ALBERT

Description: Direct numerical simulations of Rayleigh-Taylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible Navier-Stokes formulation in a non-equilibrium thermodynamic framework. The two-dimensional flow is studied in an isolated box with non-periodic walls in both vertical and horizontal directions. The non-conducting interface separating the two air masses is impulsively removed at t = 0 (depicting a heaviside function). No external perturbation has been used at the interface to instigate the instability at the onset. Computations have been carried out for rectangular and square cross sections. The formulation is free of Boussinesq approximation commonly used in many Navier-Stokes formulations for RTI. Effect of Stokes’ hypothesis is quantified, by using models from acoustic attenuation measurement for the second coefficient of viscosity from two experiments. Effects of Stokes’ hypothesis on growth of mixing layer and evolution of total entropy for the Rayleigh-Taylor system are reported. The initial rate of growth is observed to be independent of Stokes’ hypothesis and the geometry of the box. Following this stage, growth rate is dependent on the geometry of the box and is sensitive to the model used. As a consequence of compressible formulation, we capture pressure wave-packets with associated reflection and rarefaction from the non-periodic walls. The pattern and frequency of reflections of pressure waves noted specifically at the initial stages are reflected in entropy variation of the system.

Description: A rigorous and systematic computational and theoretical study, the first of its kind, for the laminar natural convective flow above rectangular horizontal surfaces of various aspect ratios ϕ (from 1 to ∞) is presented. Two-dimensional computational fluid dynamic (CFD) simulations (for ϕ → ∞) and three-dimensional CFD simulations (for 1 ≤ ϕ 〈 ∞) are performed to establish and elucidate the role of finiteness of the horizontal planform on the thermo-fluid-dynamics of natural convection. Great care is taken here to ensure grid independence and domain independence of the presented solutions. The results of the CFD simulations are compared with experimental data and similarity theory to understand how the existing simplified results fit, in the appropriate limiting cases, with the complex three-dimensional solutions revealed here. The present computational study establishes the region of a high-aspect-ratio planform over which the results of the similarity theory are approximately valid, the extent of this region depending on the Grashof number. There is, however, a region near the edge of the plate and another region near the centre of the plate (where a plume forms) in which the similarity theory results do not apply. The sizes of these non-compliance zones decrease as the Grashof number is increased. The present study also shows that the similarity velocity profile is not strictly obtained at any location over the plate because of the entrainment effect of the central plume. The 3-D CFD simulations of the present paper are coordinated to clearly reveal the separate and combined effects of three important aspects of finiteness: the presence of leading edges, the presence of planform centre, and the presence of physical corners in the planform. It is realised that the finiteness due to the presence of physical corners in the planform arises only for a finite value of ϕ in the case of 3-D CFD simulations (and not in 2-D CFD simulations or similarity theory). The presence of physical corners is related here to several significant aspects of the solution—the conversion of in-plane velocity to out-of-plane velocity near the diagonals, the star-like non-uniform distribution of surface heat flux on heated planforms, the three-dimensionality of the temperature field, and the complex spatial structure of the velocity iso-surfaces. A generic theoretical correlation for the Nusselt number is deduced for the averaged surface heat flux for various rectangular surfaces (1 ≤ ϕ 〈 ∞) over a wide range of Grashof number. Innovative use of numerical visualization images is made to generate a comprehensive, quantitative understanding of the physical processes involved.

Description: Heating of collisionless plasmas in closed adiabatic magnetic cycle comprising of a quasi static compression followed by a non quasi static constrained expansion against a constant external pressure is proposed. Thermodynamic constraints are derived to show that the plasma always gains heat in cycles having at least one non quasi static process. The turbulent relaxation of the plasma to the equilibrium state at the end of the non quasi static expansion is discussed and verified via 1D Particle in Cell (PIC) simulations. Applications of this scheme to heating plasmas in open configurations (mirror machines) and closed configurations (tokamak, reverse field pinche) are discussed.

Description: Interactions of two Li plasma plumes and shock waves are investigated at various pressures (∼10 −5 to 3 mbar) in the argon gas ambient. Fast imaging and optical emission spectroscopy are used to study the plume dynamics and characteristic emission of plasmas. The plasma plumes are created in laser-blow-off geometry. The expansion of plasma plumes in the ambient gas leads to the formation of an interaction zone. The formation of interaction zone is dependent on the ambient pressure and below a certain pressure, no significant change is observed in the shape and size of the interaction plasma. In the higher pressure, formation of interaction zone and its shape are dependent on ambient pressure. Dynamics of seed plasmas and interaction zone are also affected by the shock-shock interactions. The shock-shock interaction depends on the angle of incidence (α) between two shock waves at the initial time of interaction but as the plumes expand, the shock-shock interaction does not follow α dependence.

Description: The propagation of large amplitude ion-acoustic solitons is studied in the laboratory frame ( x , t ) using a 1-D particle-in-cell code that evolves the ion dynamics by treating them as particles but assumes the electrons to follow the usual Boltzmann distribution. It is observed that for very low Mach numbers the simulation results closely match the Korteweg-de Vries soliton solutions, obtained in the wave frame, and which propagate without distortion. The collision of two such profiles is observed to exhibit the usual solitonic behaviour. As the Mach number is increased, the given profile initially evolves and then settles down to the exact solution of the full non-linear Poisson equation, which then subsequently propagates without distortion. The fractional change in amplitude is found to increase linearly with Mach number. It is further observed that initial profiles satisfying k 2 λ d e 2 〈 1 break up into a series of solitons.

