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  • 1
    Electronic Resource
    Electronic Resource
    Flow of a Dusty Gas between Rotating Cylinders (1962)
    [s.l.] : Nature Publishing Group
    Nature 193 (1962), S. 463-464 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] In the experiments, the axes of the cylinders are vertical and there is an axial flow vertically upwards to prevent the dust settling out. The dust particles tend to move along the streamlines of the air, but they have a small downwards velocity relative to the air due to gravity and an outw^ards ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/193463a0
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  • 2
    Electronic Resource
    Electronic Resource
    Vortex Interactions (1979)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 11 (1979), S. 95-121 
    Details
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fl.11.010179.000523
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  • 3
    Electronic Resource
    Electronic Resource
    The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 978-990 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Steady, inviscid, incompressible, two-dimensional flows with vortex patches bounded by vortex sheets (Batchelor flows) are calculated numerically. Two particular cases are considered: the vortex on a plane wall (Sadovskii vortex) and the vortex in a right-angled corner. Nonlinear integral equations are derived for the shape of the bounding vortex sheet which are solved numerically. Two different formulations are employed to check the results. Previous results by Sadovskii [Appl. Math. Mech. 35, 773 (1971)] and Chernyshenko (Royal Aircraft Establishment library translations Report No. 2133, 1983) for specific values of the parameters are confirmed. Only symmetrical solutions are found to exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866718
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  • 4
    Electronic Resource
    Electronic Resource
    The effect of nonzero viscosity ratio on the stability of fingers and bubbles in a Hele–Shaw cell (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 3188-3198 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of a steadily moving bubble or a finger in a Hele–Shaw cell is considered in the case when gravity and the ratio between the viscosities of the less and more viscous fluids are nonzero. The effect of gravity is easily incorporated by a transformation of parameters introduced previously by Saffman and Taylor [Proc. R. Soc. London Ser. A 245, 312 (1958)] for the steady flow, which makes the time-dependent flows with and without gravity equivalent. For the nonzero viscosity ratio, the transformation of parameters introduced by Saffman and Taylor also makes steady finger and bubble flows with nonzero and zero viscosity ratios equivalent. However, for the unsteady case, there is no such equivalence and so a complete calculation is carried out to investigate the effect of the nonzero viscosity ratio on the stability of fingers and bubbles. The incorporation of the finite viscosity ratio is found not to qualitatively alter the linear stability features obtained in earlier work for the zero viscosity ratio, although there are quantitative differences in the growth or decay rate of various modes. For any surface tension, numerical calculation suggests that the McLean–Saffman branch of bubbles [Phys. Fluids 30, 651 (1987)] of arbitrary size is stable, whereas all the other branches are unstable. For a small bubble that is circular, the eigenvalues of the stability operator are found explicitly. The previous analytic theory for the stability of the finger in the limit of zero surface tension is extended to include the case of the finite viscosity ratio. It is found that, as in the case of bubbles, the finite viscosity ratio does not alter qualitatively any of the features obtained previously for the zero viscosity ratio.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866930
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  • 5
    Electronic Resource
    Electronic Resource
    On the Lundgren–Townsend model of turbulent fine scales (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 126-145 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The strained-spiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids 25, 2193 (1982)] is used to calculate vorticity and velocity-derivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rolling-up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity. The numerical values of two dimensionless groups are fixed in order to give a Kolmogorov constant and skewness which are within the range of experiment. This gives the result that the ratio of the ensemble average hyperskewness S2p+1≡ (∂u/∂x)2p+1/[(∂u/∂x)2](2p+1)/2 to the hyperflatness F2p≡(∂u/∂x)2p/[(∂u/∂x)2] p, p=2,3,..., is constant independent of Taylor–Reynolds number Rλ, as is the ratio of the 2pth moment of one component of the vorticity Ω2p≡ω2px/(ω2x)p to F2p. A cutoff in a relevant time integration is then used to eliminate vortex-sheet-induced divergences in the integrals corresponding to ω2px, p=2,3,..., and an assumption is made that the lateral scale of the spiral vortex in the model is the geometric mean of the Taylor and the Kolmogorov microscales. This gives Ω2p=Ωˆ2pRλp/2−3/4, F2p=Fˆ2pRλp/2−3/4 and S2p+1=Sˆ2p+1Rλp/2−3/4, p=2,3,..., with explicit calculation of the numbers Ωˆ2p, Fˆ2p, and Sˆ2p+1. The results of the model are compared with experimental compilation of Van Atta and Antonia [Phys. Fluids 23, 252 (1980)] for F4 and with the isotropic turbulence calculations of Kerr [J. Fluid Mech. 153, 31 (1985)] and of Vincent and Meneguzzi [J. Fluid Mech. 225, 1 (1991)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858798
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  • 6
    Electronic Resource
    Electronic Resource
    The three-dimensional instability of strained vortices in a viscous fluid (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2339-2342 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The recent theory describing 3-D exact solutions of the Navier–Stokes equations is applied to the problem of stability of 2-D viscous flow with elliptical streamlines. An intrinsically inviscid instability mechanism persists in all such flows provided the length scale of the disturbance is sufficiently large. Evidence is presented that this mechanism may be responsible for 3-D instabilities in high Reynolds number flows whose vortex structures can be locally described by elliptical streamlines.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866124
