Events Calendar

Aerospace and Mechanical Engineering Seminar Series

Speaker: Anirban Guha, Postdoctoral Fellow in Atmospheric and Oceanic Sciences at the University of California at Los Angeles, Los Angeles, CA

Talk Title: On the Connection between Wave Resonance, Shear Instability and Oscillator Synchronization

Abstract: Homlboe (Geophys. Publ., vol. 24, 1962, pp. 7-112) postulated that interaction between two or more progressive, linear interfacial waves produces exponentially growing instabilities in idealized (broke-line profiles), homogeneous or density-stratified, inviscid shear layers. We have generalized Holmboe's mechanistic picture of linear shear instabilities by (i) not initially specifying the wave type, and (ii) providing the option for non-normal growth. We have demonstrated the mechanism behind linear shear instabilities by proposing a purely kinematic model consisting of two linear, Doppler-shifted, progressive interfacial waves moving in opposite directions. Moreover, we have found a necessary and sufficient condition for the existence of exponentially growing instabilities in idealized shear forms. The two interfacial waves, starting from arbitrary initial conditions, eventually phase-lock and resonate (grow exponentially), provided the necessary and sufficient condition in satisfied. The theoretical underpinning of our wave interaction model is analogous to that of synchronization between two coupled harmonic oscillators. We have re-framed our model into a nonlinear autonomous dynamical system, the steady-state configuration of which corresponds to the resonant configuration of the wave interaction model. When interpreted in terms of the canonical normal-mode theory, the steady-state/resonant configuration corresponds to the growing normal mode of the discrete spectrum. The instability mechanism occurring prior to reaching steady state is non-modal, favoring rapid transient growth. Depending on the wavenumber and initial phase-shift, non-modal gain can exceed the corresponding modal gain by many orders of magnitude. Instability is also observed in the parameter space, which is deemed stable by the normal-mode theory. Using our model we have derived the discrete spectrum non-modal stability equations for three classical examples of shear instabilities: Rayleigh/Kelvin-Helmholtz, Holmboe and Taylor-Caulfield. We have shown that the necessary and sufficient condition provides a range of unstable wave numbers for each instability type, and this range matched the predictions of normal-mode theory.

Biography: Anirban Guha is currently a Postdoctoral fellow in the Atmospheric and Oceanic Sciences at UCLA. He is particularly interested in stratified shear instabilities, Rossby and gravity waves, vortices, and flow over topography. Dr. Guha obtained an Undergraduate Degree in Mechanical Engineering from Jadavpur University, India, and Ph.D. in Civil Engineering from The University of British Columbia, Canada. He received various awards during his Ph.D. studies at UBC - the Four year fellowship, the Earl R. Peterson memorial scholarship, and the Faculty of applied science graduate award. Dr. Guha was also the 2013 recipient of the prestigious David Crighton Fellowship from DAMTP, University of Cambridge.

Host: Professor Paul Ronney

Location: Seaver Science Library (SSL) - 150

Audiences: Everyone Is Invited

Contact: Valerie Childress