EXACT SOLUTION OF NAVIER-STOKES EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRACPAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅱ)

摘要/Abstract

摘要： This work is the continuation of the discussion ofref. [1]. In ref. [1] we applied the theory of functions of a complex variable under Dirac-Pauli representation, introduced the Kaluza "Ghost" coordinate, and turned Navier-Stokes equations ofviscofluid dynamics of homogeneous and incompressible fluid into nonlinear, equation with only a pair of complex unknown functions. In this paper we again combine the complex independent variable except time, and caust it to decrease in a pair to the number of complex independent variables. Lastly, we turn Navier-Stokes equations into classical Burgers equation. The Cole-Hopf transformation join up mth Burgers equation and the diffusion equation is Backlund transformation in fact, and the diffusion equation has the general solution as everyone knows. Thus, we obtain the exact solution of Navier-Stokes equations by Backlund transformation.

关键词: secondary streamwise vortex, boundary layer, transition, direct numerical simulation

Abstract: This work is the continuation of the discussion ofref. [1]. In ref. [1] we applied the theory of functions of a complex variable under Dirac-Pauli representation, introduced the Kaluza "Ghost" coordinate, and turned Navier-Stokes equations ofviscofluid dynamics of homogeneous and incompressible fluid into nonlinear, equation with only a pair of complex unknown functions. In this paper we again combine the complex independent variable except time, and caust it to decrease in a pair to the number of complex independent variables. Lastly, we turn Navier-Stokes equations into classical Burgers equation. The Cole-Hopf transformation join up mth Burgers equation and the diffusion equation is Backlund transformation in fact, and the diffusion equation has the general solution as everyone knows. Thus, we obtain the exact solution of Navier-Stokes equations by Backlund transformation.

Key words: secondary streamwise vortex, boundary layer, transition, direct numerical simulation

沈惠川. EXACT SOLUTION OF NAVIER-STOKES EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRACPAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅱ)[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(6): 557-562.

Shen Hui-chuan. EXACT SOLUTION OF NAVIER-STOKES EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRACPAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅱ)[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(6): 557-562.

参考文献

[1] Shen Hui-chuan,The theory of functions of a complex variable under Dirac-Pauli representation and its application in fluid dynamics(Ⅰ).Appl.Math.Mech.,7,4(1986).
[2] Lapedes.D.N.,McGraw-Hill Encyclopedia of Science and Technology,Quaternions.(4th ed.)McGraw-Hill(1977).
[3] Eddington.A.S.,Fundamental Theory.Cambr.Univ.Press.,London(1953).
[4] Dirac.P.A.M.,The Principle of Quantum Mechanics,Oxford(1958).
[5] Flügge.S.,Practical Quantum Mechanics.Springer-Verlag(1974).
[6] Lapedes.D.N.,McGraw-Hill Encyclopedia of Science and Technology,Cayley-Klein Parameters,McGraw-Hill,4th.ed.(1977).
[7] Klein,F.,Elementary Mathematics from an Advanced Standpoint:Arithmetic,Algebra,Analysis,Tr.from the 3rd German ed.by E.R.Hedrick and A.Nǒble,Dover,n.d.,N.Y.(1924).
[8] Branetz.V.N.and E.B.Shmouglevsky.Application of Quaternion in Orientation Problems of Rigid Body,Science,Moscow(1973).(in Russian).
[9] Fung,Y.C.,A First Course in Continuum Mechanics,(2nd ed)Prentice-Hall,Inc.(1977).
[10] Landau.L.D.and E.M.Lifshitz,Continuum Mechanics,National,Moscow(1954).(in Russian)Landau,L.D.and E.M.Lifshitz,Fluid Mechanics,London(1959).
[11] Yukawa,H.,Fundation of Modern Physics,Vol.1,Classical physics(Ⅰ),Iwanami(1975) (in Japanese).
[12] Prandtl,L.,K.Oswatitsch and K.Wieghardt,Führer durch die Strǒmungslehre,Friedr Vieweg+sohn,Braunschweig(1969).
[13] Oswatitsch,K.,Gas Dynamics,Academic(1956).
[14] Lightill,M.J.,Surveys in Mechanics,Cambr.Univ.Press,London(1956).
[15] Taniuti,T.and K.Nishihara,Nonlinear Waves.Pitman(1983).
[16] Eckhaus,W.and A.Van Harten,The Inverse Scattering Transformation and the Theory of Solitons an Introduction Mathematics Studies 50. North-Holland(1981).
[17] Shen Hui-chuan,The general solution of peristaltic fluid dynamics.Nature Journal,7,10(1984),799;7,12(1984),940. (in Chinese).