scholarly journals von Kármán–Howarth equation for three-dimensional two-fluid plasmas

2016 ◽  
Vol 93 (6) ◽  
Author(s):  
N. Andrés ◽  
P. D. Mininni ◽  
P. Dmitruk ◽  
D. O. Gómez
Keyword(s):  
Three Dimensional ◽  
Von Karman ◽  
Von Kármán ◽  
Two Fluid

Instabilities of the von Kármán Boundary Layer

2015 ◽  
Vol 67 (3) ◽  
Author(s):  
R. J. Lingwood ◽  
P. Henrik Alfredsson
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Direct Numerical Simulations ◽  
Layer Model ◽  
Complex Flow ◽  
Von Karman ◽  
Dimensional Boundary ◽  
Flow Configurations ◽  
Von Kármán

Research on the von Kármán boundary layer extends back almost 100 years but remains a topic of active study, which continues to reveal new results; it is only now that fully nonlinear direct numerical simulations (DNS) have been conducted of the flow to compare with theoretical and experimental results. The von Kármán boundary layer, or rotating-disk boundary layer, provides, in some senses, a simple three-dimensional boundary-layer model with which to compare other more complex flow configurations but we will show that in fact the rotating-disk boundary layer itself exhibits a wealth of complex instability behaviors that are not yet fully understood.

scholarly journals The Föppl-von Kármán equations for plates with incompatible strains

2010 ◽  
Vol 467 (2126) ◽  
pp. 402-426 ◽  
Author(s):  
Marta Lewicka ◽  
L. Mahadevan ◽  
Mohammad Reza Pakzad
Keyword(s):  
Three Dimensional ◽  
Active Materials ◽  
Von Karman ◽  
Solvent Absorption ◽  
Von Kármán Equations ◽  
Residual Strains ◽  
Rigorous Bounds ◽  
Low Dimensional ◽  
Von Kármán ◽  
Recent Formulation

We provide a derivation of the Föppl-von Kármán equations for the shape of and stresses in an elastic plate with incompatible or residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the three-dimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive other low-dimensional descriptions of active materials with complex non-Euclidean geometries.

scholarly journals An Observational Study of Vortex Spacing in Island Wake Vortex Streets

2006 ◽  
Vol 134 (8) ◽  
pp. 2285-2294 ◽  
Author(s):  
George S. Young ◽  
Jonathan Zawislak
Keyword(s):  
Aspect Ratio ◽  
Bluff Body ◽  
Three Dimensional ◽  
Width Ratio ◽  
Bluff Bodies ◽  
Von Karman ◽  
Vortex Streets ◽  
Moderate Resolution Imaging Spectroradiometer ◽  
Island Wake ◽  
Von Kármán

Abstract Vortex streets are a frequent occurrence in stratocumulus-topped flow downwind of mountainous islands. Theoretical studies dating back to von Kármán, supported by laboratory and numerical studies, have yielded similarity theories for the size and spacing of these vortices behind bluff bodies. Despite dynamical differences between such two-dimensional flows and the three-dimensional flow past isolated islands, satellite case studies suggest these geometric similarities may also hold for the atmospheric case. In this study, two of the resulting dimensionless ratios are measured using satellite imagery. One is the aspect ratio between cross-street and along-street spacing of the vortices. The second is the ratio of the cross-street spacing to the crosswind width of the island. A 30-image sample from the Aqua and Terra Moderate Resolution Imaging Spectroradiometer satellites is analyzed to obtain these ratios. The resulting set of values for the two dimensionless ratios is tested against the values found in bluff body studies. The aspect ratio is tested against the value of 0.28 resulting from von Kármán’s inviscid theory, and the dimensionless width ratio is tested against the value of 1.2 from Tyler’s laboratory study of flow around a bluff body. It is found that atmospheric vortex streets do indeed follow the geometric similarity theories, but with different values for the two ratios than those predicted by von Kármán and Tyler. The aspect ratio is larger than predicted as is the dimensionless width ratio. Both differences are consistent with the turbulent diffusion of vorticity in the wake of the island. The vortex streets more closely follow inviscid theory close to the island, with vortex expansion taking place a few vortex diameters downwind of the island.

