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“DNS of Turbulence from Receptivity Stage: Case of Zero-Pressure Gradient Boundary Layer”

by Tapan K. Sengupta, High Performance Computing Laboratory, Dept. of Aerospace Engineering, IIT Kanpur, INDIA

Abstract:

To understand the unit processes of transition to turbulence in fluid flow via two- and three-dimensional routes of low amplitude disturbance growth over a zero pressure gradient boundary layer (ZPG-BL) remained a canonical unsolved problem. There are numerous attempts to understand the process for ZPG-BL. In the present talk, results obtained from solutions of Navier-Stokes equation and its linearized parallel flow version will be presented which reproduce classical experiment of Schubauer-Skramstad (1947). The experiments used low disturbance tunnel at NBS and imposed deterministic harmonic excitation inside the shear layer. This scenario was studied in Sengupta and Bhaumik [Phys. Rev. Lett. 107, 154501 (2011)], where a route of transition to fully developed turbulent stage was explained for 2D disturbances in terms of the spatio-temporal wave-front (STWF). The STWF was earlier identified as the unit process by theoretical receptivity solution of Orr-Sommerfeld equation by Bromwich contour integral method in Sengupta et al [Phys. Rev. Lett. 96, 224504 (2006)] as due to spatio-temporal instability. Recently, we have reported the same process of the STWF for transition involving 3D disturbance field from DNS. These findings show the importance of choosing correct numerical method to first compute the equilibrium flow and then compute the case of excitation of this equilibrium flow from receptivity to fully developed turbulent state.