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http://lib.jncasr.ac.in:8080/jspui/handle/10572/1518
2022-05-16T09:20:14ZTHE CONTRIBUTION OF THE BHATNAGAR-GROSS-KROOK MODEL TO THE DEVELOPMENT OF RAREFIED GAS DYNAMICS IN THE EARLY YEARS OF THE SPACE AGE
http://lib.jncasr.ac.in:8080/jspui/handle/10572/2445
Title: THE CONTRIBUTION OF THE BHATNAGAR-GROSS-KROOK MODEL TO THE DEVELOPMENT OF RAREFIED GAS DYNAMICS IN THE EARLY YEARS OF THE SPACE AGE
Authors: Narasimha, Roddam
Abstract: The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar-Gross-Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of the space age. Early efforts intended to probe the limits of the BGK model showed that, in and near both the continuum Euler limit and the collisionless Knudsen limit, BGK could provide useful answers. Attempts were therefore made to tackle more ambitious nonlinear nonequilibrium problems. The most challenging of these was the structure of a plane shock wave. The first exact numerical solutions of the BGK equation for the shock appeared during 1962 to 1964, and yielded deep insights into the character of transitional nonequilibrium flows that had resisted all attempts at solution through the Boltzmann equation. In particular, a BGK weak shock was found to be amenable to an asymptotic analysis. The results highlighted the importance of accounting separately for fast-molecule dynamics, most strikingly manifested as tails in the distribution function, both in velocity and in physical space - tails are strange versions or combinations of collisionless and collision-generated flows. However, by the mid-1960s Monte-Carlo methods of solving the full Boltzmann equation were getting to be mature and reliable and interest in the BGK waned in the following years. Interestingly, it has seen a minor revival in recent years as a tool for developing more effective algorithms in continuum computational fluid dynamics, but the insights derived from the BGK for strongly nonequilibrium flows should be of lasting value.
Description: Restricted Access2014-01-01T00:00:00ZFree turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics
http://lib.jncasr.ac.in:8080/jspui/handle/10572/2444
Title: Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics
Authors: Suryanarayanan, Saikishan; Narasimha, Roddam; Dass, N. D. Hari
Abstract: This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a "vortex gas" comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via "violent" and "slow" relaxations [P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a "relative equilibrium." The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar "equilibrium" state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term "exPLoSive" as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers [J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.
Description: Restricted Access2014-01-01T00:00:00ZCumulus-Type Flows in the Laboratory and on the Computer: Simulating Cloud Form, Evolution, and Large-Scale Structure
http://lib.jncasr.ac.in:8080/jspui/handle/10572/2443
Title: Cumulus-Type Flows in the Laboratory and on the Computer: Simulating Cloud Form, Evolution, and Large-Scale Structure
Authors: Diwan, Sourabh S.; Prasanth, P.; Sreenivas, K. R.; Deshpande, S. M.; Narasimha, Roddam
Abstract: Cumulus clouds, which are among the largest sources of uncertainty in climate change science and tropical circulation, have to-date resisted the numerous attempts made during the last six decades to unravel their cloud-scale dynamics. One major reason has been the lack of a convincing fluid-dynamical model and the difficulty of making repeatable measurements in an inherently transient flow. This article summarizes recent work showing that cumulus-type f lows can be generated in the laboratory by releasing volumetric heat into a plume above a height analogous to cloud condensation level and in quantities dynamically similar to the release of latent heat in the natural cloud. Such a transient diabatic plume (TDP) seems to mimic cumulus clouds with adiabatic/pseudoadiabatic processes of latent heat release. With appropriate heating profile histories, the TDP simulates a variety of cumulus-cloud forms, from cumulus congestus to cumulus fractus, and permits tracking their evolution through a complete life cycle. Selected examples of such laboratory simulations are supported by preliminary results from direct numerical simulations based on the Navier-Stokes-Boussinesq equations. These simulations suggest that the baroclinic torque plays an important role in the dynamics of both large- and small-scale motions in cloud-type flows.
Description: Restricted Access2014-01-01T00:00:00ZA. P. J. Abdul Kalam (1931-2015)
http://lib.jncasr.ac.in:8080/jspui/handle/10572/1970
Title: A. P. J. Abdul Kalam (1931-2015)
Authors: Narasimha, Roddam; Balakrishnan, N.
Description: Restricted access2015-01-01T00:00:00Z