arXiv subjects

Mahendra K. Verma

Publications and source records attributed to Mahendra K. Verma.

At least 91 records · Page 5Linked to original sources

arXiv2014

Modeling quasi-static magnetohydrodynamic turbulence with variable energy flux

In quasi-static MHD, experiments and numerical simulations reveal that the energy spectrum is steeper than Kolmogorov's $k^{-5/3}$ spectrum. To explain this observation, we construct turbulence models based on variable energy flux, which is caused by the Joule dissipation. In the first model, which is applicable to small interaction parameters, the energy spectrum is a power law, but with a spectral exponent steeper than -5/3. In the other limit of large interaction parameters, the second model predicts an exponential energy spectrum and flux. The model predictions are in good agreement with the numerical results.

physics.flu-dyn↗

arXiv2014

Energy spectrum of Buoyancy-driven Flows

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux $Π_u$, we demonstrate that for stably stratified flows, the kinetic energy spectrum $E_u(k) \sim k^{-11/5}$, the entropy spectrum $E_θ(k) \sim k^{-7/5}$, and $Π_u(k) \sim k^{-4/5}$ (Bolgiano-Obukhov scaling). This scaling is due to the depletion of kinetic energy because of buoyancy. For weaker buoyancy in stratified flows, $E_u(k)$ follows Kolmgorov's spectrum with a constant energy flux. We also argue that for Rayleigh Bénard convection, the Bolgiano-Obukhov scaling will not hold for the bulk flow due to the positive energy supply by buoyancy and non-decreasing $Π_u(k)$.

physics.flu-dyn↗

arXiv2014

Strong anisotropy in quasi-static magnetohydrodynamic turbulence for high interaction parameters

We simulate forced quasi-static magnetohydrodynamic turbulence and investigate the anisotropy, energy spectrum, and energy flux of the flow, specially for large interaction parameters ($N$). We show that the angular dependence of the energy spectrum is well quantified using Legendre polynomials. For large $N$, the energy spectrum is exponential. Our direct computation of energy flux reveals an inverse cascade of energy at low wavenumbers, similar to that in two-dimensional turbulence. We observe the flow be two-dimensional (2D) for moderate $N$ ($N \sim 20$), and two-dimensional three-component (2D-3C) type for $N \ge 27$. In our forced simulation, the transition from 2D to 2D-3C occurs at higher value of $N$ than Favier et al., ["On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence," Phys. Fluids 22, 075104 (2010)] who employ decaying simulations.

physics.flu-dyn↗

arXiv2014

Scaling of heat flux and energy spectrum for "very large" Prandtl number convection

Under the limit of infinite Prandtl number, we derive analytical expressions for the large-scale quantities, e.g., Péclet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations $θ_\mathrm{rms}$. We complement the analytical work with direct numerical simulations, and show that $\mathrm{Nu} \sim \mathrm{Ra}^γ$ with $γ\approx (0.30-0.32)$, $\mathrm{Pe} \sim \mathrm{Ra}^η$ with $η\approx (0.57-0.61)$, and $θ_\mathrm{rms} \sim \mathrm{const}$. The Nusselt number is observed to be an intricate function of $\mathrm{Pe}$, $θ_\mathrm{rms}$, and a correlation function between the vertical velocity and temperature. Using the scaling of large-scale fields, we show that the energy spectrum $E_u(k)\sim k^{-13/3}$, which is in a very good agreement with our numerical results. The entropy spectrum $E_θ(k)$ however exhibits dual branches consisting of $k^{-2}$ and $k^0$ spectra; the $k^{-2}$ branch corresponds to the Fourier modes $\hatθ(0,0,2n)$, which are approximately $-1/(2n π)$. The scaling relations for Prandtl number beyond $10^2$ match with those for infinite Prandtl number.

physics.flu-dyn↗

arXiv2014

Energy transfers and magnetic energy growth in small-scale dynamo

In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for magnetic Prandtl number $\mathrm{Pm}=20$ on $1024^3$ grid using pseudospectral method. We demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers move towards lower wavenumbers as dynamo evolves, which is the reason why the integral scale of the magnetic field increases with time. The energy transfers $U2U$ (velocity to velocity) and $B2B$ (magnetic to magnetic) are forward and local.