Description: Excitation of wakefield in a cold homogeneous plasma, driven by an ultra-relativistic electron beam is studied in one dimension using fluid simulation techniques. For a homogeneous rigid beam having density ( n b ) less than or equal to half the plasma density ( n 0 ), simulation results are found to be in good agreement with the analytical work of Rosenzweig [Phys. Rev. Lett. 58 , 555 (1987)]. Here, Rosenzweig's work has been analytically extended to regimes where the ratio of beam density to plasma density is greater than half and results have been verified using simulation. Further in contrast to Rosenzweig's work, if the beam is allowed to evolve in a self-consistent manner, several interesting features are observed in simulation viz. splitting of the beam into beam-lets (for l b  〉  λ p ) and compression of the beam (for l b  

Description: The effects of radiation reaction force on laser driven auto-resonant particle acceleration scheme are studied using Landau-Lifshitz equation of motion. These studies are carried out for both linear and circularly polarized laser fields in the presence of static axial magnetic field. From the parametric study, a radiation reaction dominated region has been identified in which the particle dynamics is greatly effected by this force. In the radiation reaction dominated region, the two significant effects on particle dynamics are seen, viz., (1) saturation in energy gain by the initially resonant particle and (2) net energy gain by an initially non-resonant particle which is caused due to resonance broadening. It has been further shown that with the relaxation of resonance condition and with optimum choice of parameters, this scheme may become competitive with the other present-day laser driven particle acceleration schemes. The quantum corrections to the Landau-Lifshitz equation of motion have also been taken into account. The difference in the energy gain estimates of the particle by the quantum corrected and classical Landau-Lifshitz equation is found to be insignificant for the present day as well as upcoming laser facilities.

Description: Spinning cylinder rotating about its axis experiences a transverse force/lift, an account of this basic aerodynamic phenomenon is known as the Robins-Magnus effect in text books. Prandtl studied this flow by an inviscid irrotational model and postulated an upper limit of the lift experienced by the cylinder for a critical rotation rate. This non-dimensional rate is the ratio of oncoming free stream speed and the surface speed due to rotation. Prandtl predicted a maximum lift coefficient as C L max = 4 π for the critical rotation rate of two. In recent times, evidences show the violation of this upper limit, as in the experiments of Tokumaru and Dimotakis [“The lift of a cylinder executing rotary motions in a uniform flow,” J. Fluid Mech. 255 , 1–10 (1993)] and in the computed solution in Sengupta et al. [“Temporal flow instability for Magnus–robins effect at high rotation rates,” J. Fluids Struct. 17 , 941–953 (2003)]. In the latter reference, this was explained as the temporal instability affecting the flow at higher Reynolds number and rotation rates (〉2). Here, we analyze the flow past a rotating cylinder at a super-critical rotation rate (=2.5) by the enstrophy-based proper orthogonal decomposition (POD) of direct simulation results. POD identifies the most energetic modes and helps flow field reconstruction by reduced number of modes. One of the motivations for the present study is to explain the shedding of puffs of vortices at low Reynolds number ( Re = 60), for the high rotation rate, due to an instability originating in the vicinity of the cylinder, using the computed Navier-Stokes equation (NSE) from t = 0 to t = 300 following an impulsive start. This instability is also explained through the disturbance mechanical energy equation, which has been established earlier in Sengupta et al. [“Temporal flow instability for Magnus–robins effect at high rotation rates,” J. Fluids Struct. 17 , 941–953 (2003)].

Description: Space-time evolution of a relativistic electron beam driven wake-field in a cold, homogeneous plasma is studied using 1D-fluid simulation techniques. It is observed that the wake wave gradually evolves and eventually breaks, exhibiting sharp spikes in the density profile and sawtooth like features in the electric field profile [Bera et al ., Phys. Plasmas 22 , 073109 (2015)]. It is shown here that the excited wakefield is a longitudinal Akhiezer-Polovin mode [A. I. Akhiezer and R. V. Polovin, Sov. Phys. JETP 3 , 696 (1956)] and its steepening (breaking) can be understood in terms of phase mixing of this mode, which arises because of relativistic mass variation effects. Further, the phase mixing time (breaking time) is studied as a function of beam density and beam velocity and is found to follow the well known scaling presented by Mukherjee and Sengupta [Phys. Plasmas 21 , 112104 (2014)].

Description: Spatio-temporal evolution of the relativistic Buneman instability has been investigated in one dimension using an in-house developed particle-in-cell simulation code. Starting from the excitation of the instability, its evolution has been followed numerically till its quenching and beyond. The simulation results have been quantitatively compared with the fluid theory and are found to be in conformity with the well known fact that the maximum growth rate ( γ max ) reduces due to relativistic effects and varies with γ e 0 and m/M as γ m a x ∼ 3 2 γ e 0 ( m 2 M ) 1 / 3 , where γ e 0 is the Lorentz factor associated with the initial electron drift velocity ( v 0 ) and (m/M) is the electron to ion mass ratio. Further it is observed that in contrast to the non-relativistic results [A. Hirose, Plasma Phys. 20 , 481 (1978)] at the saturation point, the ratio of electrostatic field energy density ( ∑ k | E k | 2 / 8 π ) to initial drift kinetic energy density ( W 0 ) scales with γ e 0 as ∼ 1 / γ e 0 2 . This novel result on the scaling of energy densities has been found to be in quantitative agreement with the scalings derived using fluid theory.