MAE Department - PG Seminar - Transient growth of wavelet-based resolvent modes in turbulent channel flow
In this work, we study the transient growth of the principal resolvent modes in the minimal flow unit using a reformulation of resolvent analysis in a time-localized wavelet basis. We target the most energetic spatial wavenumbers for the minimal flow unit and obtain modes that are constant in the streamwise direction and once-periodic in the spanwise direction. The forcing modes are in the shape of streamwise rolls, though pulse-like in time, and the response modes are in the form of transiently growing streaks. We inject the principal transient forcing mode at different intensities into a simulation of the minimal flow unit and compare the resulting nonlinear response to the linear one. The peak energy amplification scales quadratically with the intensity of the injected mode, and this peak occurs roughly at the same time for all forcing intensities. However, the larger energy amplification intensifies the magnitude of the nonlinear terms, which play an important role in damping the energy growth and accelerating energy decay of the principal resolvent mode. We also observe that the damping effect of the nonlinearities is less prominent close to the wall.
Jane Bae is an Assistant Professor of Aerospace at the Graduate Aerospace Laboratories at Caltech. She received her Ph.D. in Computational and Mathematical Engineering from Stanford University in 2018. She was a postdoctoral fellow in the Graduate Aerospace Laboratories at Caltech and the Institute for Applied Computational Science at Harvard University before joining the Caltech faculty. Her main research focuses on computational fluid mechanics, in particular on modeling and control of wall-bounded turbulence.