arXiv subjects

Kannabiran Seshasayanan

Publications and source records attributed to Kannabiran Seshasayanan.

At least 19 recordsLinked to original sources

arXiv2026

Effects of radial conductivity variation on the Ponomarenko dynamo

We study the effects of conductivity variation on the Ponomarenko dynamo. Taking monotonically increasing/decreasing and sinusoidally varying radial profiles, we study the kinematic dynamo problem. The threshold of the dynamo, given by the critical magnetic Reynolds number Rm$_c$, is found to strongly depend on the form of conductivity variation near the discontinuity of the velocity field where the shear is dominant. For monotonically varying profiles in the limit of sharp variation, this threshold maps to the problem of the dynamo with a jump in conductivity, while for the sinusoidal profile with large variations/wavenumbers, the threshold increases due to effective diffusivity arising from the rapid changes in conductivity. Far from the threshold, it is found that the growth rate depends only on the local gradient of the conductivity near the discontinuity, with the opposite sign of shear and conductivity gradient leading to a larger growth rate, thereby aiding the dynamo instability in regenerating B$_ϕ$ from B$_r$. We calculate the expression for the growth rate in the limit of large Rm$(\gg 1)$ and find that the conductivity variation leads to a modification proportional to the local gradient of conductivity times Rm$^{-1/2}$. This correction is found to depend only on the local gradient of the conductivity at the discontinuity. Similar dependencies are found for realistic, smooth velocity profiles and for different magnetic boundary conditions.

astro-ph.SR↗

arXiv2026

Large ${\rm Pm}$ small-scale kinematic dynamo in protoneutron stars

Magnetars are young, isolated neutron stars that possess an exceptionally strong magnetic field, with surface dipolar strengths on the order of $10^{15}$ G. One of the plausible scenarios for generating such a strong field is an exponential amplification by a turbulent convective dynamo during the protoneutron star phase. However, the short expected duration of the convection ($\sim 10$ s) imposes a stringent constraint on the dynamo growth rate. We perform an extensive set of 82 three-dimensional convective dynamo simulations in the anelastic approximation and investigate the kinematic phase to quantify the dynamo growth rate $γ$. We find that $γ$ increases with both the magnetic Prandtl number ${\rm Pm}$ and the Rayleigh number ${\rm Ra}$, with the most unstable mode becoming highly non-axisymmetric and multipolar. We further observe a gradual transition from large-scale to small-scale dynamo as the magnetic Reynolds number ${\rm Rm}$ increases, resulting in a magnetic field that is predominantly concentrated at small scales. The trend remains unchanged when the outer magnetic boundary condition is varied. Since resolving the increasingly small scales becomes numerically impractical, we employ the theoretical small-scale Kazantsev dynamo model to explore the large ${\rm Pm}$ regime characteristic of protoneutron stars. The model qualitatively captures the growth rate behaviour observed in simulations and, upon extrapolation to the large ${\rm Pm}$ limit, indicates that $γ$ is only weakly dependent on the resistivity in a PNS. Under conditions relevant to the PNS, this model predicts a magnetic energy growth rate of the order of $\sim 1$ ms$^{-1}$.

astro-ph.HE↗

arXiv2026

Relaxation and statistical equilibria in generalised two-dimensional flows

We study relaxation toward statistical equilibrium states of inviscid generalised two-dimensional flows, where the generalised vorticity $q$ is related to the streamfunction $ψ$ via $q=(-\nabla^2)^{\fracα{2}}ψ$, with the parameter $α$ controlling the strength of the nonlinear interactions. The equilibrium solutions exhibit an $α\mapsto -α$ symmetry, under which generalised energy $E_G$ and enstrophy $Ω_G$ are interchanged. For initial conditions that produce condensates, we find long-lived quasi-equilibrium states far from the thermalised solutions we derive using canonical ensemble theory. Using numerical simulations we find that in the limit of vanishing nonlinearity, as $α\to 0$, the time required for partial thermalisation $τ_{th}$ scales like $1/α$. So, the relaxation of the system toward equilibrium becomes increasingly slow as the system approaches the weakly nonlinear limit. This behaviour is also captured by a reduced model we derive using multiple scale asymptotics. These findings highlight the role of nonlinearity in controlling the relaxation toward equilibrium and that the inherent symmetry of the statistical equilibria determines the direction of the turbulent cascades.

