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  • 1
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    A small-scale turbulence model (1993)
    In:  Other Sources
    Details
    Publication Date: 2011-08-24
    Description: A previously derived analytical model for the small-scale structure of turbulence is reformulated in such a way that the energy spectrum may be computed. The model is an ensemble of two-dimensional (2D) vortices with internal spiral structure, each stretched by an axially symmetric strain flow. Stretching and differential rotation produce an energy cascade to smaller scales in which the stretching represents the effect of instabilities and the spiral structure is the source of dissipation at the end of the cascade. The energy spectrum of the resulting flow may be expressed as a time integration involving only the enstrophy spectrum of the time evolving 2D cross section flow, which may be obtained numerically. Examples are given in which a k exp -5/3 spectrum is obtained by this method. The k exp -5/3 inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the 2D enstrophy spectrum. The results are found to be insensitive to time dependence of the strain rate, including even intermittent on-or-off strains.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids A (ISSN 0899-8213); 5; 6; p. 1472-1483.
    Format: text
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  • 2
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    A small-scale turbulence model (1992)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: A model for the small-scale structure of turbulence is reformulated in such a way that it may be conveniently computed. The model is an ensemble of randomly oriented structured two dimensional vortices stretched by an axially symmetric strain flow. The energy spectrum of the resulting flow may be expressed as a time integral involving only the enstrophy spectrum of the time evolving two-dimensional cross section flow, which may be obtained numerically. Examples are given in which a k(exp -5/3) spectrum is obtained by this method without using large wave number asymptotic analysis. The k(exp -5/3) inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the two-dimensional enstrophy spectrum. The results are insensitive to time dependence of the strain-rate, including even intermittent on-or-off strains.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Stanford Univ., Studying Turbulence Using Numerical Simulation Databases. 4: Proceedings of the 1992 Summer Program; p 5-20
    Format: application/pdf
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  • 3
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    Strained spiral vortex model for turbulent fine structure (1982)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: A model for the intermittent fine structure of high Reynolds number turbulence is proposed. The model consists of slender axially strained spiral vortex solutions of the Navier-Stokes equation. The tightening of the spiral turns by the differential rotation of the induced swirling velocity produces a cascade of velocity fluctuations to smaller scale. The Kolmogorov energy spectrum is a result of this model.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids; 25; Dec. 198
    Format: text
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  • 4
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    Vortex ring bubbles (1991)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: Toroidal bubbles with circulation are studied numerically and by means of a physically motivated model equation. Two series of computations are performed by a boundary-integral method. One set shows the starting motion of an initially spherical bubble as a gravitationally driven liquid jet penetrates through the bubble from below causing a toroidal geometry to develop. The jet becomes broader as surface tension increases and fails to penetrate if surface tension is too large. The dimensionless circulation that develops is not very dependent on the surface tension. The second series of computations starts from a toroidal geometry, with circulation determined from the earlier series, and follows the motion of the rising and spreading vortex ring. Some modifications to the boundary-integral formulation were devised to handle the multiply connected geometry. The computations uncovered some unexpected rapid oscillations of the ring radius. These oscillations and the spreading of the ring are explained by the model equation which provides a more general description of vortex ring bubbles than previously available.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics (ISSN 0022-1120); 224; 177-196
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  • 5
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    Oscillations of drops in zero gravity with weak viscous effects (1988)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: Nonlinear oscillations and other motions of large axially symmetric liquid drops in zero gravity are studied numerically by a boundary-integral method. The effect of small viscosity is included in the computations by retaining first-order viscous terms in the normal stress boundary condition. This is accomplished by making use of a partial solution of the boundary-layer equations which describe the weak vortical surface layer. Small viscosity is found to have a relatively large effect on resonant mode coupling phenomena.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics (ISSN 0022-1120); 194; 479-510
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  • 6
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    A free surface vortex method with weak viscous effects (1989)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: The advantage of vortex methods for inviscid flows of several fluids separated by interfaces is that problems of this kind may be posed and solved numerically entirely on the interface surface. For free surface problems, where one of the fluids has negligible inertia, a small amount of viscosity produces a thin, weak rotational layer adjacent to the potential flow vortex sheet. Here, a method is described for including this weak viscous effect as a modification of the boundary conditions for the potential part of the flow, thus allowing this slightly viscous flow to be formulated as a vortex method on the free surface. This is important for unsupported free drops where the viscosity at the free surface is the only source of damping for oscillations, and for gas-filled bubbles, where it provides both drag and damping. Small applied shear stresses from aerodynamic, electrostatic, or other sources may be included provided they are of the same order as the potential flow shear stress or smaller.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Mathematical Aspects of Vortex Dynamics; Apr 25, 1988 - Apr 27, 1988; Leesburg, VA; United States
    Format: text
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