025

Classical 1/3 Nusselt number scaling in highly turbulent compressible convection

Planetary and stellar convection, which are compressible and turbulent, remain poorly understood. In this paper, we report numerical results on the scaling of Nusselt number ($\mathrm{Nu}$) and Reynolds number ($\mathrm{Re}$) for extreme convection. Using computationally-efficient MacCormack-TVD finite difference method, we simulate compressible turbulent convection in a two-dimensional Cartesian box up to $\mathrm{Ra} = 10^{16}$, the highest $\mathrm{Ra}$ achieved so far, and in a three-dimensional box up to $\mathrm{Ra} = 10^{11}$. We show adiabatic temperature drop in the bulk flow, leading to the Reynolds number scaling $\mathrm{Ra}^{1/2}$. More significantly, we show classical $1/3$ Nusselt number scaling: $\mathrm{Nu} \propto \mathrm{Ra}^{0.32}$ in 2D, and $\mathrm{Nu} \propto \mathrm{Ra}^{0.31}$ in 3D up to the highest $\mathrm{Ra}$.

physics.flu-dyn↗

arXiv2025

Energy spectra and fluxes of two-dimensional turbulent quantum droplets

We explore the energy spectra and associated fluxes of turbulent two-dimensional quantum droplets subjected to a rotating paddling potential which is removed after a few oscillation periods. A systematic analysis on the impact of the characteristics (height and velocity) of the rotating potential and the droplet atom number reveals the emergence of different dynamical response regimes. These are classified by utilizing the second-order sign correlation function and the ratio of incompressible versus compressible kinetic energies. They involve, vortex configurations ranging from vortex dipoles to vortex clusters and randomly distributed vortex-antivortex pairs. The incompressible kinetic energy spectrum features Kolmogorov ($k^{-5/3}$) and Vinen like ($k^{-1}$) scaling in the infrared regime, while a $k^{-3}$ decay in the ultraviolet captures the presence of vortices. The compressible spectrum shows $k^{-3/2}$ scaling within the infrared and $k$ power law in the case of enhanced sound-wave emission suggesting thermalization. Significant distortions are observed in the droplet periphery in the presence of a harmonic trap. A direct energy cascade (from large to small length scales) is mainly identified through the flux. Our findings offer insights into the turbulent response of exotic phases-of-matter, featuring quantum fluctuations, and may inspire investigations aiming to unravel self-similar nonequilibrium dynamics.

cond-mat.quant-gas↗

arXiv2024

Contrasting thermodynamic and hydrodynamic entropy

In this paper, using \textit{hydrodynamic entropy} we quantify the multiscale disorder in Euler and hydrodynamic turbulence. These examples illustrate that the hydrodynamic entropy is not extensive because it is not proportional to the system size. Consequently, we cannot add hydrodynamic and thermodynamic entropies, which measure disorder at macroscopic and microscopic scales, respectively. In this paper, we also discuss the hydrodynamic entropy for the time-dependent Ginzburg-Landau equation and Ising spins.

cond-mat.stat-mech↗

arXiv2024

Macroscopic arrow of time from multiscale perspectives

Fundamental laws of physics are symmetric under time reversal ($T$) symmetry, but the $T$ symmetry is strongly broken in the macroscopic world. In this Perspective, I review $T$ symmetry breaking frameworks: \textit{second law of thermodynamics, multiscale energy transfer}, and \textit{open systems}. In driven dissipative nonequilibrium systems, including turbulence, the multiscale energy flux from large scales to small scales helps determine the arrow of time. In addition, open systems are often irreversible due to particle and energy exchanges between the system and the environment. Causality is another important factor that breaks the $T$ symmetry.

cond-mat.stat-mech↗

arXiv2024

Compressible turbulent convection at very high Rayleigh numbers

Heat transport in highly turbulent convection is not well understood. In this paper, we simulate compressible convection in a box of aspect ratio 4 using computationally-efficient MacCormack-TVD finite difference method on single and multi-GPUs, and reach very high Rayleigh number ($\mathrm{Ra}$) -- $10^{15}$ in two dimensions and $10^{11}$ in three dimensions. We show that the Nusselt number $\mathrm{Nu} \propto \mathrm{Ra}^{0.3}$ (classical scaling) that differs strongly from the ultimate-regime scaling, which is $\mathrm{Nu} \propto \mathrm{Ra}^{1/2}$. The bulk temperature drops adiabatically along the vertical even for high $\mathrm{Ra}$, which is in contrast to the constant bulk temperature in Rayleigh-Bénard convection (RBC). Unlike RBC, the density decreases with height. In addition, the vertical pressure-gradient ($-dp/dz$) nearly matches the buoyancy term ($ρg$). But, the difference, $-dp/dz-ρg$, is equal to the nonlinear term that leads to Reynolds number $\mathrm{Re} \propto \mathrm{Ra}^{1/2}$.

physics.flu-dyn↗

arXiv2024

Critical dimension for hydrodynamic turbulence

Hydrodynamic turbulence exhibits nonequilibrium behaviour with $k^{-5/3}$ energy spectrum, and equilibrium behaviour with $k^{d-1}$ energy spectrum and zero viscosity, where $d$ is the space dimension. Using recursive renormalization group {in Craya-Herring basis}, we show that the nonequilibrium solution is valid only for $d < 6$, whereas equilibrium solution with zero viscosity is the only solution for $d>6$. Thus, $d=6$ is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near $d=2.15$. We also compute the energy flux and Kolmogorov's constants for various $d$'s, and observe that our results are in good agreement with past numerical results.

