On the Lamb vector and the hydrodynamic charge

Rousseaux, Germain; Seifer, Shahar; Steinberg, Victor; Wiebel, Alexander

doi:10.1007/s00348-006-0238-2

Cited by 22 publications

(17 citation statements)

References 19 publications

(21 reference statements)

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“…. This is slightly different from the variant of that formal analogy discussed previously in Marmanis (1998) and pursued in fluid experiments by Rousseaux, Seifer, Steinberg & Wiebel (2007). For completeness, we list the comparison in Table 1 Marmanis (1998), the current Maxwellhydrodynamics analogy distinguishes between (E, B) and (D, H).…”

Section: The Evolution Of D For the Incompressible Euler Equationsmentioning

confidence: 91%

“…The evolution of D is of interest : its divergence, for example, plays a role in the production of jet-noise in compressible flows, wherever the mean of div D = 0. For recent discussions of the utility of the this vector as a diagnostic in fluid dynamics or as an important source of jet noise, see Rousseaux, Seifer, Steinberg & Wiebel (2007), Hamman, Klewick & Kirby (2008) and Cabana, Fortuné & Jordan (2008), respectively. In the incompressible case, existence of solutions is assured provided the Beale, Kato, Majda (1984) condition is fulfilled.…”

Section: Transport Equations For the Curl And Divergence Of The Lamb mentioning

confidence: 99%

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Stretching and folding diagnostics in solutions three-dimensional Euler and Navier–Stokes equations

Gibbon¹,

Holm²

2012

Mathematical Aspects of Fluid Mechanics

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Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vorticity (q = ω · ∇θ) associated with solutions of the three-dimensional Euler and Navier-Stokes equations. The vector B = ∇q × ∇θ satisfies the same type of stretching and folding equation as that for the vorticity field ω in the incompressible Euler equations (Gibbon & Holm, 2010). The quantity θ may be chosen as the potential temperature for the stratified, rotating Euler/Navier-Stokes equations, or it may play the role of a seeded passive scalar for the Euler equations alone. The first discussion of these S&F-flow diagnostics concerns a numerical test for Euler codes and also includes a connection with the two-dimensional surface quasi-geostrophic equations. The second S&F-flow diagnostic concerns the evolution of the Lamb vector D = ω × u, which is the nonlinearity for Euler's equations apart from the pressure. The curl of the Lamb vector (̟ := curl D) turns out to possess similar stretching and folding properties to that of the B-vector.

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Section: The Evolution Of D For the Incompressible Euler Equationsmentioning

confidence: 91%

Section: Transport Equations For the Curl And Divergence Of The Lamb mentioning

confidence: 99%

Stretching and folding diagnostics in solutions three-dimensional Euler and Navier–Stokes equations

Gibbon¹,

Holm²

2012

Mathematical Aspects of Fluid Mechanics

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“…Analysis of the Lamb vector has already been shown to be useful for the detection of vortex cores (Rousseaux et al 2005) and regions of shear in axisymmetric swirling flows in jets (Kollmann and Umont 2004).…”

Section: Interpretations and Scalar Fields Derived From The Lamb Vectormentioning

confidence: 98%

“…As pointed out in Rousseaux et al (2005), these components are governed by separate parts of the momentum equation…”

Section: Interpretations and Scalar Fields Derived From The Lamb Vectormentioning

confidence: 98%

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CFD visualisation: challenges of complex 3D and 4D data fields

Mallinson

2008

International Journal of Computational Fluid Dynamics

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A review of CFD visualisation methods together with policy statements by visualisation experts conclude that the visualisation of complex 3D and 4D CFD data fields is still a major research challenge. Potential methodologies are discussed and it is suggested that a suitable approach and target for research is to understand how derived scalar and vector fields, such as dual stream functions and the Lamb vector, relate to the structure and physical characteristics of a flow. A particular focus is to use these fields to generate 'structural' stream functions with isosurfaces that divide the flow into self contained regions.

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