Studies of an impressionistic dynamical model that mimics open flow turbulence, Part 1

Despite much progress in understanding chaos in dynamical13; systems and the connections established with flow transitions in certain closed systems, doubts remain about the relevance of dynamical chaos especially to open, shear flow turbulence. We study here the general behaviour of a13; simple dynamical model consisting of two nonlinear ordinary differential equations whose structure, based on physical arguments on large and small eddy motions respectively , should be able to mimic a broad class of flows. Using the Melnikov technique, it is shown that the system possesses chaotic solutions when subjected to deterministic forcing. The model exhibits many generic features of shear flow transition; in particular: (i) a cascade process is inherent in the model, (ii) the value of the control parameter (the analog of inverse Reynolds number) at onset of chaos is not unique but depends on13; the forcing amplitude (i.e. disturbance level), and (iii) chaos persists as the control parameter tends to zero, the forcing amplitude required to induce chaos simultaneously tending to zero