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Browsing School of Mathematics and Statistics · Te Kura Mātai Tatauranga by Author "Harper, J F"

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Browsing School of Mathematics and Statistics · Te Kura Mātai Tatauranga by Author "Harper, J F"

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  • The Axisymmetric Prandtl-Batchelor Eddy Behind a Circular Disc in a Uniform Stream 
    Harper, J F (Victoria University of Wellington, 1998)
    Analytical support is given to Fornberg's numerical evidence that the steady axially symmetric flow of a uniform stream past a bluff body has a wake eddy which tends towards a large Hill's spherical vortex as the Reynolds ...
  • Bubble Rise in a Liquid With a Surfactant Gas, in Particular Carbon Dioxide 
    Harper, J F (Victoria University of Wellington, 2007)
    When a gas bubble rises in a surfactant solution, the velocity field and the distribution of surfactant affect each other. This paper gives the theory for small Reynolds and internal Peclet numbers if the surfactant is ...
  • A Bubble Rising in Viscous Fluid: Lagrange's Equations For Motion at a High Reynolds Number 
    Harper, J F (Victoria University of Wellington, 2001)
    A gas bubble rising steadily in a pure liquid otherwise at rest at a moderate Weber number is, to a good approximation, of oblate spheroidal shape. Previous analytical calculations of that shape at high Reynolds numbers ...
  • Bubbles Rising in Line: Why is the First Approximation So Bad? 
    Harper, J F (Victoria University of Wellington, 1997)
    An analytical theory is given for the viscous wake behind a spherical bubble rising steadily in a pure liquid at high Reynolds number, and for that wake's effect on the motion of a second bubble rising underneath the first. ...
  • The Coulomb Potential of a Line of Charges 
    Harper, J F (Victoria University of Wellington, 1993)
    Recently Lekner gave formulae for the total Coulomb force and potential on a charged particle due to a line of other charged particles, and showed how to use it for a regular array of charges in two or three dimensions. ...
  • Fortran 95 for Fortran 77 Users 
    Harper, J F (Victoria University of Wellington, 2007)
    For 50 years Fortran has been a computer language used mainly by engineers and scientists (but by few computer scientists), mainly for numerical work. Five versions were standardised and are commonly referred to as f66, ...
  • Growing Bubbles Rising in Line 
    Harper, J F (Victoria University of Wellington, 2001)
    Over many years the author and others have given theories for bubbles rising in line in a liquid. Theory has usually suggested that the bubbles will tend towards a stable distance apart, but experiments have often showed ...
  • Reducing Parabolic Partial Differential Equations to Canonical Form 
    Harper, J F (Victoria University of Wellington, 1994)
    A simple method of reducing a parabolic partial differential equation to canonical form if it has only one term involving second derivatives is the following: find the general solution of the first-order equation obtained ...
  • Stagnant-Cap Bubbles With Both Diffusion and Adsorption Rate-Determining 
    Harper, J F (Victoria University of Wellington, 2004)
    When a gas bubble rises in an impure liquid, its surface often has an upper spherical cap with negligible shear stress, a lower spherical cap with negligible tangential velocity, and a very small transition region between ...
  • What Really is a Continuous Function? 
    Harper, J F (Victoria University of Wellington, 2007)
    There are surprisingly many essentially different definitions of continuity even of a real function of one real variable. This paper shows that the definitions in various textbooks published from 1893 to 1992 have some ...

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