scholarly journals Three-dimensional instabilities of a stratified cylinder wake

2014 ◽  
Vol 759 ◽  
pp. 149-180 ◽  
Author(s):  
M. Bosco ◽  
P. Meunier
Keyword(s):  
Tilt Angle ◽  
Unstable Mode ◽  
Three Dimensional ◽  
Axial Flow ◽  
Cylinder Wake ◽  
Homogeneous Fluid ◽  
Recirculation Bubble ◽  
Von Karman ◽  
Strong Shear ◽  
Von Kármán

AbstractThis paper describes experimentally, numerically and theoretically how the three-dimensional instabilities of a cylinder wake are modified by the presence of a linear density stratification. The first part is focused on the case of a cylinder with a small tilt angle between the cylinder’s axis and the vertical. The classical mode A well-known for a homogeneous fluid is still present. It is more unstable for moderate stratifications but it is stabilized by a strong stratification. The second part treats the case of a moderate tilt angle. For moderate stratifications, a new unstable mode appears, mode S, characterized by undulated layers of strong density gradients and axial flow. These structures correspond to Kelvin–Helmholtz billows created by the strong shear present in the critical layer of each tilted von Kármán vortex. The last two parts deal with the case of a strongly tilted cylinder. For a weak stratification, an instability (mode RT) appears far from the cylinder, due to the overturning of the isopycnals by the von Kármán vortices. For a strong stratification, a short wavelength unstable mode (mode L) appears, even in the absence of von Kármán vortices. It is probably due to the strong shear created by the lee waves upstream of a secondary recirculation bubble. A map of the four different unstable modes is established in terms of the three parameters of the study: the Reynolds number, the Froude number (characterizing the stratification) and the tilt angle.

Low-Reynolds-number wakes of elliptical cylinders: from the circular cylinder to the normal flat plate

2014 ◽  
Vol 751 ◽  
pp. 570-600 ◽  
Author(s):  
Mark C. Thompson ◽  
Alexander Radi ◽  
Anirudh Rao ◽  
John Sheridan ◽  
Kerry Hourigan
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Flat Plate ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Near Wake ◽  
Aspect Ratios ◽  
Von Karman ◽  
Von Kármán ◽  
Mode A

AbstractWhile the wake of a circular cylinder and, to a lesser extent, the normal flat plate have been studied in considerable detail, the wakes of elliptic cylinders have not received similar attention. However, the wakes from the first two bodies have considerably different characteristics, in terms of three-dimensional transition modes, and near- and far-wake structure. This paper focuses on elliptic cylinders, which span these two disparate cases. The Strouhal number and drag coefficient variations with Reynolds number are documented for the two-dimensional shedding regime. There are considerable differences from the standard circular cylinder curve. The different three-dimensional transition modes are also examined using Floquet stability analysis based on computed two-dimensional periodic base flows. As the cylinder aspect ratio (major to minor axis) is decreased, mode A is no longer unstable for aspect ratios below 0.25, as the wake deviates further from the standard Bénard–von Kármán state. For still smaller aspect ratios, another three-dimensional quasi-periodic mode becomes unstable, leading to a different transition scenario. Interestingly, for the 0.25 aspect ratio case, mode A restabilises above a Reynolds number of approximately 125, allowing the wake to return to a two-dimensional state, at least in the near wake. For the flat plate, three-dimensional simulations show that the shift in the Strouhal number from the two-dimensional value is gradual with Reynolds number, unlike the situation for the circular cylinder wake once mode A shedding develops. Dynamic mode decomposition is used to characterise the spatially evolving character of the wake as it undergoes transition from the primary Bénard–von Kármán-like near wake into a two-layered wake, through to a secondary Bénard–von Kármán-like wake further downstream, which in turn develops an even longer wavelength unsteadiness. It is also used to examine the differences in the two- and three-dimensional near-wake state, showing the increasing distortion of the two-dimensional rollers as the Reynolds number is increased.

