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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 2375-2395 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A three-dimensional theory of vorticity dynamics on an incompressible viscous and immiscible fluid–fluid interface, or interfacial vorticity dynamics for short, is presented as a counterpart of the vorticity dynamics on an arbitrarily curved rigid wall [J. Fluid Mech. 254, 183 (1993)]. General formulas with arbitrary Reynolds numbers Re are derived for determining (1) how much vorticity exists on an interface S, (2) how much vorticity is created from S and sent into the fluid per unit area in per unit time, and (3) the force and moment acted on a closed interface by the created vorticity thereon. The common feature and fundamental difference between interfacial vorticity dynamics and its rigid-wall counterpart are analyzed. In particular, on a free surface, the primary driving mechanism of vorticity creation is the balance between the shear stress (measured by tangent vorticity) and the tangent components of the surface-deformation stress alone, which results in a weak creation rate of O (Re−1/2) at large Re. Therefore, the exact form of the theory with its full complexity is of importance mainly at low Reynolds numbers, especially in understanding the small-scale coherent structures of interfacial turbulence. The vorticity creation rate at high-Re approximations, including an interfacial boundary layer of finite thickness and the limit of Re→∞ (the so-called Euler limit), is also studied, both allowing for a rotational inviscid outer flow. While for the former this leads to a generalization of Lundgren's theory [in Mathematic Aspects of Vortex Dynamics, edited by R. E. Caflish (SIAM, Philadelphia, PA, 1989), pp. 68–79] and amounts to solving a linear boundary-layer problem, for the latter the creation rate can be directly obtained from an inviscid solution, leading to a dynamic evolution equation of interfacial vortex sheet. In three dimensions, a vortex sheet may bifurcate into a normal vorticity field, upon which the dependence of the sheet velocity is determined. A few examples are examined to illustrate different aspects and approximation levels of the general theory. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 627-635 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In Reynolds-average Navier–Stokes equation it is the divergence of Reynolds stress tensor, i.e., the turbulent force, rather than the tensor itself, is to be simulated and partially modeled. Thus, directly working on turbulent force could bring significant simplification. In this paper a novel exact equation for incompressible turbulent force f is derived: (∂/∂t −ν∇2)f=∇⋅S, where ν is the molecular viscosity and all source terms in tensor S to be modeled are vortical. The dominant mechanism is the advection and stretching (with an opposite sign) of a "pseudo-Lamb vector" by fluctuating velocity field. No coupling with pressure is involved. The equation follows from a study of the mean fluctuating Lamb vector and kinetic energy, which constitute the turbulent force. Both constituents are governed by the same kind of equations as f. This innovative turbulent-force equation is similar to Lighthill's acoustic analogy and naturally calls one's attention to studying the vortical sources of turbulent force. The methodology described here may lead to turbulence models which provide more complete treatment than that of two-equation models, but relatively easier computation than that of second-order closures. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 503-505 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We show that the dissipation rate of a Newtonian fluid with constant shear viscosity has three constituents from dilatation, vorticity, and surface strain. The last one, being associated with the most complicated manners of fluid deformation, only contributes to the change of internal energy but not that of kinetic energy. The distinction of these dissipation constituents is used to identify typical compact flow structures at high Reynolds numbers, such as shock waves, thin vortex layers, and filaments. This identification is of particular interest in studying turbulence structures. We then cast the incompressible version of the simplified kinetic-energy transport equation to a novel form, which is free from the work rate done by surface stresses but in which the full dissipation reenters. This result is of relevance to the physical routes via which turbulent energy is transferred to small scales. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 905-938 
    ISSN: 0271-2091
    Keywords: Dynamic vorticity condition ; Theoretical analysis ; 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 dynamic boundary conditions for vorticity, derived from the incompressible Navier-Stokes equations, are examined from both theoretical and computational points of view. It is found that these conditions can be either local (Neumann type) or global (Dirichlet type), both containing coupling with the boundary pressure, which is the main difficulty in applying vorticity-based methods. An integral formulation is presented to analyse the structure of vorticity and pressure solutions, especially the strength of the coupling. We find that for high-Reynolds-number flows the coupling is weak and, if necessary, can be effectively bypassed by simple iteration. In fact, even a fully decoupled approximation is well applicable for most Reynolds numbers of practical interest. The fractional step method turns out to be especially appropriate for implementing the decoupled approximation. Both integral and finite difference methods are tested for some simple cases with known exact solutions. In the integral approach smoothed heat kernels are used to increase the accuracy of numerical quadrature. For the more complicated problem of impulsively started flow over a circular cylinder at Re = 9500 the finite difference method is used. The results are compared against numerical solutions and fine experiments with good agreement. These numerical experiments confirm our thoeretical analysis and show the advantages of the dynamic condition in computing high-Reynolds-number flows.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Book
    Book
    Berlin :Springer,
    Title: Vorticity and vortex dynamics /
    Author: Wu, Jie-Zhi
    Contributer: Ma, Hui-Yang , Zhou, J. Z.
    Edition: 1. Ed.
    Publisher: Berlin :Springer,
    Year of publication: 2006
    Pages: XIV, 776 S.
    ISBN: 3-540-29027-3
    Type of Medium: Book
    Language: English
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