an:00709383
Zbl 0814.76043
Pavithran, S.; Redekopp, L. G.
The coupling of gravity waves and convection: Amplitude equations and planform selection
EN
Stud. Appl. Math. 93, No. 3, 209-250 (1994).
00022520
1994
j
76E15 76E30 76R10 76D33
density jump; Galilean invariance; large-scale interfacial mode; phase dynamics
Summary: Convective motion in a layer of fluid heated from below is considered where the boundaries are stress free and the upper surface supports interfacial gravity waves. Inviscid, immiscible, constant density, ambient fluid is separated from the convecting layer below by a stable density jump. An important parameter in the problem is \(\delta\) representing the ratio of the interfacial density jump to the density change across the convecting layer. Amplitude equations are derived describing convective motion in the plane, and a planform selection analysis is performed. It is demonstrated that the breaking of the translational and Galilean invariance of the problem allows a strong coupling between a large-scale interfacial mode and convection. The resulting phase dynamics is third order in time.