Dynamics of the wall jet in transcritical regime

A nonlinear dynamical system with few DOF for describing the time evolution of a flow at the onset of turbulence is derived from the equations of motion of the perturbed flow. The velocity field of the disturbance is represented as a linear combination of modes drawn from the linear analysis. The resulting system of equations yields asymptotic trajectories which are sensitively dependent on initial conditions. The solution of the system characterizes chaos typical of hydrodynamic quantities in turbulent flow.