physics.flu-dyn↗

arXiv2025

Cascades transition in generalised two-dimensional turbulence

Generalised two-dimensional (2D) fluid dynamics is characterised by a relationship between a scalar field $q$, called generalised vorticity, and the stream function $ψ$, namely $q = (-\nabla^2)^\fracα{2} ψ$. We study the transition of cascades in generalised 2D turbulence by systematically varying the parameter $α$ and investigating its influential role in determining the directionality (inverse, forward, or bidirectional) of these cascades. We derive upper bounds for the dimensionless dissipation rates of generalised energy $E_G$ and enstrophy $Ω_G$ as the Reynolds number tends to infinity. These findings corroborate numerical simulations, illustrating the inverse cascade of $E_G$ and forward cascade of $Ω_G$ for $α> 0$, contrasting with the reverse behaviour for $α< 0$. The dependence of dissipation rates on system parameters reinforces these observed transitions, substantiated by spectral fluxes and energy spectra, which hint at Kolmogorov-like scalings at large scales but discrepancies at smaller scales between numerical and theoretical estimates. These discrepancies are possibly due to nonlocal transfers, which dominate the dynamics as we go from positive to negative values of $α$. Intriguingly, the forward cascade of $E_G$ for $α< 0$ reveals similarities to three-dimensional turbulence, notably the emergence of vortex filaments within a 2D framework, marking a unique feature of this generalised model.

physics.flu-dyn↗

arXiv2025

Nonequilibrium Continuous Transition in a Fast Rotating Turbulence

We study the saturation of three-dimensional unstable perturbations on a fast rotating turbulent flow using direct numerical simulations (DNSs). Under the effect of Kolmogorov forcing, a transition between states dominated by coherent two-dimensional modes to states with three-dimensional variations (quasi-two-dimensional) is observed as we change the global rotation rate. We find this akin to a critical phenomenon, wherein the order parameter scales with the distance to the critical point raised to an exponent. The exponent itself deviates from the predicted mean field value. Also, the nature of the fluctuations of the order parameter near the critical point indicate the presence of on-off intermittency. The critical rotation rate at which the transition occurs exhibits a linear scaling behaviour with the forcing wave number. A reduced model based on linear stability analysis is used to find the linear threshold estimates; we find these to be in good agreement with the 3D nonlinear DNS results.

physics.flu-dyn↗

arXiv2023

Effect of confinement on the transition from 2D to 3D fast rotating flows

We study the effect of confinement on the three-dimensional linear instability of fastly rotating two-dimensional turbulent flows. Using the large scale friction to model the effect of top and bottom boundaries, we study the onset of three-dimensional perturbations on a rapidly rotating flow. The friction term is taken to affect both the evolution of the two-dimensional turbulent flow and the perturbations that evolve on top of it. Using direct numerical simulations, the threshold for the onset of three-dimensional perturbations is traced out as a function of the control parameters. As reported in the earlier work (K. Seshasayanan and B. Gallet. 2020. Onset of three-dimensionality in rapidly rotating turbulent flows), two different mechanisms, namely the centrifugal and parametric type instabilities, are responsible for the destabilisation across the wide range of parameters explored in this study. In the turbulent regime, we find that the large scale friction term does not affect the threshold in the case of centrifugal instability while in the case of the parametric instability the instability threshold is shifted to larger Rossby numbers. For the parametric instability, the length scale of the unstable mode is found to scale as the inverse square root of the rotation rate and the growth rate of the unstable mode is found to be correlated with the minimum of the determinant of the strain rate tensor of the underlying two-dimensional turbulent flow, showing resemblance with elliptical type instabilities. Results from the turbulent flow are then compared with the oscillatory Kolmogorov flow, which undergoes a parametric instability resulting into inertial waves. The dependence of the threshold on the aspect ratio of the system is discussed for both the turbulent and the oscillating Kolmogorov flows.

