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Tapan K. Sengupta

2012-11-05
10:40:00 - 12:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Deterministic route to turbulence creation in 2D wall boundary layer is shown here by solving full Navier-Stokes equation by dispersion relation preserving (DRP) numerical methods for wall and free stream excitations. Results show that the transition by wall excitation is predominantly due to nonlinear growth of the Spatio-temporal wave front, even when Tollmien-Schlichting (TS) wave packets are created. The existence and linear mechanism of creating the Spatio- temporal wave front was established in Sengupta, et al. [Phys. Rev. Lett. 96, 224504 (2006)] via the solution of Orr-Sommerfeld equation. Effects of Spatio-temporal front(s) in the nonlinear phase of disturbance evolution have been documented by Sengupta et al. [Phys. Rev. Lett. 107, 154501 (2011) and Phys. Rev. E, 85, 026308 (2012)], where a flow is taken from the receptivity stage to a fully developed turbulent state by solving the Navier-Stokes equation. Details of the physical mechanism will be presented, along with the problem of forced excitation of flow over a natural laminar flow (NLF) airfoil for Re = 10.3 million. The wall excitation is monochromatic and time-harmonic, while free stream convecting vortical excitation is neither monochromatic, nor Spatio-temporal wave front is created, yet all cases show energy spectrum, which has been shown experimentally for atmospheric dynamics in Nastrom, Gage & Jasperson [Nature 310, 36 (1984)]. Reproduction of the spectrum noted in atmospheric data (showing dominance of the spectrum over the spectrum) in lab scale indicates universality of this spectrum. Creation of universal features of 2D turbulence by a deterministic route has been established for the first time by solving the Navier-Stokes equation without any modelling or artifice. The case of 3D excitation field will also be shown to establish the role of Spatio-temporal front vis-à-vis TS wave packet. This is solved by compact schemes for velocity- vorticity formulation. All of these works have been made possible due to correct dispersion analysis of space-time discretization methods; developing optimized dispersion relation preserving methods and upwind multi-dimensional filters. This heralds a new beginning for DNS of actual transitional and inhomogeneous turbulent flows, which is distinctly different from solving homogeneous isotropic turbulence problem by pseudospectral methods.