AN ANALYTICAL STUDY OF CHAOTIC STIRRING IN TIDAL AREAS

Chaotic advection is studied in a flow representative of tidal areas. The flow consists of a residual flow, represented by a lattice of eddi es, perturbed by a tidal flow. The physical background of the flow is given by means of a dynamical model for tide-topography interaction. L agrangian advection in this flow can be described in terms of perturbe d Hamiltonian systems. For small perturbations analytical techniques, like Melnikov's method, provide mixing coefficients. But also in the l imit of large perturbations analytical results can be achieved. In thi s paper the method of orbit expansion is presented. The coordinates ar e transformed into a system, moving with the perturbation. By integrat ion over the period of the perturbation, one obtains an (first-order) approximation of the Poincare map. The next order can be obtained by a new coordinate transformation, this time moving with both the perturb ation and the lower-order displacement. Again the moving system is int egrated over a period of the perturbation. In this way an analytical a pproximation of the Poincare map can be constructed. Using this approx imate map one can find analytical expressions for the mixing coefficie nts. This method is applied successfully to a model of a tidal area. I t can explain the non-monotonic dependence of the mixing on the topogr aphic wavenumber.