Research

MHD Turbulence

  1. Using renormalization group analysis we showed that the Alfvèn waves are modulated by the "local mean magnetic field" that scales as k^{-1/3}. As a result, Kraichnan's -3/2 arguments are modified and we recover Kolmogorov's -5/3 spectrum for MHD turbulence.
  2. We also computed renormalized viscosity and mangetic diffusivity with renormalization group formulism.
  3. We formulated how to compute energy transfers and flux for MHD turbulence, and then computed them using numerical simulations.
  4. We related the above fluxes to the dynamo mechanism, and observed many interesting patterns.
  5. We studied the anisotropic energy spectrum and energy transfers in quasi-static MHD turbulence.

Dynamo

  1. We compute various energy fluxes of dynamo for large-scale and small-scale dynamos, and discover interesting insights which are given below.
  2. For large scale dynamos, the dominant contribution is from the large-scale velocity field to the large-scale magnetic field.
  3. For small-scale dynamos, the maximal energy transfer is from the large-scale velocity field to the small-scale magnetic field. However, the length scale to which the energy is transferred keeps getting larger and larger with time.
  4. We studied the dynamo transitions for small Prandtl number and large Prandtl number dynamos. For Taylor-Green forcing, the former class exhibits subcritical transition, while the latter one exhibits supercritical transition.
  5. We also construct several low-dimensional models of dynamo that provide valuable insights.


Turbulent Thermal Convection

  1. Based on energy flux arguments, we showed that turbulent thermal convection has Kolmogorov-like spectrum (5/3), and almost constant energy flux. These arguments rule out the Bolgiano-Obukhov scaling for the this flow. These predictions were verified using direct numerical simulation on 4096^3 grid.
  2. The walls affect the flow in many ways. For example, the temperature spectrum exhibits dual cascade with one branch directly coming from the constancy of the temperature in the bulk.
  3. We showed that the correlations induced by the walls are one of the factors for Nu scaling exponent to be around 0.3 (not 1/2).
  4. We have studied the dynamics of flow reversals and show that large-scale fields play a critical role in these reversals. we constructed several nonlinear dynamics models of such reversals. We also related them the to the magnetic field reversals in dynamo.
  5. We constructed shell models for turbulent thermal convection. The results of the shell model are close to those of direct numerical simulations.

Stably Stratified Turbulence

  1. We provided a numerical validation of Bolgiano-Obukhov scaling of moderately stably-stratified turbulence.
  2. We constructed a shell model of stably stratified turbulence that explains scaling for small and moderate Richardson numbers.

Computational Physics and High Performance Computing

  1. SPECTRAL CODE TARANG: A general-purpose, opensource, parallel and modular C++ flow solver with with around 1 lacs lines of code; it can solve incompressible fluid flow, Rayleigh–Bénard convection, passive and active scalars, magnetohydrodynamics, liquid metals, rotating flows, etc. It scales up to 196608 processors of Cray XC40. It is being used by around 15 research groups across the world. I received Dr. APJ Abdul Kalam Cray HPC award for TARANG.
  2. FINITE DIFFERENCE PDE SOLVER: Flow and electromagnetic solver. Uses multigrid method for pressure solver. Being ported to GPU.

Nonequilibrium Statistical Mechanics

  1. We show that the asymmetric energy transfers from the large scales to small scales play an important role in determining arrow of time in driven dissipative nonequilibrium systems. This mechanism clarifies the role of dissipation in such systems.
  2. We derived universal scaling laws for driven nonequilibrium systems that relate the amplitude and recurrence time interval distribution of large events.
  3. We show that self-organized critiicality could be used to derive 1/f noise observed in Anion channels of neural cells.
  4. We computed the intermittency exponents and energy spectra of the Burgers and KPZ equations with correlated noise.

Astrophysical Flows

  1. For the solar wind, we showed that the turbulent heating plays a major role in the evolution of temperature of the solar wind.
  2. We computed the nonclassical (anomalous) viscosity and resistivity of the solar wind plasma using turbulence modelling.
  3. Using the estimates of the magnetic Reynolds number in protostars, we predict the existence of dynamo in such systems.