Tapan Sengupta (IIT Kanpur) - Linear and Nonlinear Receptivity for Transition to Turbulence: Theoretical and Computational Studies

To understand the unit processes of transition to turbulence by 2D and 3D routes of low amplitude disturbance growth over a zero pressure gradient boundary layer (ZPG-BL) remained as one of the unsolved problems of classical physics. Numerous attempts have been made to understand these processes including those at IIT Kanpur for ZPG-BL. In the present talk, results obtained from solutions of Orr-Sommerfeld and Navier-Stokes equations will be presented with a view to reproduce classical experiment of Schubauer-Skramstad (1947). The experiments used low disturbance tunnel and imposed deterministic harmonic excitation inside the ZPG-BL. 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) by solving 2D NSE. 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 a spatiotemporal linear instability. Of late, we have reported the same process of the STWF for transition involving 3D disturbance field from DNS. These findings clarify our understanding of transition to be primarily due to STWF and not by Tollmien-Schlichting waves.

URL of HPCL: http://spectral.iitk.ac.in