scholarly journals A hierarchy of multilayered plate models

2020 ◽  
Author(s):  
Miguel de Benito Delgado ◽  
Bernd Schmidt
Keyword(s):  
Nonlinear Elasticity ◽  
Curvature Tensor ◽  
Elastic Constants ◽  
Three Dimensional ◽  
Spontaneous Curvature ◽  
Multilayered Plate ◽  
Von Karman ◽  
Plate Models ◽  
Γ Convergence ◽  
Von Kármán

We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of Γ-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary significantly in the small film direction and which also may have a (small) pre-stress. By computing the Γ-limits in the energy regimes in which the scaling of the pre-stress is non-trivial, we arrive at linearised Kirchhoff, von Kármán, and fully linear plate theories, respectively, which contain an additional spontaneous curvature tensor. The effective (homogenised) elastic constants of the plates will turn out to be given in terms of the moments of the pointwise elastic constants of the materials.

scholarly journals Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons

2022 ◽  
Vol 29 (2) ◽  
Author(s):  
Manuel Friedrich ◽  
Lennart Machill
Keyword(s):  
Metric Spaces ◽  
Three Dimensional ◽  
Gradient Flows ◽  
Dimensional Model ◽  
Discrete Approximations ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Von Karman ◽  
Von Kármán ◽  
Appl Math

AbstractWe consider a two-dimensional model of viscoelastic von Kármán plates in the Kelvin’s-Voigt’s rheology derived from a three-dimensional model at a finite-strain setting in Friedrich and Kružík (Arch Ration Mech Anal 238: 489–540, 2020). As the width of the plate goes to zero, we perform a dimension-reduction from 2D to 1D and identify an effective one-dimensional model for a viscoelastic ribbon comprising stretching, bending, and twisting both in the elastic and the viscous stress. Our arguments rely on the abstract theory of gradient flows in metric spaces by Sandier and Serfaty (Commun Pure Appl Math 57:1627–1672, 2004) and complement the $$\Gamma $$ Γ -convergence analysis of elastic von Kármán ribbons in Freddi et al. (Meccanica 53:659–670, 2018). Besides convergence of the gradient flows, we also show convergence of associated time-discrete approximations, and we provide a corresponding commutativity result.

Experimental and Theoretical Study of Three-Dimensional Effects on Vertical Wave-in-Deck Forces

2009 ◽  
Author(s):  
Rolf Baarholm
Keyword(s):  
Model Test ◽  
Three Dimensional ◽  
Water Entry ◽  
Scale Model ◽  
Two Dimensional ◽  
Wave Impact ◽  
Dimensional Effects ◽  
Von Karman ◽  
Von Kármán ◽  
Water Exit

In order to validate theory for computing wave-in-deck loads of offshore platforms, a small scale model test campaign of wave impact on an idealized platform deck is performed at Towing Tank no. II at MARINTEK. The main objectives of the tests were to assess three-dimensional effects and to better understand the effect transverse and longitudinal structural members have on the fluid flow. The emphasis in the present paper is to demonstrate the three-dimensional effects. Model tests of the same structure were performed for both two-dimensional and three-dimensional flow conditions. The model test results show that three-dimensional effects significantly reduce the wave-in-deck loads. In particular, for the water exit phase, the vertical force is almost halved due to three-dimensional effects. Two different two-dimensional methods are used to study water impact on the deck: one method is based on a generalization of Wagner’s impact theory while the latter is a simple von Karman approach. Moreover, a three-dimensional correction is introduced. Comparisons show that the Wagner based method yields good results for the water entry phase, but it overestimates the water exit force and underestimates the duration of the wave-in-deck event. The von Karman type approach underestimates the water entry force.

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