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  • 1
    Electronic Resource
    Electronic Resource
    Evidence for solitary wave behavior in Marangoni–Bénard convection (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 921-926 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recent studies have elucidated the possibility of solitary wave behavior in Marangoni–Bénard instability flows. The present paper takes a look at experiments in both heat-transfer- and mass-transfer-driven Marangoni systems to discern nonlinear behavior of the type associated with solitary wave interactions. Direct observation of phase shifts incurred by two Marangoni waves having undergone a head-on collision are reported. Analysis of experiments exhibiting wave reflection at a solid wall and obliquely interacting waves in Marangoni instability flows also show remarkable similarities with nonlinear behavior in Korteweg–de Vries systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858272
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  • 2
    Electronic Resource
    Electronic Resource
    The effect of slab width on the stability of natural convection in confined saturated porous media (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1941-1947 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Stability boundaries separating different states of bimodal convection in a box of saturated porous material with impermeable bounding faces are determined. Two opposing vertical end walls are always insulated, while the thermal conditions on the other set of opposing vertical side walls range from insulated to perfectly conducting, as measured by the Biot number based on box height. The temperature difference between the hot lower plate and the cooler upper plate provides the mechanism for instability. The eigenvalue problem for the critical Rayleigh number is solved numerically over a range of box sizes and side-wall heat transfer conditions. For small values of the distance H2 between conducting side walls, agreement with previous asymptotic analysis is obtained. New results for boxes with planform dimensions both comparable to the box height show the existence of isolated regions rich in bimodal structure. These islands are separated by broad regions having modal properties identical to those found for conducting side walls in the limit H2→0. The numerical results for O(1) box dimensions continue to exhibit the stabilizing effect of side-wall heat transfer as previously observed for thin slabs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866208
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  • 3
    Electronic Resource
    Electronic Resource
    Stokes drag on hollow cylinders and conglomerates (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 3921-3934 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An experimental study of the drag on hollow cylinders and conglomerates falling in a viscous fluid under Stokes flow conditions is described. The experiments were carried out in a tank of square cross section using silicone oil as the Newtonian fluid. Settling velocities of the free falling objects were measured and corrected to conditions of zero Reynolds number flow in an unbounded fluid. The results reveal that all objects tested have Stokes settling velocities smaller than that of a sphere of equal mass and volume. Measurements are reported in terms of the settling speed ratio defined as the ratio of the Stokes settling speed to that of a sphere of equal mass and volume. For the hollow cylinders two parameters are varied: the aspect ratio (length to outside diameter) and the radius ratio (inner to outer radius). Measurements show that the settling speed ratio decreases markedly as the hollowness of the cylinder increases. Each fixed radius ratio data set exhibits a maximum settling speed ratio near an aspect ratio of 1.65. For conglomerates composed of n spheres two trends appear: one for planar configurations and the other for globular clusters. Experimental data for two spheres and three spheres in point contact are in good agreement with recent theoretical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865732
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  • 4
    Electronic Resource
    Electronic Resource
    Blasius boundary layer flow over an irregular leading edge (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 1470-1472 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Uniform flow over a flat plate with an irregular leading edge is investigated. A similarity reduction to Blasius's equation for the three-dimensional flow is obtained in the context of boundary layer theory. Now, however, the similarity variable is y/Δ(x,z), where x is the streamwise coordinate, y is the plate-normal coordinate, z is the spanwise coordinate, and Δ(x,z) is the planform distribution function which takes into account the position of the irregular leading edge. The wall shear stress and also the boundary layer, displacement, and momentum thicknesses are proportional to this common distribution function. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869268
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  • 5
    Electronic Resource
    Electronic Resource
    On the linear stability of cellular spiral Couette flow (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1188-1200 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stability of flow in an annulus capped at both ends and bounded by a fixed outer cylinder and a spiraling inner rod is determined in the context of linear theory. For infinite aspect ratio and constant fluid properties the problem is governed by a Taylor number Ta, an axial Reynolds number Re, and the radius ratio η. Linear stability is tested with respect to both axisymmetric (n=0) and nonaxisymmetric (n≠0) disturbances for η=0.2, 0.4, 0.6, 0.8 over the range 0≤Re≤2000. The evolution of axial wave number, axial phase speed, and spiral inclination angle with increasing Re at each η through all mode transitions to an asymptotic state n=N is reported. It is found that N=2, 4, 7, 19 for η=0.2, 0.4, 0.6, 0.8, respectively, and that the asymptotic state is reached at Re(approximately-equal-to)2000 for all radius ratios. The asymptotic state is characterized by critical Taylor numbers and frequencies that approach constant values while critical wave numbers fall off as Re−1. In this same limit the counter-rotating vortex pairs align themselves axially within the annulus. A conjecture is made on the influence of η on stability in the high Reynolds number limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858604
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  • 6
    Electronic Resource
    Electronic Resource
    Local vortex pairing in a free shear layer (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 3804-3806 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The evolution of large scale vortices as coherent structures in a free shear layer and the corresponding energetics in Fourier space are investigated numerically. The results confirm that vortex pairing as a result of selective energy transfer directly to the subharmonic is a rare event when other instability modes are present with random phases. For this naturally perturbed shear flow, vortices are observed to coalesce locally and intermittently in a manner that leaves isolated vortices between paired states. The spatial and temporal intermittency results in a gradual energy transfer from the linearly unstable mode to larger length scales.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866848
