摘要A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 (a measure of the fluid relaxation) and De2 (a measure of the fluid retardation) appear in the equation. Then we study this generalized Lorenz equation numerically and find that the values of De1 and De2 can greatly influence the behavior of the solution. The fluid relaxation De1 is found to precipitate the onset of periodic solution (limit cycle) in the system and impedes the onset of chaos while the fluid retardation (De2) tends to delay the onset of the periodic solution and precipitate the onset of chaos in the system.
Abstract：A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 (a measure of the fluid relaxation) and De2 (a measure of the fluid retardation) appear in the equation. Then we study this generalized Lorenz equation numerically and find that the values of De1 and De2 can greatly influence the behavior of the solution. The fluid relaxation De1 is found to precipitate the onset of periodic solution (limit cycle) in the system and impedes the onset of chaos while the fluid retardation (De2) tends to delay the onset of the periodic solution and precipitate the onset of chaos in the system.
YANG Fan;ZHU Ke-Qin. Generalized Lorenz Equation Derived from Thermal Convection of Viscoelastic Fluids in a Loop[J]. 中国物理快报, 2010, 27(3): 34601-034601.
YANG Fan, ZHU Ke-Qin. Generalized Lorenz Equation Derived from Thermal Convection of Viscoelastic Fluids in a Loop. Chin. Phys. Lett., 2010, 27(3): 34601-034601.
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130 [2] Saltzman B 1962 J. atmos. Sci. 19 329 [3] Tritton D J 1988 Physical Fluid Dynamics (Oxford: Clarendon) [4] Burroughs E A et al 2005 J. Fluid Mech. 543 203 [5] Rodr\'{\iguez-Bernal A and Vleck E S V 1998 Intl J. Bifurcation Chaos 8 41 [6] Oldroyd J G 1950 Proc. R. Soc. London Ser. A 200 523 [7] Khayat R E 1994 J. Non-Newtonian Fluid Mech. 53 227 [8] Khayat R E 1995 J. Non-Newtonian Fluid Mech. 5 8 331 [9] Li Z and Khayat R E 2005 J. Fluid Mech. 529 221 [10] Bird R B, Armstrong R C and Hassager O 1987 Dynamics of Polymeric Liquids (New York: Wiley) vol 1 [11] Khayat R E 1997 Phys. Rev. Lett. 78 4918 [12] Al-Sawalha M M et al 2008 Chin. Phys. Lett. 25 1217
2010, Vol. 27 
