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  • 1
    Electronic Resource
    Electronic Resource
    Linear stability of shear profiles and relation to the secondary instability of the Dean flow (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2161-2171 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Solutions of the Navier–Stokes equations for flow in a curved channel have previously been computed [Bottaro, J. Fluid Mech. 251, 627 (1993)] and the spatial development of the Dean flow is available at different supercritical Reynolds number. In this work the viscous instability of local longitudinal vortex structures (obtained from the nonlinear simulations) is investigated, with a focus toward the secondary instability of Dean vortices. Such a secondary instability takes the form of streamwise traveling waves. High-frequency waves are termed twisting waves, low frequency are defined undulating waves. Instead of performing analyses in which the basic flow in the cross section is two dimensional, significant shear profiles along y and z are considered as base flows at constant x before the establishment of a fully developed state. Thus one is able to discover that the twist instability is of shear type and is caused by inflectional spanwise profiles of the streamwise velocity component. Sinuous waves are always preferred to varicose waves, and the latter mode of instability is destabilized only at large Reynolds numbers. Undulating waves are related to normal profiles of the streamwise velocity; this type of secondary instability is of centrifugal origin. Results of the analyses for both types of waves are in good agreement with experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858555
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  • 2
    Electronic Resource
    Electronic Resource
    Nonlinear spatially developing Görtler vortices in curved wall jet flow (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 2375-2384 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Linear and nonlinear spatial developments of two-dimensional wall jets on curved surfaces are computed using pseudospectral-finite difference methods. Inviscid analysis shows that the instability originates from the inner/outer region on a concave/convex wall; the shear layer is thus always unstable regardless of the curvature. This primary instability is a steady spanwise vortex structure similar to Görtler instability in a Blasius flow. In the present study, a perturbation of prescribed wave number α is assumed. In the limit of high Reynolds number (Re) and small curvature (ε), a parabolic set of nonlinear equations describes the spatial evolution of the disturbance. Direct marching simulation of the perturbation and a parabolic stability approach are employed. Both give the same results with different computational efficiencies. For the concave case at low Görtler numbers (G2=ε(square root of)Re), perturbations are unstable for small α. Their energy reaches a maximum and then decays. At high G, the most unstable disturbance occurring at larger α will grow exponentially and reach saturation. The convex case is the most unstable situation. But as for the concave case, the most dangerous disturbance moves from small to larger α as G increases. The numerical results are able to capture the primary instability as observed in the experiment of Matsson [Phys. Fluids 7, 3048 (1995)]. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869022
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Thermocapillary-Coriolis instabilities in liquid bridges (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 2539-2545 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Coriolis effects on thermocapillary instabilities in a liquid bridge of infinite length are investigated. The flow is driven by an imposed temperature gradient along the z direction in a (r,θ,z) rotating frame of reference. When the rotation vector is parallel to the z axis, the return flow, obtained as the unperturbed velocity profile with no rotation, is not modified. In this case, rotation is stabilizing and traveling waves are the prefered mode of instability. If the rotation is orthogonal to the z axis, the base flow is modified and is no longer one-dimensional. Asymptotic methods valid for small rotation are used to calculate the base flow which may become multicellular, both in the radial and azimuthal directions, depending on the Prandtl, Marangoni, and Biot numbers. Linear stability analysis of the new base flow indicates that this type of rotation can be destabilizing while traveling azimuthal waves continue to be the prefered form of convection. Finally, the effect of rotation is studied in a finite length cylinder by direct numerical simulation. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870116
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  • 4
    Electronic Resource
    Electronic Resource
    Görtler-crossflow vortices (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 2519-2528 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Crossflow influence on steady Görtler vortices is studied in a pressure-driven boundary layer developing along a curved wall. Linear theory shows that crossflow is destabilizing in the long wavelength range. In the non-linear simulations, co-rotating vortices are transformed into counter-rotating vortices for accelerated boundary layers. The streamwise location, where counter-rotating vortices appear, depends on the amplitude of the pressure gradient. Linear studies indicate that a secondary instability may develop on the steady vortex profile. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869369
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