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  • 7
    Electronic Resource
    Electronic Resource
    Stability of bubbles in a Hele–Shaw cell (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2624-2635 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of steadily moving bubbles in a Hele–Shaw cell is investigated. It is shown analytically that without the effect of surface tension, the bubbles are linearly unstable with the stability operator having a continuous spectrum. For small bubbles that are circular, analytical calculations also show that any amount of surface tension stabilizes a bubble. Numerical calculations suggest that the branch of bubble solutions that, in the limit of large area, corresponds to the McLean–Saffman finger is stable for any nonzero surface tension. However, the decay rate of disturbances on the McLean–Saffman branch depends appreciably on the bubble size even for large bubbles. This suggests that the stability results on this branch cannot be immediately extrapolated to the McLean–Saffman fingers. For another branch of bubble solution, which in the limit or large area corresponds to the first of the Romero–Vanden-Broeck finger solutions, numerical evidence suggests that it is unstable to one symmetric and one antisymmetric mode for any surface tension. The symmetric unstable mode tends to break the tip of the bubble and the growth rate of this mode is unaffected by further increase in bubble size, once the bubble is large enough. This suggests that there is an analogous instability for the finger, and this agrees with the numerical findings of Kessler and Levine [Phys. Rev. A 33, 2632 (1986)]. Agreement is noted in the quantitative comparison of the growth rate with the predictions [Tanveer, Phys. Fluids 30, xxxx (1987)] on the limiting growth rate for the symmetric unstable mode for the first Romero–Vanden-Broeck branch of finger solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866106
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  • 8
    Electronic Resource
    Electronic Resource
    Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 1787-1796 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Homogeneous anisotropic turbulence consisting of a collection of straight vortex structures is considered, each with a cylindrically unidirectional, but otherwise arbitrary, internal vorticity field. The orientations of the structures are given by a distribution P of appropriate Euler angles describing the transformation from laboratory to structure-fixed axes. One-dimensional spectra of the velocity components are calculated in terms of P, and the shell-summed energy spectrum. An exact kinematic relation is found in which volume-averaged Reynolds stresses are proportional to the turbulent kinetic energy of the vortex collection times a tensor moment of P. A class of large-eddy simulation models for nonhomogeneous turbulence is proposed based on application of the present results to the calculation of subgrid Reynolds stresses. These are illustrated by the development of a simplified model using a rapid-distortion-like approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868240
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  • 9
    Electronic Resource
    Electronic Resource
    Difficulties with three-dimensional weak solutions for inviscid incompressible flow (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 2373-2375 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The representation of an inviscid three-dimensional incompressible flow by vortex singularities is considered and shown to lead to dynamical inconsistencies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865529
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  • 10
    Electronic Resource
    Electronic Resource
    On the spectrum of a stretched spiral vortex (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 3010-3027 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Corrections are found to the k−5/3 spectrum of Lundgren [Phys. Fluids 25, 2193 (1982)] for a stretched spiral vortex model (a is the stretching strain rate and k the scalar wave number) of turbulent fine scales. These take the form of additional terms arising from the early time evolution, when the stretching of vortex lines is small. For the special case when the spiral takes the form of a rolled-up shear layer, it is shown that the composite spectrum is divergent, thus requiring the introduction of a finite early cutoff time τ1 in the time integral for the nonaxisymmetric contribution. The identity νω2 = 2ν∫0∞k2E(k)dk which gives the dissipation is then satisfied self-consistently. Direct numerical calculation of the energy spectrum from the approximate vorticity field for a special choice of spiral structure nevertheless indicates that the one-term k−5/3-spectrum result is asymptotically valid in the inertial range provided aτ1 is O(1) but that the numerically calculated dissipation spectrum appears to lie somewhere between an exp(−B1k2) and an exp(−B2k) form. It is also shown that the stretched, rolled-up shear-layer model predicts asymptotic shell-summed spectra of the energy dissipation and of the square of the vorticity, each asymptotically constant, with no power-law dependence, for k smaller than the Kolmogorov wave number.The corresponding one-dimensional spectra each show −log(k1) behavior for small k1. The extension of the model given by Pullin and Saffman [Phys. Fluids A 5, 126 (1993)] is reformulated by the introduction of a long-time cutoff in the vortex lifetime and an additional requirement that the vortex structures be approximately space filling. This gives a reduction in the number of model free-parameters but introduces a dependence of the calculated Kolmogorov constant and skewness on the ratio of the initial vortex radius to the equivalent Burgers-vortex radius. A scaling for this ratio in terms of the Taylor microscale Reynolds number is proposed in which the stretching strain is assumed to be provided by the large scales with spatial coherence limited to the maximum stretched length of the structures. Postdictions of the fourth-order flatness factor and of higher moments of the longitudinal velocity gradient statistics are compared with numerical simulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868127
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