Fluid dynamical Lorentz force law and Poynting theorem—derivation and implications

Scofield, D. F.; Huq, Pablo

doi:10.1088/0169-5983/46/5/055514

Cited by 17 publications

(24 citation statements)

References 40 publications

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“…The diffusion-type equation of the form ∂ t u = ν∇ 2 u predicts that a signal of u propagates at infinite speed, and the Navier-Stokes equation has such a property. This is remarked by Scofield & Huq (2014).…”

Section: Streaky Channel Turbulence and Large Scalesmentioning

confidence: 77%

“…¶ In fluid turbulence, the current conservation is a basic property, hence it is reasonable to introduce a TW field in turbulence. Although the present study of TW-field is motivated by the study of Scofield & Huq (2014), the fluid-dynamic mechanisms formulated here are the present author's own, which are (i) the dynamical mechanism exciting the TW-waves, (ii) existence of a channel supplying energy to TW-field, and (iii) a new dissipation mechanism by a drift current in turbulence field. + The mechanism of energy dissipation of (iii) is introduced by expressing the current flux j in terms of two components: the convection current j c and a new drift current j d :…”

Section: (B) Transient Growth and Bypass Transitionmentioning

confidence: 99%

“…respectively (Appendix B.3;and Jackson (1999), Scofield & Huq (2014)), (See Jackson (1999, §12.10), where T (M) ij = −M ij is used in stead of M ij for the Maxwell stress. ), where w e and g are the energy density and momentum density of TW-field, defined respectively by…”

Section: Equations Of a New Field Of Transverse Waves (Tw-field)mentioning

confidence: 99%

“…In order to represent H 2 of (A.19), it is proposed by analogy with electromagnetism that the excitation H 2 is related to the field strength F 2 by a constitutive relation H 2 = C (4) * F 2 , according to Theorem 1 of Scofield & Huq (2010, 2014, where C (4) is a parameter matrix of fourth order in general. Here, assuming that the matter under consideration is homogeneous and isotropic in the space, we express C (4) by using two parameters µ and ǫ as follows:…”

Section: Appendix A2 Excitation Field and Another Pair Of Maxwell Ementioning

confidence: 99%

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New scenario of turbulence theory and wall-bounded turbulence: theoretical significance

Kambe

2017

Geophysical & Astrophysical Fluid Dynamics

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New general scenario of turbulence theory is proposed and applied to wall-bounded turbulence. This scenario introduces a new field of transverse waves. Significance of the theory rests on a mathematical theorem associated with the fundamental conservation law of fluid current flux, expressed in a form of 4d physical space-time representation, which predicts a system of Maxwell-type equation and supports transverse waves traveling with a phase speed c t . In regard to the streaky wall flows, there exist both dynamical mechanism and energy channel which excite transverse waves and exchange energy between flow field and transverse wave field. In developed state of the wave field, energy is supplied from the flow field to the wave field if wavelengths are sufficiently large. The waves are accompanied with a new mechanism of energy dissipation, i.e. an internal friction analogous to the Ohm's effect. Energy is supplied from the main flow to the wave field, and some part of the energy is dissipated into heat. Thus, there exists a sustaining mechanism, which implies that the streaky structure of wall-bounded turbulence is a dissipative structure.The predictions are consistent with characteristic features of wall turbulence observed in experimental studies, with respect to three points. (i) Existence of traveling waves and their relation to streamwise streaks and streamwise vortices: The traveling waves are characterized by two scales of wavelength λ and damping-length d. (ii) Existence of two large scales (LSM and VLSM) observed in turbulent shear flows: Those are interpreted by the waves amplified with the transient growth mechanism and maintained by interaction with the new transverse wave field. The waves are robust since they have their own energy and momentum. (iii) Enhanced energy dissipation in wavy turbulence. Its bulk rate of energy dissipation takes a form resembling the models of eddy-viscosity, and its coefficient ν D is estimated to be of the order of c t d and much larger than the molecular viscosity.It must be emphasized as a physical theory that no self-contradiction is incurred by the new field introduced. dt ∧ j (2) = 0.(A.14)On the other hand, on a 4-dimensional manifold x µ , one can define a 4-volume form by Frankel (1997, §7.2) for the symbol i J ). * Taking exterior differential of J (3) , we obtainThis vanishing is due to (A.10). This states that the 3-form J (3) is closed. Let us consider a 4-dimensional simply connected region Ω 4 = [t 1 , t 2 ] × V 3 , enclosed by 3-dimensional boundary ∂Ω 4 . Using the current 3-form J (3) = −(ρ (3) + dt ∧ j (2) ), the equation (A.14) can be transformed to ∂Ω 4 J (3) = 0. (A.17) [See Hehl & Obukhov (2003, Part B) for the electrodynamics case].♯ By the generalized Stokes theorem in the differential geometry, the expression (A.17) is transformed to Ω 4 dJ (3) = 0 for an arbitrarily chosen Ω 4 . This is equivalent to (A.16). Having shown the properties (A.16) and (A.17) of the current 3-form J (3) , we recognize the equation (A.17) as the statement that the cur...

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Section: Streaky Channel Turbulence and Large Scalesmentioning

confidence: 77%

Section: (B) Transient Growth and Bypass Transitionmentioning

confidence: 99%

Section: Equations Of a New Field Of Transverse Waves (Tw-field)mentioning

confidence: 99%

Section: Appendix A2 Excitation Field and Another Pair Of Maxwell Ementioning

confidence: 99%

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New scenario of turbulence theory and wall-bounded turbulence: theoretical significance

Kambe

2017

Geophysical & Astrophysical Fluid Dynamics

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“…The analogy between equations of hydrodynamics and electrodynamics is widely discussed for a long time. In particular, there are several attempts to describe the fluid dynamics by the vector fields (analogous to electric and magnetic fields) satisfying the Maxwell-like equations and corresponding second-order wave equation [1][2][3][4][5][6][7][8]. This approach enables the application of useful electrodynamics' relations to the description of fluid behavior.…”

Section: Introductionmentioning

confidence: 99%

Sedeonic equations of ideal fluid

Миронов

Mironov

2017

Journal of Mathematical Physics

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In the present paper we propose the generalized equations for ideal fluid based on space-time algebra of sixteen-component sedeons. It is shown that the dynamics of isentropic fluid can be described by sedeonic first-order wave equation for fluid potentials. The key features of the proposed formalism are illustrated on the problem of the sound waves propagation. We consider the plane wave solution of linearized sedeonic wave equation and derive the second-order relations for the sound potentials analogues to the Pointing theorem in electrodynamics. The generalization of proposed sedeonic equations for the description of viscous fluid is also discussed.

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Field equations for incompressible non-viscous fluids using artificial intelligence

et al. 2021

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Fluid dynamical Lorentz force law and Poynting theorem—derivation and implications

Cited by 17 publications

References 40 publications

New scenario of turbulence theory and wall-bounded turbulence: theoretical significance

New scenario of turbulence theory and wall-bounded turbulence: theoretical significance

Sedeonic equations of ideal fluid

Field equations for incompressible non-viscous fluids using artificial intelligence

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