Comparison of regularizations of vortex sheet motion

Nitsche, Monika; Taylor, Mark A.; Krasny, Robert

doi:10.1016/b978-008044046-0.50259-1

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Here, we use a split method in time in which advection is treated using a semi-Lagrangian scheme, diffusion is treated with a three-level Crank-Nicholson method, and all finite difference and interpolation approximations are of fourth order. The method uses ideas from several previous works, including Staniforth & Côté (1991), E & Liu (1996), Johnston & Krasny (2002), Luchini & Tognaccini (2002), Seaid (2002) and Nitsche, Taylor & Krasny (2003). It is of second order for the present highly singular flow.…”

Section: Introductionmentioning

confidence: 98%

Scaling behaviour in impulsively started viscous flow past a finite flat plate

Nitsche

2014

J. Fluid Mech.

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Viscous flow past a finite flat plate which is impulsively started in the direction normal to itself is studied numerically using a high-order mixed finite-difference and semi-Lagrangian scheme. The goal is to resolve the details of the vorticity generation, and to determine the dependence of the flow on time and Reynolds number. Vorticity contours, streaklines and streamlines are presented for a range of times t ∈ [0.0002, 5] and Reynolds numbers Re ∈ [250, 2000], non-dimensionalized with respect to the driving velocity and the plate length. At early times, the starting vortex is small relative to the plate length and is expected to grow as if an external length scale were absent. We identify three different types of scaling behaviours consistent with this premise. (i) At early times, solutions with different values of Re are identical up to rescaling. (ii) The solution for fixed Re satisfies a viscous similarity law in time, locally in space, as illustrated by the core vorticity maximum, the upstream boundary layer thickness, and the maximum speed, in three different regions of the flow. (iii) The vortex core trajectory and the shed circulation satisfy inviscid scaling laws for several decades in time, and are consequently essentially Re-independent at these times. In addition, the computed induced drag and tangential forces are found to follow approximate scaling laws that define their dependence on time and Re.

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Section: Introductionmentioning

confidence: 98%

Scaling behaviour in impulsively started viscous flow past a finite flat plate

Nitsche

2014

J. Fluid Mech.

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“…But prior to our work the mathematically rigorous construction of algebraic spiral flows was unsuccessful; see [12,19,23] for various attempts and insights. Even numerical approximation is notoriously difficult and unstable [13,20,21,22]. Since our initial data is self-similar, one would expect self-similar solutions as well, and indeed [11] show: Remark 2.…”

Section: Main Results Theorem ([11]) Consider the 2d Incompressible Ementioning

confidence: 91%

Algebraic spiral solutions of the 2d incompressible Euler equations

Elling

2016

Bull Braz Math Soc, New Series

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We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The regions of positive and negative vorticity form algebraic spirals. Main result Theorem ([11]). Consider the 2d incompressible Euler equationswith self-similar initial data (see Fig. 1 where ω = ∇ × v is vorticity and (r, θ) are polar coordinates centered in x = 0. Given > 0 and μ ∈ ] 2 3 , ∞[, there is an N 0 ∈ N so that a weak solution of (1) and (3) exists for all initial dataω satisfying the following conditions:1. Sufficiently high symmetry:ω is 2π N -periodic for N ≥ N 0 . Dominant sign: the Fourier coefficients satisfy

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Large-amplitude membrane flutter in inviscid flow

Mavroyiakoumou

Alben

2020

J. Fluid Mech.

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We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in 2D inviscid fluid flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free, the membranes flutter with very small amplitudes and high spatial and temporal frequencies at small mass density. As mass density increases, the membranes transition to periodic and then increasingly aperiodic motions, and the amplitudes increase and spatial and temporal frequencies decrease. With both edges free, the membranes flutter similarly to the fixedfree case but also translate vertically with steady, periodic, or aperiodic trajectories, and with nonzero slopes that lead to small angles of attack with respect to the oncoming

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Comparison of regularizations of vortex sheet motion

Cited by 6 publications

References 14 publications

Scaling behaviour in impulsively started viscous flow past a finite flat plate

Scaling behaviour in impulsively started viscous flow past a finite flat plate

Algebraic spiral solutions of the 2d incompressible Euler equations

Large-amplitude membrane flutter in inviscid flow

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