Mahendra K Verma
Articles written in Pramana – Journal of Physics
Volume 61 Issue 3 September 2003 pp 577-594
Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence
Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimension
Volume 61 Issue 4 October 2003 pp 707-724 Reasearch Articles
Energy fluxes in helical magnetohydrodynamics and dynamo action
Renormalized viscosity, renormalized resistivity, and various energy fluxes are calculated for helical magnetohydrodynamics using perturbative field theory. The calculation is of firstorder in perturbation. Kinetic and magnetic helicities do not affect the renormalized parameters, but they induce an inverse cascade of magnetic energy. The sources for the large-scale magnetic field have been shown to be (1) energy flux from large-scale velocity field to large-scale magnetic field arising due to non-helical interactions and (2) inverse energy flux of magnetic energy caused by helical interactions. Based on our flux results, a primitive model for galactic dynamo has been constructed. Our calculations yield dynamo time-scale for a typical galaxy to be of the order of 10^{8} years. Our field-theoretic calculations also reveal that the flux of magnetic helicity is backward, consistent with the earlier observations based on absolute equilibrium theory.
Volume 62 Issue 6 June 2004 pp 1327-1328 Errata
Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence
Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the ﬂux equations to the ﬁrst order in perturbation. For zero cross helicity and space dimension $d = 3$, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy ﬂuxes from large-scale magnetic ﬁeld to small-scale velocity ﬁeld, large-scale velocity ﬁeld to small-scale magnetic ﬁeld, and large-scale velocity ﬁeld to large-scale magnetic ﬁeld. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for ﬂuid turbulence $(\approx 1.6)$ for Alfvén ratio $0.5\leq r_{A}\leq \infty$. For higher space-dimensions, the energy ﬂuxes are qualitatively similar, and Kolmogorov’s constant varies as $d^{1/3}$. For the normalized cross helicity $\sigma_{c}\to 1$, the cascade rates are proportional to $(1-\sigma_{c})/(1+\sigma_{c})$, and the Kolmogorov’s constants vary signiﬁcantly with $\sigma_{c}$.
Volume 63 Issue 3 September 2004 pp 553-561
Large-eddy simulations of fluid and magnetohydrodynamic turbulence using renormalized parameters
Mahendra K Verma Shishir Kumar
In this paper a procedure for large-eddy simulation (LES) has been devised for fluid and magnetohydrodynamic turbulence in Fourier space using the renormalized parameters. The parameters calculated using field theory have been taken from recent papers by Verma [1,2]. We have carried out LES on 64^{3} grid. These results match quite well with direct numerical simulations of 128^{3}. We show that proper choice of parameter is necessary in LES.
Volume 64 Issue 3 March 2005 pp 333-341
Incompressible turbulence as non-local field theory
It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.
Volume 65 Issue 2 August 2005 pp 297-310
Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence
Mahendra K Verma Arvind Ayyer Olivier Debliquy Shishir Kumar Amar V Chandra
In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wave-number shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimensions, magnitude of triad interactions is large for nonlocal triads, and small for local triads. However, the shell-to-shell energy transfer rate is found to be local and forward. This result is due to the fact that the nonlocal triads occupy much less Fourier space volume than the local ones. The analytical results on three-dimensional shell-to-shell energy transfer match with their numerical counterparts. In two-dimensional turbulence, the energy transfer rates to the nearby shells are forward, but to the distant shells are backward; the cumulative effect is an inverse cascade of energy.
Volume 66 Issue 2 February 2006 pp 447-453
Field-theoretic calculation of kinetic helicity flux
V Avinash Mahendra K Verma Amar V Chandra
In this paper we apply perturbative field-theoretic technique to helical turbulence. In the inertial range the kinetic helicity flux is found to be constant and forward. The universal constant
Volume 74 Issue 1 January 2010 pp 75-82 Research Articles
Chaotic travelling rolls in Rayleigh–Bénard convection
Supriyo Paul Krishna Kumar Mahendra K Verma Daniele Carati Arnab K De Vinayak Eswaran
In this paper we investigate two-dimensional (2D) Rayleigh–B ́enard convection using direct numerical simulation in Boussinesq fluids with Prandtl number $P = 6.8$ confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number $r (770 < r < 890)$ the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to a global flow reversal of the convective motion. The chaotic travelling rolls are observed in simulations with free-slip as well as no-slip boundary conditions on the velocity field. We show that the travelling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.
Volume 81 Issue 4 October 2013 pp 617-629 Research Articles
Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations
Mahendra K Verma Anando Chatterjee K Sandeep Reddy Rakesh K Yadav Supriyo Paul Mani Chandra Ravi Samtaney
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
Volume 81 Issue 6 December 2013 pp 1037-1043
Mahendra K Verma Bidya Binay Karak Rohit Kumar
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 kilogauss, which is in good agreement with observations.
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