physics.flu-dyn↗

arXiv2023

Spatial extreme values of vorticity and velocity gradients in two-dimensional turbulent flows

We study the distribution of spatial extrema of vorticity and the determinant of the strain rate tensor for a two-dimensional turbulent flow forced by a Kolmogorov forcing. The distribution of these quantities follow non-Gaussian behaviour and they do not fall into the Generalised Extreme value distributions. It is found that for the truncated Euler equations the spatial extrema of vorticity and strain rate tensor are well described by the Gumbel distribution. The spatial extrema for the vorticity is found to be at the core of the vortices while the velocity gradients are found near the edges of the vortices or at the shear layers in the regions between the vortices. Temporal correlations of the velocity gradients shed light on the extreme value distributions obtained for turbulence and the truncated Euler equations.

physics.flu-dyn↗

arXiv2022

Physics-informed data based neural networks for two-dimensional turbulence

Turbulence remains a problem that is yet to be fully understood, with experimental and numerical studies aiming to fully characterise the statistical properties of turbulent flows. Such studies require huge amount of resources to capture, simulate, store and analyse the data. In this work, we present physics-informed neural network (PINN) based methods to predict flow quantities and features of two-dimensional turbulence with the help of sparse data in a rectangular domain with periodic boundaries. While the PINN model can reproduce all the statistics at large scales, the small scale properties are not captured properly. We introduce a new PINN model that can effectively capture the energy distribution at small scales performing better than the standard PINN based approach. It relies on the training of the low and high wavenumber behaviour separately leading to a better estimate of the full turbulent flow. With 0.1 % training data, we observe that the new PINN model captures the turbulent field at inertial scales leading to a general agreement of the kinetic energy spectra upto eight to nine decades as compared with the solutions from direct numerical simulation (DNS). We further apply these techniques to successfully capture the statistical behaviour of large scale modes in the turbulent flow. We believe such methods to have significant applications in enhancing the retrieval of existing turbulent data sets at even shorter time intervals.

physics.flu-dyn↗

arXiv2021

Equivalence of nonequilibrium ensembles: Two-dimensional turbulence with a dual cascade

We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of energy and enstrophy conservation. A comparative study of the statistical properties of its solutions with those obtained from the standard Navier-Stokes equations clearly show that a formally time-reversible system is able to reproduce the features of a 2D turbulent flow. Statistical quantities based on one- and two-point measurements show an excellent agreement between the two systems, for the inverse- and direct cascade regions. Moreover, we find that the conjecture holds very well for 2D turbulent flows with both conserved energy and enstrophy at finite Reynolds number, which goes beyond the original conjecture for three-dimensional turbulence in the limit of infinite Reynolds number.

physics.flu-dyn↗

arXiv2021

Symmetry breaking in a turbulent environment

In this work we investigate symmetry breaking in the presence of a turbulent environment. The transition from a symmetric state to a symmetry-breaking state is demonstrated using two examples: (i) the transition of a two-dimensional flow to a three dimensional flow as the fluid layer thickness is varied and (ii) the dynamo instability in a thin layer flow as the magnetic Reynolds number is varied. We show that these examples have similar critical exponents that differ from the mean-field predictions. The critical behavior can be related to the multiplicative nature of the fluctuations and can be predicted in certain limits using results from the statistical properties of random interfaces. Our results indicate the possibility of existence of a new class of out-of-equilibrium phase transition controlled by the multiplicative noise.

physics.flu-dyn↗

arXiv2021

Onset of three-dimensionality in rapidly rotating turbulent flows

Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences for the energy dissipation rate. However, its location in parameter space is not provided by the bounding procedure. To determine this precise threshold between exactly 2D and partially 3D flows, we perform a linear stability analysis over a fully turbulent 2D base state. This requires integrating numerically a quasi-2D set of equations over thousands of turnover times, to accurately average the growth rate of the 3D perturbations over the statistics of the turbulent 2Dbase flow. We leverage the capabilities of modern GPUs to achieve this task, which allows us to investigate the parameter space up to Re = 10^5. At Reynolds numbers typical of 3D DNS and laboratory experiments, Re in [10^2, 5x10^3], the turbulent 2D flow becomes unstable to 3D motion through a centrifugal-type instability. However, at even higher Reynolds number another instability takes over. A candidate mechanism for the latter instability is the parametric excitation of inertial waves by the modulated 2D flow, a phenomenon that we illustrate with an oscillatory 2D Kolmogorov flow.