physics.flu-dyn↗

arXiv2013

Supercriticality to subcriticality in dynamo transitions

Evidence from numerical simulations suggest that the nature of dynamo transition changes from supercritical to subcritical as the magnetic Prandtl number is decreased. To explore this interesting crossover we first use direct numerical simulations to investigate the hysteresis zone of a subcritical Taylor-Green dynamo. We establish that a well defined boundary exists in this hysteresis region which separates dynamo states from the purely hydrodynamic solution. We then propose simple dynamo models which show similar crossover from supercritical to subcritical dynamo transition as a function of the magnetic Prandtl number. Our models show that the change in the nature of dynamo transition is connected to the stabilizing or de-stabilizing influence of governing non-linearities.

physics.flu-dyn↗

arXiv2013

Variable energy flux in quasi-static magnetohydrodynamic turbulence

Experiments and numerical simulations show that the energy spectrum of the magnetohydrodynamic turbulence in the quasi-static limit deviates from Kolmogorov's $k^{-5/3}$ spectrum as the external magnetic field, or equivalently the interaction parameter, is increased. To explain this phenomena, we construct an analytical turbulence model with variable energy flux that arises due to the Lorentz-force induced dissipation. The energy spectra computed using our model for various interaction parameters are in qualitative agreement with earlier experimental and numerical results.

physics.flu-dyn↗

arXiv2013

Dynamo in Protostar

In this paper, we estimate the magnetic Reynolds number of a typical protostar before and after deuterium burning, and claim for the existence of dynamo process in both the phases, because the magnetic Reynolds number of the protostar far exceeds the critical magnetic Reynolds number for dynamo action. Using the equipartition of kinetic and magnetic energies, we estimate the steady-state magnetic field of the protostar to be of the order of kilo-gauss, which is in good agreement with observations.

astro-ph.SR↗

arXiv2013

Role of Bulk flow in Turbulent Convection

In this paper we present scaling of large-scale quantities like Peclét and Nusselt numbers, and the dissipation rates of kinetic energy and entropy. Our arguments are based on the scaling of bulk quantities and earlier experimental and simulation results. We also present the inertial-range properties of spectra and fluxes of kinetic energy and entropy.

physics.flu-dyn↗

arXiv2012

Flow reversals in turbulent convection via vortex reconnections

We employ detailed numerical simulations to probe the mechanism of flow reversals in two-dimensional turbulent convection. We show that the reversals occur via vortex reconnection of two attracting corner rolls having same sign of vorticity, thus leading to major restructuring of the flow. Large fluctuations in heat transport are observed during the reversal due to this flow reconfiguration. The flow configurations during the reversals have been analyzed quantitatively using large-scale modes. Using these tools, we also show why flow reversals occur for a restricted range of Rayleigh and Prandt numbers.

physics.flu-dyn↗

arXiv2012

Benchmarking and scaling studies of a pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh-Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on $1024^3$, $2048^3$, and $4096^3$ grids using the {\em HPC system} of IIT Kanpur and {\em Shaheen} of KAUST. We observe good "weak" and "strong" scaling for Tarang on these systems.

physics.comp-ph↗

arXiv2012

Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction

Experiments and numerical simulations reveal that in the forward cascade regime, the energy spectrum of two-dimensional turbulence with Ekman friction deviates from Kraichnan's prediction of $k^{-3}$ power spectrum. In this letter we explain this observation using an analytic model based on variable enstrophy flux arising due to Ekman friction. We derive an expression for the enstrophy flux which exhibits a logarithmic dependence in the inertial range for the Ekman-friction dominated flows. The energy spectrum obtained using this enstrophy flux shows a power law scaling for large Reynolds number and small Ekman friction, but has an exponential behaviour for large Ekman friction and relatively small Reynolds number.

