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 eddies, perturbed by a tidal flow. The physical background of the flow is given by means of a dynamical model for tide-topography interaction. Lagrangian advection in this flow can be described in terms of perturbed Hamiltonian systems. For small perturbations analytical techniques, like Melnikov's method, provide mixing coefficients. But also in the limit of large perturbations analytical results can be achieved. In this paper the method of orbit expansion is presented. The coordinates are transformed into a system, moving with the perturbation. By integration 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 perturbation and the lower-order displacement. Again the moving system is integrated over a period of the perturbation. In this way an analytical approximation of the Poincare map can be constructed. Using this approximate map one can find analytical expressions for the mixing coefficients. This method is applied successfully to a model of a tidal area. It can explain the non-monotonic dependence of the mixing on the topographic wavenumber.