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  • 1
    Electronic Resource
    Electronic Resource
    Capillary Effects on Surface Waves (2000)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 32 (2000), S. 241-274 
    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
    Notes: Abstract We concentrate on the rich effects that surface tension has on free and forced surface waves for linear, nonlinear, and especially strongly nonlinear waves close to or at breaking or their limiting form. These effects are discussed in the context of standing gravity and gravity-capillary waves, Faraday waves, and parasitic capillary waves. Focus is primarily on post-1989 research. Regarding standing waves, new waveforms and the large effect that small capillarity can have are considered. Faraday waves are discussed principally with regard to viscous effects, hysteresis, and limit cycles; nonlinear waveforms of low mode numbers; contact-line effects and surfactants; breaking and subharmonics; and drop ejection. Pattern formation and chaotic and nonlinear dynamics of Faraday waves are mentioned only briefly. Gravity and gravity-capillary wave generation of parasitic capillaries and dissipation are considered at length. We conclude with our view on the direction of future research in these areas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fluid.32.1.241
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  • 2
    Electronic Resource
    Electronic Resource
    Capillary–gravity waves in a surface tension gradient. I: Discontinuous change (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 966-972 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: When waves enter a region covered with a surfactant, the spatial variation of the surface tension causes reflection and refraction of the waves. The simplified inviscid-flow problem of two adjacent half-spaces with different surface tension coefficients is solved analytically for plane waves at oblique incidence. The linearized wave potential is described by a complex contour integral representation for which uniqueness is obtained from the requirement of energy conservation. The reflection is found to be small for some typical cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858640
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  • 3
    Electronic Resource
    Electronic Resource
    Taylor vortices between elliptical cylinders (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2578-2581 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Critical parameters (Reynolds number and wave number) signaling the onset of Taylor vortices are calculated for the flow between "elliptical'' cylinders. The spinning inner cylinder is circular; the stationary outer cylinder is composed of two circular arcs and is similar to an ellipse. It is shown that increasing ellipticity destabilizes the flow and increasing eccentricity stabilizes the flow. The spectral element method is used to calculate the base flow and to solve the linear stability problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858445
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  • 4
    Electronic Resource
    Electronic Resource
    Nonisothermal model of glass fiber drawing stability (1996)
    Springer
    Rheologica acta 35 (1996), S. 584-596 
    Details
    ISSN: 1435-1528
    Keywords: Glass ; Fiber drawing ; draw resonance nonisothermal ; White-Metzner model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Draw resonance is caused by a constant speed winder that leads to non-constant axial forces (Schultz, 1984). The well studied isothermal Newtonian fiber drawing predicts very modest critical draw ratios (around 20, much less than the typical production draw ratios for glass fibers of 103 – 105). The nonisothermal fiber drawing model presented here shows that cooling along the spin line strongly stabilizes the process. However, we show that the conclusion of Shah and Pearson (1972a,b) that non-isothermal Newtonian fiber spinning is unconditionally stable is based on non-converged numerical results. The choice of viscosity-temperature correlation function has a strong influence in determining the stability of the process. While viscoelasticity generally has an adverse effect on the stability, low viscoelasticity in the presence of extensional thinning helps to slightly improve the maximum critical draw ratio.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396509
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  • 5
    Electronic Resource
    Electronic Resource
    A singular finite element for Stokes flow: The stick-slip problem (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1353-1367 
    Details
    ISSN: 0271-2091
    Keywords: Singular finite elements ; Stokes flow ; Stress singularity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abrupt changes in boundary conditions in viscous flow problems give rise to stress singularities. Ordinary finite element methods account effectively for the global solution but perform poorly near the singularity. In this paper we develop singular finite elements, similar in principle to the crack tip elements used in fracture mechanics, to improve the solution accuracy in the vicinity of the singular point and to speed up the rate of convergence. These special elements surround the singular point, and the corresponding field shape functions embody the form of the singularity. Because the pressure is singular, there is no pressure node at the singular point. The method performs well when applied to the stick-slip problem and gives more accurate results than those from refined ordinary finite element meshes.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091105
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  • 6
    Electronic Resource
    Electronic Resource
    Singular finite elements for the sudden-expansion and the die-swell problems (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 357-372 
    Details
    ISSN: 0271-2091
    Keywords: Singular finite elements ; Die swell ; Sudden expansion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The singular finite element method is used to solve the sudden-expansion and the die-swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The method requires minor modifications to standard finite element schemes, and even coarse meshes give more accurate results than refined ordinary finite element meshes. Improved normal stress results for the sudden-expansion problem have been obtained for various Reynolds numbers up to 100 using the singular elements constructed for the creeping flow problem. In addition, the normal stresses at the walls appear to be insensitive to the singularity powers used in the construction of the singular basis functions. The die-swell problem is solved using the singular elements constructed for the stick-slip problem. The singular elements accelerate the convergence of the free surface dramatically.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100402
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  • 7
    Electronic Resource
    Electronic Resource
    Three-dimensional desingularized boundary integral methods for potential problems (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 785-803 
    Details
    ISSN: 0271-2091
    Keywords: Boundary integrals ; Potential problems ; Three-dimensional waves ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The concept of desingularization in three-dimensional boundary integral computations is re-examined. The boundary integral equation is desingularized by moving the singular points away from the boundary and outside the problem domain. We show that the desingularization gives better solutions to several problems. As a result of desingularization, the surface integrals can be evaluated by simpler techniques, speeding up the computation. The effects of the desingularization distance on the solution and the condition of the resulting system of algebraic equations are studied for both direct and indirect versions of the boundary integral method. Computations show that a broad range of desingularization distances gives accurate solutions with significant savings in the computation time. The desingularization distance must be carefully linked to the mesh size to avoid problems with uniqueness and ill-conditioning. As an example, the desingularized indirect approach is tested on unsteady non-linear three-dimensional gravity waves generated by a moving submerged disturbance; minimal computational difficulties are encountered at the truncated boundary.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120807
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  • 8
    Electronic Resource
    Electronic Resource
    Numerical computations of two-dimensional solitary waves generated by moving disturbances (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 905-920 
    Details
    ISSN: 0271-2091
    Keywords: Solitary waves ; Korteweg-de Vries equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional solitary waves generated by disturbances moving near the critical speed in shallow water are computed by a time-stepping procedure combined with a desingularized boundary integral method for irrotational flow. The fully non-linear kinematic and dynamic free-surface boundary conditions and the exact rigid body surface condition are employed. Three types of moving disturbances are considered: a pressure on the free surface, a change in bottom topography and a submerged cylinder. The results for the free surface pressure are compared to the results computed using a lower-dimensional model, i.e. the forced Korteweg-de Vries (fKdV) equation. The fully non-linear model predicts the upstream runaway solitons for all three types of disturbances moving near the critical speed. The predictions agree with those by the fKdV equation for a weak pressure disturbance. For a strong disturbance, the fully non-linear model predicts larger solitons than the fKdV equation. The fully non-linear calculations show that a free surface pressure generates significantly larger waves than that for a bottom bump with an identical non-dimensional forcing function in the fKdV equation. These waves can be very steep and break either upstream or downstream of the disturbance.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650171006
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