physics.flu-dyn↗

arXiv2012

Field correlations and the ultimate regime of turbulent convection

Using direct numerical simulations of Rayleigh-Bénard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ for moderately large Rayleigh number $Ra$. This scaling accounts for the Nusselt number ($Nu$) exponent to be around 0.3 observed in experiments. Numerical simulations also reveal that the above normalized correlation functions are constants for the convection simulation under periodic boundary conditions.

physics.flu-dyn↗

arXiv2011

Bistability and chaos in Taylor-Green dynamo

Using direct numerical simulations we study dynamo action under the Taylor-Green forcing with Prandtl number less than one. We observe bistability with a weak magnetic field branch and a strong magnetic field branch. Both the dynamo branches undergo subcritical dynamo transition. We also observe host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic state originates through a quasiperiodic route with phase locking, while another chaotic attractor appears to follow Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions among quasiperiodic and chaotic states for a given Taylor-Green forcing.

nlin.CD↗

arXiv2011

Dynamics and symmetries of flow reversals in turbulent convection

Based on direct numerical simulations and symmetry arguments, we show that the large-scale Fourier modes are useful tools to describe the flow structures and dynamics of flow reversals in Rayleigh-Bénard convection (RBC). We observe that during the reversals, the amplitude of one of the large-scale modes vanishes, while another mode rises sharply, very similar to the "cessation-led" reversals observed earlier in experiments and numerical simulations. We find anomalous fluctuations in the Nusselt number during the reversals. Using the structures of the RBC equations in the Fourier space, we deduce two symmetry transformations that leave the equations invariant. These symmetry transformations help us in identifying the reversing and non-reversing Fourier modes.

nlin.CD↗

arXiv2011

Object-oriented Pseudo-spectral code TARANG for turbulence simulation

In this paper we describe the design and implementation of TARANG, a pseudospectral code to simulate turbulent flows in fluids, magnetohydrodynamics (MHD), convection, passive scalar, etc. We use the object-oriented features of C++ to abstract operations involved in the simulation. TARANG has been validated and used for solving problems in convection and MHD.

physics.flu-dyn↗

arXiv2010

Dynamics of reorientations and reversals of large scale flow in Rayleigh-Benard convection

We present a numerical study of the reversals and reorientations of the large scale circulation (LSC) of convective fluid in a cylindrical container of aspect ratio one. We take Prandtl number to be 0.7 and Rayleigh numbers in the range from $6\times10^5$ to $3\times10^7$. It is observed that the reversals of the LSC are induced by its reorientation along the azimuthal direction, which are quantified using the phases of the first Fourier mode of the vertical velocity measured near the lateral surface in the mid plane. During a ``complete reversal'', the above phase changes by around $180^0$ leading to reversals of the vertical velocity at all the probes. On the contrary, the vertical velocity reverses only at some of the probes during a ``partial reversal'' with phase change other than $180^0$. Numerically we observe rotation-led and cessation-led reorientations, in agreement with earlier experimental results. The ratio of the amplitude of the second Fourier mode and the first Fourier mode rises sharply during the cessation-led reorientations. This observation is consistent with the quadrupolar dominant temperature profile observed during the cessations. We also observe reorientations involving double cessation.

physics.flu-dyn↗

arXiv2010

Dynamics of zero-Prandtl number convection near the onset

In this paper we present various convective states of zero-Prandtl number Rayleigh-Bénard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the energetic modes of DNS. The origin of these convective states have been explained using bifurcation analysis. The system is chaotic at the onset itself with three coexisting chaotic attractors that are born at two codimension-2 bifurcation points. One of the bifurcation points with a single zero eigenvalue and a complex pair $(0,\pm i ω)$ generates chaotic attractors and associated periodic, quasiperiodic, and phase-locked states that are related to the wavy rolls observed in experiments and simulations. The frequency of the wavy rolls are in general agreement with $ω$ of the above eigenvalue of the stability matrix. The other bifurcation point with a double zero eigenvalue produces the other set of chaotic attractors and ordered states such as squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations with intermediate squares, some of which are common to the 13-mode model of Pal et al.(2009).

physics.flu-dyn↗