title: Tricritical spiral vortex instability in cross-slot flow.
abstract: We examine fluid flow through cross-slot devices with various depth to width ratios α. At low Reynolds number, Re, flow is symmetric and a sharp boundary exists between the two incoming fluid streams. Above an α-dependent critical value, Re(c)(α), a steady symmetry-breaking bifurcation occurs and a spiral vortex structure develops. Order parameters characterizing the instability grow according to a sixth-order Landau potential, and show a progression from second- to first-order transitions as α increases beyond a tricritical value of α ≈ 0.55. Flow simulations indicate the instability is driven by vortex stretching at the stagnation point.
authors.affiliation: Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan.
authors.forename: Simon J
authors.initials: SJ
authors.lastname: Haward
authors.affiliation: School of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, United Kingdom.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Poole
authors.affiliation: Faculdade de Engenharia da Universidade do Porto, DEQ, CEFT, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal.
authors.forename: Manuel A
authors.initials: MA
authors.lastname: Alves
authors.affiliation: Departamento de Engenharia Electromecânica, C-MAST, Universidade Beira Interior, 6201-001 Covilhã, Portugal.
authors.forename: Paulo J
authors.initials: PJ
authors.lastname: Oliveira
authors.affiliation: Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA.
authors.forename: Nigel
authors.initials: N
authors.lastname: Goldenfeld
authors.affiliation: Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan.
authors.forename: Amy Q
authors.initials: AQ
authors.lastname: Shen