physics.flu-dyn↗

arXiv2020

Transitions between turbulent states in a two-dimensional shear flow

We study the bifurcations of the large scale jets in the turbulent regime of a forced shear flow using direct numerical simulations of the Navier-Stokes equations. The bifurcations are seen in the probability density function (PDF) of the largest scale mode with the control parameter being the Reynolds number based on the friction coefficient denoted as $Rh$. As one increases $Rh$ in the turbulent regime, the PDF of the large scale mode first bifurcates from a Gaussian to a bimodal behaviour, signifying the emergence of reversals of the large scale flow where the flow fluctuates between two distinct turbulent states. Further increase in $Rh$ leads to a bifurcation from bimodal to unimodal PDF which denotes the disappearance of the reversals of the largest scale mode. We attribute the latter transition to the long-time memory that the large scale flow exhibits related to low frequency $1/f^α$ type of noise with $0 < α< 2$. We also demonstrate that a minimal model with 15 modes, obtained from the truncated Euler equation, is able to capture the bifurcations of the large scale jets exhibited by the Navier-Stokes equations.

physics.flu-dyn↗

arXiv2020

Bifurcations of a plane parallel flow with Kolmogorov forcing

We study the primary bifurcations of a two-dimensional Kolmogorov flow in a channel subject to boundary conditions chosen to mimic a parallel flow, i.e. periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. The control parameter is the Reynolds number based on the friction coefficient, denoted as $Rh$. We find that as we increase $Rh$ the laminar steady flow goes through a degenerate Hopf bifurcation with both the oscillation frequency and the amplitude of the growing mode being zero at the threshold. A reduced four-mode model captures the scalings that are obtained from the numerical simulations. As we increase $Rh$ further we observe a secondary instability which excites the largest mode in the domain. The saturated amplitude of the largest mode is found to scale as a $3/2$ power-law of the distance to the threshold which is also explained using a low-dimensional model.

physics.flu-dyn↗

arXiv2019

Surface gravity waves propagating in a rotating frame: the Ekman-Stokes instability

We report on an instability arising when surface gravity waves propagate in a rotating frame. The Stokes drift associated to the uniform wave field, together with global rotation, drives a mean flow in the form of a horizontally invariant Ekman-Stokes spiral. We show that the latter can be subject to an instability that triggers the appearance of an additional horizontally-structured cellular flow. We determine the instability threshold numerically, in terms of the Rossby number Ro associated to the Stokes drift of the waves and the Ekman number E. We confirm the numerical results through asymptotic expansions at both large and low Ekman number. At large E the instability reduces to that of a standard Ekman spiral driven by the wave-induced surface stress instead of a wind stress, while at low E the Stokes-drift profile crucially determines the shape of the unstable mode. In both limits the instability threshold asymptotes to an Ekman-number-independent critical Rossby number, which in both cases also corresponds to a critical Reynolds number associated to the Lagrangian base-flow velocity profile. Parameter values typical of ocean swell fall into the low-E unstable regime: the corresponding "anti-Stokes" flows are unstable, with possible consequences for particle dispersion and mixing.

physics.flu-dyn↗

arXiv2018

Dynamo saturation down to vanishing viscosity: strong-field and inertial scaling regimes

We present analytical examples of fluid dynamos that saturate through the action of the Coriolis and inertial terms of the Navier-Stokes equation. The flow is driven by a body force and is subject to global rotation and uniform sweeping velocity. The model can be studied down to arbitrarily low viscosity and naturally leads to the strong-field scaling regime for the magnetic energy produced above threshold: the magnetic energy is proportional to the global rotation rate and independent of the viscosity. Depending on the relative orientations of global rotation and large-scale sweeping, the dynamo bifurcation is either supercritical or subcritical. In the supercritical case, the magnetic energy follows the scaling-law for supercritical strong-field dynamos predicted on dimensional grounds by Petrelis & Fauve (2001). In the subcritical case, the system jumps to a finite-amplitude dynamo branch. The magnetic energy obeys a magneto-geostrophic scaling-law (Roberts & Soward 1972), with a turbulent Elsasser number of the order of unity, where the magnetic diffusivity of the standard Elsasser number appears to be replaced by an eddy diffusivity. In the absence of global rotation, the dynamo bifurcation is subcritical and the saturated magnetic energy obeys the equipartition scaling regime. We consider both the vicinity of the dynamo threshold and the limit of large distance from threshold to put these various scaling behaviors on firm analytical ground.

