title: Modeling velocity in gradient flows with coupled-map lattices with advection.
abstract: We introduce a simple model to investigate large scale behavior of gradient flows based on a lattice of coupled maps which, in addition to the usual diffusive term, incorporates advection, as an asymmetry in the coupling between nearest neighbors. This diffusive-advective model predicts traveling patterns to have velocities obeying the same scaling as wind velocities in the atmosphere, regarding the advective parameter as a sort of geostrophic wind. In addition, the velocity and wavelength of traveling wave solutions are studied. In general, due to the presence of advection, two regimes are identified: for strong diffusion the velocity varies linearly with advection, while for weak diffusion a power law is found with a characteristic exponent proportional to the diffusion.
authors.affiliation: Unidade de Meteorologia e Climatologia, Instituto de Ciência Aplicada e Tecnologia, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal.
authors.forename: Pedro G
authors.initials: PG
authors.lastname: Lind
authors.forename: João
authors.initials: J
authors.lastname: Corte-Real
authors.forename: Jason A C
authors.initials: JA
authors.lastname: Gallas