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  • 7
    Electronic Resource
    Electronic Resource
    The influence of side wall heat transfer on convection in a confined saturated porous medium (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 349-355 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effect of side wall heat transfer on the stability of natural convection in a vertically oriented finite slab of saturated porous material is considered. All six bounding faces are impermeable. A temperature contrast between the top and bottom horizontal surfaces provides the mechanism for destabilization. The narrow vertical end walls are perfectly insulated. The thermal conditions on the broad vertical side walls range from perfectly insulating to fully conducting as determined by the value of B, the Biot number based on slab height. An asymptotic analysis of the general solution is made in the narrow gap limit ε(very-much-less-than)1, where ε is the cross-slab width-to-height ratio. In this case the relevant heat transfer variable is B¯=εB, the Biot number based on the narrow slab width. In the limit ε → 0 when B¯=O(1), including the case B¯→∞ that corresponds to a linear side wall temperature profile, tall, vertical, three-dimensional, finger-like cells are found at the critical Rayleigh number Rc=π2/ε2. In the limit B¯ → 0 corresponding to perfect insulation, one obtains two-dimensional, O(1) aspect ratio rolls with axes normal to the side walls at the critical value Rc=4π2. These two-dimensional rolls predominate only for B¯=O(ε2), and transition to tall narrow three-dimensional cells occurs when O(ε2)(very-much-less-than) B (very-much-less-than) O(1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865718
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  • 8
    Electronic Resource
    Electronic Resource
    Instability of natural convection in a tall vertical annulus (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 776-787 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An experimental study has been made of the hydrodynamic stability of viscous fluid flow contained between the differentially heated walls of a tall vertical annulus. Tests were conducted using different glycerol solutions spanning a range of Rayleigh numbers (104–106) and moderately high Prandtl numbers (15–150) for a height/gap ratio of 64 and a radius ratio equal to 0.62. Visualization studies show that the unstable flow consists of two separate progressive wave systems, one ascending the hot inner wall and the other descending the cold outer wall. The approximate Rayleigh number, phase speed, and wavelength at the onset of instability for each wave system were determined for several Prandtl numbers. The regular wave patterns observed near the stability boundary persist over only a very limited range of supercritical Rayleigh numbers above which flow dislocations set in. At higher Rayleigh numbers these random dislocations appear in increasing numbers and ultimately render the flow turbulent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865045
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  • 9
    Electronic Resource
    Electronic Resource
    On the instability of inviscid, rigidly rotating immiscible fluids in zero gravity (1997)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 48 (1997), S. 921-950 
    Details
    ISSN: 1420-9039
    Keywords: Key words. Instability, rotating flow, surface tension.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. The linear stability of an axisymmetric rotating two-fluid column in zero gravity is investigated. The inner core fluid of radius a and density $\rho_1$ is surrounded by fluid of density $\rho_2$ itself bounded by an outer impermeable cylinder of radius b. The surface tension coefficient at the immiscible interface is $\gamma$ . The parameters governing instability are the density ratio $\lambda = \rho _1/ \rho _2$ , the radius ratio $\kappa = b/a$ and the generalized Hocking parameter $L_i = \gamma / \rho _i\Omega^2 a^3$ . While the necessary and sufficient condition for stability $L_2 \le (1 - \lambda )$ is known, the preferred modes and wavenumbers at onset of instability have not been determined over the space of dimensionless parameters. Analytically and numerically determined maximum growth rates and corresponding preferred instability wavelengths for a rotating liquid column show that axisymmetric disturbances are most unstable for $L_1 〉 0.1053$ while planar disturbances determine instability when $L_1 〈 0.1053$ . The rotating two-fluid system bounded by an outer cylinder with statically stable density ratios $0 \le \lambda \le 1$ is unstable only to axisymmetric disturbances. Maximum growth rates and preferred wavelengths are computed as a function of $\lambda$ and $L_2$ at radius ratios $\kappa = 1.2$ and $\kappa = 5.0$ , respectively corresponding to relatively large and relatively small fluid cores. Complete results for the hollow-core vortex $(\lambda = 0)$ and a stationary two-fluid system $(L_2 \to \infty)$ are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000330050073
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  • 10
    Electronic Resource
    Electronic Resource
    New solutions for laminar boundary layers with cross flow (1997)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 48 (1997), S. 341-356 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Boundary layers, cross flow, similarity solutions.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. In some three-dimensional laminar boundary layer problems a coordinate decomposition reduces the governing equations to a primary nonlinear ordinary differential equation describing the streamwise flow in a semi-infinite domain and a secondary linear equation coupled to the primary solution describing the cross flow of infinite spanwise extent. Five new cross-flow problems of this type are investigated within the confines of laminar boundary layer theory. First, the equation for uniform flow transverse to a planar laminar wall jet is found and solved exactly. Second, two solutions for motion transverse to a uniform shear flow along a flat plate are given. A third problem considered is the transverse motion over a flat plate aligned with the uniform mainstream and advancing toward or receding from the mainstream. In the fourth problem, a family of solutions for transverse uniform streams above and below a planar laminar jet is given in closed form. This solution depends on the momentum J of the planar jet and the velocity ratio $\kappa\$ of the transverse streams. The last problem addresses the motion of transverse uniform streams above and below a planar laminar wake. At leading order the cross flow depends only on the velocity ratio $\kappa\$ and not on the drag D produced by the body forming the wake. The influence of the drag first appears at $O(x^{-1} \ln x)$ in the streamwise coordinate expansion of the cross-flow solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000330050035
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