Dynamic transitions of surface tension driven convection

Dijkstra H., Sengul T., Wang S.

PHYSICA D-NONLINEAR PHENOMENA, cilt.247, sa.1, ss.7-17, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 247 Sayı: 1
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.physd.2012.12.008
  • Dergi Adı: PHYSICA D-NONLINEAR PHENOMENA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.7-17
  • Anahtar Kelimeler: Surface tension driven convection, Dynamic transition theory, Marangoni convection, Benard convection, Hexagonal pattern, Well-posedness, MARANGONI CONVECTION
  • Marmara Üniversitesi Adresli: Hayır

Özet

We study the well-posedness and dynamic transitions of the surface tension driven convection in a three-dimensional (3D) rectangular box with non-deformable upper surface and with free-slip boundary conditions. It is shown that as the Marangoni number crosses the critical threshold, the system always undergoes a dynamic transition. In particular, two different scenarios are studied. In the first scenario, a single mode losing its stability at the critical parameter gives rise to either a Type-I (continuous) or a Type-II (jump) transition. The type of transition is dictated by the sign of a computable non-dimensional parameter, and the numerical computation of this parameter suggests that a Type-I transition is favorable. The second scenario deals with the case where the geometry of the domain allows two critical modes which possibly characterize a hexagonal pattern. In this case we show that the transition can only be either a Type-II or a Type-III (mixed) transition depending on another computable non-dimensional parameter. We only encountered Type-III transitions in our numerical calculations. The second part of the paper deals with the well-posedness and existence of global attractors for the problem. (C) 2012 Elsevier B.V. All rights reserved.