Abstract
The propagation of thermoconvective waves in a horizontal layer of viscoelastic liquid (Oldroyd's liquid B) heated from below is investigated. It is shown that the wave propagates without damping at the critical condition for the onset of overstability and that as the elastic parameter increases the damping length (the logarithmic decrement) becomes large (small) near the critical Rayleigh number for the onset of stationary instability. When the ratio of retardation time to relaxation time is very small, the weakly damped wave can exist for high frequencies even if the liquid layer is isothermal.
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