6/4/2011: Talk on hydrodynamic stability of linearized perturbed systems: the 2D bluff-body wake

Wednesday April 6, 2011, 09:15 - 10:00

ETH Zurich, Zentrum, CAB F84

Hydrodynamic stability and energy spectrum power-law decay of linearized perturbed systems: the 2D bluff-body wake

Dr. Stefania Scarsoglio
Hydraulics Department, Politecnico di Torino

The stability of the two-dimensional wake behind a circular cylinder - a free shear flow problem of general interest for its application in several fields, from aerodynamics to environmental physics and biology - is studied by means of two different and complementary theoretical methods. The normal mode analysis, a robust approach which allows to evaluate whether a flow is asymptotically stable or unstable, is first considered including nonparallel effects. The stability analysis is then performed as an initial-value problem to capture the early transient as well as the long term behaviour of initially imposed disturbances, revealing the presence of different non trivial transient phenomena. The two analyses combined together lead to a quite rich description of the wake stability.
The energy spectrum of the linearized perturbed system - evaluated as the wavenumber distribution of the perturbation kinetic energy density in asymptotic condition - is then studied and compared with the fully developed turbulent state. By observing a decay rate close to -5/3 for the collection of arbitrary perturbative waves, we think it possible to formulate the hypotheses that the nonlinear interaction is maybe not the main factor responsible of the specific value of the -5/3 decay exponent in the energy spectrum and the spectral power-law scaling of intermediate waves is a general dynamical property of the Navier-Stokes solutions which encompasses the nonlinear interaction.