## Fluid Mechanics Seminar: Martin Oberlack

- Date: 11/17/2016
- Time: 16:00

University of British Columbia

New non-modal hydrodynamic stability and resulting non-exponential growth rates - a symmetry approach

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable - independent of the base flow, which is analyzed on its stability. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode.

However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Oseen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

**Bio**: Martin Oberlack is a Full Professor and Chair of Fluid Dynamics in the Department of Mechanical Engineering at Darmstadt University of Technology in Germany. Previously he completed his Ph.D. in Mechanical Engineering at Aachen University of Technology (RWTH) followed by a postdoctoral fellowship at the Center for Turbulence Research at Stanford University. Professor Oberlack was recently named a Fellow of the American Physical Society for "pioneering the use of symmetry methods for the study of turbulence, combustion, stability theory, aerodynamic noise, and modelling concepts with a special focus on turbulent shear flows; and for employing the concept of statistical symmetries to derive new conservation laws."

Location: ESB 2012