Supriyo Paul

Benchmarking and scaling studies of 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 10243, 20483, and 40963 grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.

Bifurcation and chaos in zero-Prandtl-number convection

We present a detailed bifurcation structure and associated flow patterns near the onset of zero-Prandtl-number Rayleigh-Benard convection. We employ both direct numerical simulation and a low-dimensional model ensuring qualitative agreement between the two. Various flow patterns originate from a stationary square observed at a higher Rayleigh number through a series of bifurcations starting from a pitchfork followed by a Hopf and finally a homoclinic bifurcation as the Rayleigh number is reduced to the critical value. Homoclinic chaos, intermittency, and crises are observed near the onset.

Dynamics of zero-Prandtl number convection near onset.

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Bénard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.

Scalings of field correlations and heat transport in 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 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.

Dynamo transition under Taylor-Green forcing

We perform pseudo-spectral simulations of the Taylor-Green dynamo for magnetic Prandtl number of one and produce a bifurcation diagram near the dynamo transition. We observe that the primary dynamo transition is through a supercritical pitchfork bifurcation. We show that the planar magnetic structures near the dynamo transition are due to the emergence of the B(0, 0, 1) and B(0, 0, 2) magnetic Fourier modes, which are born as a result of triadic interactions. Near the transition, the kinetic energy (Eu) and the magnetic energy (Eb) grow linearly with the forcing amplitude F0 with the same slope. The ratio Eb/Eu for F0=[0, 40] ranges from 0 to 3. Beyond the transition, the numerical simulations reveal complex dynamo states with windows of constant, periodic, quasiperiodic, and chaotic magnetic field configurations.

Effect of magnetic field on parametrically driven surface waves

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

Energy Spectra in Rayleigh-Benard Convection

We present a numerical study of the energy spectra and fluxes in the inertial range of turbulent Rayleigh-Benard convection for a wide range of Prandtl number. We consider both free-slip and no-slip conditions for our simulation. Our results support the Kolmogorov-Obukhov (KO) scaling for velocity field for zero-Prandtl number and low-Prandtl number (P 1) convection. For large Prandtl number (P > 1) convection, the Bolgiano-Obukhov scaling (BO) appears to agree with the numerical results better than the KO scaling. We provide phenomenological arguments for the zero-Prandtl and low-Prandtl number convection.

Large Eddy Simulation of Smoke Spread in a Multi-storied Building

A fire dynamics simulator (FDS) code, based on large eddy simulation (LES) technique, has been used for simulation studies of smoke spread due to fire in a multi-storied building. The existing natural ventilation system is found to be inefficient in smoke extraction. To safeguard the stairs from smoke accumulation, various methodologies of mechanical ventilation have been adopted to analyze the situation. Suggestions on improving the safety of the building have been provided and their feasibilities have been discussed.

Nonlinear Dynamics of Low-Prandtl Number Rayleigh-Bénard Convection

We present a detailed bifurcation structure and associated flow patterns for lowPrandtl-number (P = 0.005, 0.02) Rayleigh-Benard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. The main flow patterns observed for this range are 2D straight rolls, stationary squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares. The range of Rayleigh numbers for which the stationary 2D rolls exist decreases rapidly with decreasing Prandtl numbers and vanishes in the zero-P limit giving rise to chaotic solutions at the onset itself. Our results are in qualitative agreement with results reported earlier on this topic.

Bifurcations and Chaos in Taylor‐Green Dynamo

We present simulation results near the dynamo transition for the Taylor‐Green dynamo for magnetic Prandtl number, PM, of 0.5 and 1. We construct bifurcation diagrams for one of the dominant Fourier mode, B(0,0,1), and the ratio of magnetic and kinetic energy (Eb/Eu) as a function of the forcing amplitude of Taylor‐Green forcing. It is observed that the dynamo transition for PM = 1 is via a supercritical bifurcation, while that for PM = 0.5 is via a subcritical bifurcation. The ratio Eb/Eu varies from 0 to 3 for PM = 1, but it is typically less than 1 for PM = 0.5. Different dynamo states, such as those with constant, time‐periodic, quasiperiodic, and chaotic magnetic fields, have been reported. We also observe coexisting dynamo states.