Optimal growth (Re=2000,A=1,Wo=15): value of TG as function to and tf (computed) - Xu, Duo; Song, Baofang; Avila, Marc (PANGAEA, 2022)
The data are obtained via an in-house Matlab script (developed by Dr. Baofang Song) to compute the non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows. In this study, a Newtonian fluid driven by pulsatile and oscillatory flow rate flows in a straight pipe. In pulsatile flow, there are three governing parameters: steady Reynolds number (defined by the steady flow component), pulsation amplitude (ratio of oscillatory and steady flow component) and Womersley number (dimensionless pulsation and oscillation frequency). In oscillatory flow, due to vanishment of steady flow component, oscillatory Reynolds number (defined by the oscillation flow component) and Womersley number. The Reynolds number defined by the thickness of Stokes layer is alternatively used for the oscillatory Reynolds number. The study was carried out in a manner that one governing parameter varies while other governing parameters are fixed. The data file 't0_TG_contour.dat' shows the maximum energy amplification over modes in the parameter regime of initial time and final time. This file includes three columns: the first column indicates initial time of perturbations normalized by pulsation period; the second column indicates the evolution time of the perturbation normalized by period; the third column indicates the energy amplification corresponding to the initial time (first column) and the evolution time (second column).
Keywords: nonlinear instability; transition to turbulence