Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

Volume 46, 2019 Volume 45, 2018 Volume 44, 2017 Volume 43, 2016 Volume 42, 2015 Volume 41, 2014 Volume 40, 2013 Volume 39, 2012 Volume 38, 2011 Volume 37, 2010 Volume 36, 2009 Volume 35, 2008 Volume 34, 2007 Volume 33, 2006 Volume 32, 2005 Volume 31, 2004 Volume 30, 2003 Volume 29, 2002 Volume 28, 2001 Volume 27, 2000 Volume 26, 1999 Volume 25, 1998 Volume 24, 1997 Volume 23, 1996 Volume 22, 1995

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v29.i1.30
13 pages

On the Relationship between Fluid Velocity and de Broglie's Wave Function and the Implications to the Navier - Stokes Equation

V. V. Kulish
School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Ave., Singapore, 639798
Jose' L. Lage
Southern Methodist University, Department of Mechanical Engineering, POBox 750337, Dallas, TX 75275-0337, USA


By exploring the relationship between the group velocity of the de Broglie's waves and a particle velocity we can demonstrate the existence of a close relationship between the continuity equation and the Schrodinger's equation. This relationship leads to the proportionality between the fluid velocity v and the corresponding de Broglie's wave's phase at the same location. That is, the existence of a scalar function q proportional to the phase of the de Broglie's wave, such that v = Сq can be proven without reference to the flow being inviscid. We then proceed to show that the Navier-Stokes equation in the case of constant viscosity incompressible fluid is equivalent to a reaction-diffusion equation for the wave function of the de Broglie's wave associated to the moving fluid element. A general solution to this equation, written in terms of the Green's functions, and the criterion for the solution to be stable is presented. Finally, in order to provide an example, the procedure is applied to obtain the solution for the simplest case of the Burgers' equation.

Articles with similar content:

Effect of Viscous Dissipation on the Darcy Forced-Convection Flow Past a Plane Surface
Journal of Porous Media, Vol.6, 2003, issue 2
Ioan Pop, B. Keller, E. Magyari
Steering a Solid body in a Resistive Medium to a Terminal Set
Journal of Automation and Information Sciences, Vol.28, 1996, issue 5-6
Dmitriy V. Lebedev
The Investigation of the Stressed-Deformed State of the Compound Rotation Body with Controlled Pressure in the Contact Part
Journal of Automation and Information Sciences, Vol.33, 2001, issue 1
Olga A. Marchenko
Games With Polynomials
Journal of Automation and Information Sciences, Vol.29, 1997, issue 2-3
Nikolay N. Petrov, E. A. Protasova
Heat Transfer Research, Vol.31, 2000, issue 5
V. I. Mikhin