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.