Objective analysis of experimental measurements indicates that there are recurrent streamwise rolls present in the wall region, at least in the quadratic mean sense. Representation theorems permit optimal expansion of the instantaneous velocity field in the wall region in terms of these streamwise rolls. Without involving ourselves in the question of the source of these rolls, we ask how they will behave dynamically. Severely truncating our system, and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. The methods of dynamical systems theory are applied to these equations. Loss to unresolved modes is represented by a Heisenberg parameter. Authors find that for large values of the Heisenberg parameter (large loss), they obtain stable streamwise rolls having the experimentally observed spacing. For smaller values of the parameter, authors have traveling waves (corresponding to cross-stream drift of the rolls); authors also find a heteroclinic attracting orbit giving rise to intermittency; and finally a chaotic state showing ghosts of all of the above. The behavior is quite robust, much of it being due to the symmetries present. Authors have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude.
|Number of pages
|Published - 1988
|International Symposium on Flow-Induced Vibration and Noise: Nonlinear Interaction Effects and Chaotic Motions - 1988 - Chicago, IL, USA
Duration: Nov 27 1988 → Dec 2 1988
|International Symposium on Flow-Induced Vibration and Noise: Nonlinear Interaction Effects and Chaotic Motions - 1988
|Chicago, IL, USA
|11/27/88 → 12/2/88