The effect of phase mixing on 2D waves propagating in inhomogeneous dissipative media is studied. As an example, for Alfvén waves propagating transverse to the inhomogenenity, phase mixing occurs, and it is found that the damping rate [e.g., by viscosity, μ, resistivity, η] is proportional to exp [-(t/τ)³], instead of the usual exp (-t/τ), where τ is proportional to 1/η ...... The phenomenon will be investigated in both traveling waves and standing waves and illustrated with simple convection equations and also MHD equations, with μ (and η) as the expansion parameter. The results are also verified by simulation with a dissipative MHD code. Such an effect was used as an explanation of solar coronal heating by Alfvén waves. In addition, the possibility of observing phase mixing and this enhanced dissipative effect for geodesic acoustic modes (GAMS) in Tokamak will be discussed.

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