Spectral properties and transport mechanisms of partially chaotic bounded flows in the presence of diffusion

The spectral properties of the Poincare operator associated with the advection-diffusion equation for partially chaotic periodic flows defined in bounded domains are analyzed in this Letter. For vanishingly small diffusivities (i.e., for the Peclet number tending to infinity) the dominant eigenvalue Lambda exhibits the scaling Lambdasimilar toPe(-alpha), where the exponent alphais an element of(0,1) depends on the global property of the flow (shape, geometry, and symmetry of quasiperiodic islands). The value of the exponent alpha is an indicator of qualitatively different transport mechanisms and depends on the localization properties of the corresponding eigenfunctions.