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Proceedings of the Royal Society of London Series A Mathematical and Physical Sc 465, 2101 (2008) 109-121
Solitary waves on a free surface of a heated Maxwell fluid
D. Comissiong, R.A. Kraenkel, Miguel Manna1

The existence of an oscillatory instability in the Bénard?Marangoni phenomenon for a viscoelastic Maxwell's fluid is explored. We consider a fluid that is bounded above by a free deformable surface and below by an impermeable bottom. The fluid is subject to a temperature gradient, inducing instabilities. We show that due to balance between viscous dissipation and energy injection from thermal gradients, a long-wave oscillatory instability develops. In the weak nonlinear regime, it is governed by the Korteweg?de Vries equation. Stable nonlinear structures such as solitons are thus predicted. The specific influence of viscoelasticity on the dynamics is discussed and shown to affect the amplitude of the soliton, pointing out the possible existence of depression waves in this case. Experimental feasibility is examined leading to the conclusion that for realistic fluids, depression waves should be more easily seen in the Bénard?Marangoni system.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
Physique/Mécanique/Mécanique des fluides
nonlinear waves – viscoelastic fluids – free surface