We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number R is raised above its critical value R_c. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.

The effects of time-periodic forcing in a few-mode model for zero-Prandtl-number convection with rigid body rotation is investigated. The time-periodic modulation of the rotation rate about the vertical axis and gravity modulation are considered separately. In the presence of periodic variation of the rotation rate, the model shows modulated waves with a band of frequencies. The increase in the external forcing amplitude widens the frequency band of the modulated waves, which ultimately leads to temporally chaotic waves. The gravity modulation, on the other hand, with small frequencies, destroys the quasiperiodic waves at the onset and leads to chaos through intermittency. The spectral power density shows more power to a band of frequencies in the case of periodic modulation of the rotation rate. In the case of externally imposed vertical vibration, the spectral density has more power at lower frequencies. The two types of forcing show different routes to chaos.

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.

We present a study of the effect of laser pulse temporal profile on the energy/momentum acquired by the ions as a result of the ultraintense laser pulse focussed on a thin plasma layer in the radiation pressuredominant(RPD) regime. In the RPD regime, the plasma foil is pushed by ultraintense laser pulse when the radiation cannot propagate through the foil, while the electron and ion layers move together. The nonlinear character of laser–matter interaction is exhibited in the relativistic frequency shift, and also change in the wave amplitude as the EM wave gets reflected by the relativistically moving thin dense plasma layer. Relativistic effects in a highenergy plasma provide matching conditions that make it possible to exchange very effectively ordered kineticenergy and momentum between the EM fields and the plasma. When matter moves at relativistic velocities, the efficiency of the energy transfer from the radiation to thin plasma foil is more than 30% and in ultrarelativisticcase it approaches one. The momentum/energy transfer to the ions is found to depend on the temporal profile of the laser pulse. Our numerical results show that for the same laser and plasma parameters, a Lorentzian pulse canaccelerate ions upto 0.2 GeV within 10 fs which is 1.5 times larger than that a Gaussian pulse can.