physics.flu-dyn↗

arXiv2018

Growth rate distribution and intermittency in kinematic turbulent dynamos : which moment predicts the dynamo onset?

We consider the generation of magnetic field by a turbulent flow. For the linear induction equation (i.e. the kinematic dynamo problem), we show that the statistical moments of the magnetic field display multiscaling and in particular moments of different order turn unstable for different values of the control parameter. On a canonical example, we map the problem onto the calculation of the injected power by a time correlated fluctuating force acting on a Brownian particle. We are then able to calculate analytically the growth rate of the moments of the magnetic field and explain the origin of this intermittency. We finally show that the onset for the nonlinear problem is predicted by the linear onset of the moment of order 0 + (i.e. the logarithm of the magnetic field)

physics.flu-dyn↗

arXiv2017

Transition to turbulent dynamo saturation

While the saturated magnetic energy is independent of viscosity in dynamo experiments, it remains viscosity-dependent in state-of-the-art 3D direct numerical simulations (DNS). Extrapolating such viscous scaling-laws to realistic parameter values leads to an underestimation of the magnetic energy by several orders of magnitude. The origin of this discrepancy is that fully 3D DNS cannot reach low enough values of the magnetic Prandtl number $Pm$. To bypass this limitation and investigate dynamo saturation at very low $Pm$, we focus on the vicinity of the dynamo threshold in a rapidly rotating flow: the velocity field then depends on two spatial coordinates only, while the magnetic field consists of a single Fourier mode in the third direction. We perform numerical simulations of the resulting set of reduced equations for $Pm$ down to $2\cdot 10^{-5}$. This parameter regime is currently out of reach to fully 3D DNS. We show that the magnetic energy transitions from a high-$Pm$ viscous scaling regime to a low-$Pm$ turbulent scaling regime, the latter being independent of viscosity. The transition to the turbulent saturation regime occurs at a low value of the magnetic Prandtl number, $Pm \simeq 10^{-3}$, which explains why it has been overlooked by numerical studies so far.

physics.flu-dyn↗

arXiv2017

Condensates in rotating turbulent flows

Using a large number of numerical simulations we examine the steady state of rotating turbulent flows in triple periodic domains, varying the Rossby number $Ro$ (that measures the inverse rotation rate) and the Reynolds number $Re$ (that measures the strength of turbulence). The examined flows are sustained by either a helical or a non-helical Roberts force, that is invariant along the axis of rotation. The forcing acts at a wavenumber $k_f$ such that $k_fL=4$, where $2πL$ is the size of the domain. Different flow behaviours were obtained as the parameters are varied. Above a critical rotation rate the flow becomes quasi two dimensional and transfers energy to the largest scales of the system forming large coherent structures known as condensates. We examine the behaviour of these condensates and their scaling properties close and away from this critical rotation rate. Close to the the critical rotation rate the system transitions super-critically to the condensate state displaying a bimodal behaviour oscillating randomly between an incoherent-turbulent state and a condensate state. Away from the critical rotation rate, it is shown that two distinct mechanisms can saturate the growth of the large scale energy. The first mechanism is due to viscous forces and is similar to the saturation mechanism observed for the inverse cascade in two-dimensional flows. The second mechanism is independent of viscosity and relies on the breaking of the two-dimensionalization condition of the rotating flow. The two mechanisms predict different scaling with respect to the control parameters of the system (Rossby and Reynolds), which are tested with the present results of the numerical simulations. A phase space diagram in the $Re,Ro$ parameter plane is sketched.

physics.flu-dyn↗