cond-mat.stat-mech↗

arXiv2023

Insights into the Energy Transfers in Hydrodynamic Turbulence Using Field-theoretic Tools

Turbulent flows exhibit intriguing energy transfers. In this paper, we compute the renormalized viscosities, mode-to-mode energy transfers, energy fluxes, and shell-to-shell energy transfers for the two-dimensional (2D) and three-dimensional (3D) hydrodynamic turbulence (HDT) using field-theoretic methods. We employ Craya-Herring basis that provides separate renormalized viscosities and energy transfers for its two components. In addition, Craya-Herring basis eliminates complex tensor algebra and simplifies the calculations considerably. In the $k^{-5/3}$ spectral regime of 2D HDT, the energy transfers between neighbouring (local) wavenumbers are forward, but they are backwards for distant (nonlocal) wavenumbers. The individual transfers between the distant wavenumber shells are small, but their cumulative sum is significant and it overcomes the forward local transfer to yield a constant inverse energy cascade. For 3D HDT, the mode-to-mode and shell-to-shell energy transfers reveal forward energy transfers for both local and nonlocal wavenumbers. More importantly, using scale-by-scale energy transfers we show that the cumulative nonlocal and local energy transfers are of the same order, which is contrary to the assumption of local energy transfers in turbulence. For 3D HDT, the renormalized viscosity, $ν_2(k)$, computed by us and other authors are in general agreement, and it varies as $k^{-4/3}$. For 2D HDT, our the renormalized viscosity, $ν_1(k)>0$, but $ν_1(k)$ reported in literature shows significant variations including a negative $ν_1(k)$. In this paper, we argue that the inconsistencies in $ν_1(k)$ indicate inadequacy of renormalization group analysis that takes into account only local interactions and excludes nonlocal ones. In 2D HDT, the opposing nature of local and nonlocal energy transfers amplifies the error in $ν_1(k)$.

physics.flu-dyn↗

arXiv2023

Equilibrium and nonequilibrium properties of Euler turbulence

In this article, we report the equilibrium and nonequilibrium features of two-dimensional (2D) and three-dimensional (3D) Euler turbulence. To obtain a full range of equilibrium spectra, we perform pseudo-spectral simulations of Euler turbulence using $δ$-correlated velocity field as an initial condition. These simulations provide zero energy flux and Maxwell-Boltzmann distribution for the velocity field, thus providing direct verification of the absolute equilibrium theory of turbulence. However, for ordered initial condition, 2D Euler turbulence remains out of equilibrium, with flow getting more ordered with time. We show that the hydrodynamic entropy of 2D Euler turbulence decreases with time, even though the system is isolated.

physics.flu-dyn↗

arXiv2023

Renormalization of shell model of turbulence

Renormalization enables a systematic scale-by-scale analysis of multiscale systems. In this paper, we employ \textit{renormalization group} (RG) to the shell model of turbulence and show that the RG equation is satisfied by $ |u_n|^2 =K_\mathrm{Ko} ε^{2/3} k_n^{-2/3}$ and $ ν_n = ν_* \sqrt{K_\mathrm{Ko}} ε^{1/3} k_n^{-4/3}$, where $k_n, u_n $ are the wavenumber and velocity of shell $ n $; $ν_*, K_\mathrm{Ko}$ are RG and Kolmogorov's constants; and $ ε$ is the energy dissipation rate. We find that $ν_* \approx 0.5$ and $K_\mathrm{Ko} \approx 1.7$, consistent with earlier RG works on Navier-Stokes equation. We verify the theoretical predictions using numerical simulations.

physics.flu-dyn↗

arXiv2022

Turbulent Drag Reduction in Magnetohydrodynamic Turbulence and Dynamo from Energy Flux Perspectives

In this review, we describe turbulent drag reduction in a variety of flows using a universal framework of energy flux. In a turbulent flow with dilute polymers and magnetic field, the kinetic energy injected at large scales cascades to the velocity field at intermediate scales, as well as to the polymers and magnetic field at all scales. Consequently, the kinetic energy flux, $ Π_u(k) $, is suppressed in comparison to the pure hydrodynamic turbulence. We argue that the suppression of $Π_u(k)$ is an important factor in the reduction of the inertial force $\langle {\bf u \cdot \nabla u} \rangle$ and \textit{turbulent drag}. This feature of turbulent drag reduction is observed in polymeric, magnetohydrodynamic, quasi-static magnetohydrodynamic, and stably-stratified turbulence, and in dynamos. In addition, it is shown that turbulent drag reduction in thermal convection is due to the smooth thermal plates, similar to the turbulent drag reduction over bluff bodies. In all these flows, turbulent drag reduction often leads to a strong large-scale velocity in the flow.

physics.plasm-ph↗

arXiv2022

Hydrodynamic Entropy and Emergence of Order in Two-dimensional Euler Turbulence

Using numerical simulations, we show that the asymptotic states of two-dimensional (2D) Euler turbulence exhibit large-scale flow structures due to nonzero energy transfers among small wavenumber modes. These asymptotic states, which depend on the initial conditions, are out of equilibrium, and they are different from the predictions of Onsager and Kraichnan. We propose ``hydrodynamic entropy'' to quantify order in 2D Euler turbulence; we show that this entropy decreases with time, even though the system is isolated with no dissipation and no contact with a heat bath.

cond-mat.stat-mech↗