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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2161-2171 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1206-1210 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The equations which describe a boundary layer on a curved wall in a rotating system are derived and a linear stability analysis of a basic Blasius velocity profile is performed. Rotation can be either stabilizing or destabilizing corresponding to whether a rotation number is negative or positive, respectively. The stability boundaries at different rotation numbers and curves of constant positive growth rates are presented. It is shown that the flow is completely stabilized when the rotation number is ≤−1 in agreement with an inviscid Rayleigh-type analysis. For the cases examined growth rates increase linearly, in the initial phase, with streamwise distance.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1473-1476 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Three-dimensional finite-volume simulations of the spatial development of centrifugally unstable flow in a curved channel have been performed, and compared with detailed hot-wire measurements. Both approaches revealed spatially developing streamwise vortex pairs at the concave wall, which gave rise to regions of alternating negative and positive streamwise perturbation velocities. The computational box size was chosen large enough so that the flow was allowed to naturally select the spanwise wave number. The computed velocity field was found to be in excellent agreement with the experimentally determined one.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 495-501 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical simulations using a finite volume method with primitive variables formulation are presented for a natural convection flow in the Czochralski melt. In the limit of very small Prandtl numbers it is shown that unsteadiness appears in the form of regular oscillations for sufficiently high values of the Rayleigh number. Such regular oscillations are preceded by a multicell motion structure in the melt, with flow separation at the wall. The critical value of the Rayleigh number for the onset of the oscillations is determined by carrying out a series of time dependent calculations.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 451-459 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Linear theory is used to analyze the stability of two-dimensional boundary layer flows to stationary Görtler vortices. The basic flow profiles in the boundary layer are described by the Falkner–Skan similarity solutions. We approach the problem both with local linear theory (with the streamwise position held fixed) and with a streamwise marching technique (to represent the evolution of the inlet disturbance). Comparisons of solutions obtained by the two methods are presented: The results are consistent in showing that adverse pressure gradients are destabilizing, as in the case of Tollmien–Schlichting waves. This is at odds with recent findings by Otto and Denier and underscores the sensitivity of the results to initial conditions. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 655-663 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The onset of two-dimensional convection with strongly temperature-dependent viscosity has been considered for a fluid obeying an Arrhenius law. The critical Rayleigh number Rc and the basic features of the flow field at criticality have been identified based on a linear stability analysis. Convective flow patterns near and beyond criticality have been determined based on a direct numerical simulation. It is shown that, as the Rayleigh number R increases beyond Rc, steady rolls first emerge supercritically and that at sufficiently large values of R there is a secondary Hopf bifurcation corresponding to pulsating cells; the peculiar structure of the flow field in each case has been described.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 2087-2096 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Optimal control theory is used to determine the wall transpiration (unsteady blowing/suction) with zero net mass flux capable of attenuating Tollmien–Schlichting waves in a spatially developing boundary layer. The flow state is determined from the parabolized stability equations, in a linear setting. An appropriate cost functional is introduced and minimized iteratively by the numerical solution of the equations for the state and the dual state, coupled via transfer and optimality conditions. Central to the control is the determination of the wall Green's function expressing the receptivity of the flow to wall inhomogeneities. The optimal wall velocity is obtained in few iterations and a reduction of several orders of magnitude in output disturbance energy is demonstrated, as compared to the uncontrolled case, for control laws operating both over the whole wall length and over a finite strip. Finally, white noise disturbances are applied to the optimal wall velocities already determined, to assess the influence of an imperfectly operating controller on the final result, and to decide on the practical feasibility of the approach. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 502-503 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 41 (1990), S. 313-314 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and computational fluid dynamics 8 (1996), S. 325-347 
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract. The steady primary instability of Görtler vortices developing along a curved Blasius boundary layer subject to spanwise system rotation is analysed through linear and nonlinear approaches, to clarify issues of vortex growth and wavelength selection, and to pave the way to further secondary instability studies. A linear marching stability analysis is carried out for a range of rotation numbers, to yield the (predictable) result that positive rotation, that is rotation in the sense of the basic flow, enhances the vortex development, while negative rotation dampens the vortices. Comparisons are also made with local, nonparallel linear stability results (Zebib and Bottaro, 1993) to demonstrate how the local theory overestimates vortex growth. The linear marching code is then used as a tool to predict wavelength selection of vortices, based on a criterion of maximum linear amplification. Nonlinear finite volume numerical simulations are performed for a series of spanwise wave numbers and rotation numbers. It is shown that energy growths of linear marching solutions coincide with those of nonlinear spatially developing flows up to fairly large disturbance amplitudes. The perturbation energy saturates at some downstream position at a level which seems to be independent of rotation, but that increases with the spanwise wavelength. Nonlinear simulations performed in a long (along the span) cross section, under conditions of random inflow disturbances, demonstrate that: (i) vortices are randomly spaced and at different stages of growth in each cross section; (ii) “upright” vortices are the exception in a universe of irregular structures; (iii) the average nonlinear wavelengths for different inlet random noises are close to those of maximum growth from the linear theory; (iv) perturbation energies decrease initially in a linear filtering phase (which does not depend on rotation, but is a function of the inlet noise distribution) until coherent patches of vorticity near the wall emerge and can be amplified by the instability mechanism; (v) the linear filter represents the receptivity of the flow: any random noise, no matter how strong, organizes itself linearly before subsequent growth can take place; (vi) the Görtler number, by itself, is not sufficient to define the state of development of a vortical flow, but should be coupled to a receptivity parameter; (vii) randomly excited Görtler vortices resemble and scale like coherent structures of turbulent boundary layers.
    Type of Medium: Electronic Resource
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