Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analyt...
Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analytical results on both exponents and amplitudes of the correlation functions is good. It is shown that a small-scale noise dominates large-scale, long-time (k→0,ω→0) behavior of the system and, as a consequence, no microscopic system of interacting particles described by Burgers equation in the hydrodynamic limit (k→0,ω→0) exists.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
A three‐mode projection of the Navier–Stokes equations for nonlinear perturbations to an elliptical vortex is studied numerically. It is found that, as the Reynolds number increases, the perturbations undergo a sequ...
A three‐mode projection of the Navier–Stokes equations for nonlinear perturbations to an elliptical vortex is studied numerically. It is found that, as the Reynolds number increases, the perturbations undergo a sequence of period doublings leading to chaos according to the Feigenbaum scenario [J. Statis. Phys. 19, 25 (1978); Phys. Lett. 74 A, 375 (1979)].
We discuss an alternative technique to the lattice-gas automata for the study of hydrodynamic properties, namely, we propose to model the lattice gas with a Boltzmann equation. This approach completely eliminates the ...
We discuss an alternative technique to the lattice-gas automata for the study of hydrodynamic properties, namely, we propose to model the lattice gas with a Boltzmann equation. This approach completely eliminates the statistical noise that plagues the usual lattice-gas simulations and therefore permits simulations that demand much less computer time. It is estimated to be more efficient than the lattice-gas automata for intermediate to low Reynolds number R≲100.
Direct numerical simulation techniques are used to study the effect of spontaneous symmetry breaking leading to the phenomenon of large‐scale secondary flow generation by anisotropic small‐scale flow. It is shown th...
Direct numerical simulation techniques are used to study the effect of spontaneous symmetry breaking leading to the phenomenon of large‐scale secondary flow generation by anisotropic small‐scale flow. It is shown that anisotropy is a major factor that determines the ability of the small‐scale flow to generate the inverse energy cascade, that the large‐scale secondary flow is strongly anisotropic—almost unidirectional, and that the helical property of the primary flow is irrelevent. The pairing instability and long‐wave modulation of the subharmonic are important in the process of generation of the large‐scale structure.
A field-theoretic approach, analogous to Kraichnan’s direct-interaction approximation, to the stability theory of complex three-dimensional flows is developed. The long-wavelength stability of a class of Beltrami flo...
A field-theoretic approach, analogous to Kraichnan’s direct-interaction approximation, to the stability theory of complex three-dimensional flows is developed. The long-wavelength stability of a class of Beltrami flows in an unbounded, viscous fluid is considered. We examine two flows in detail, to illustrate the effects of strong isotropy versus strong anisotropy in the basic flow. The effect of the small-scale flow on the long-wavelength perturbations may be interpreted as an effective viscosity. Using diagrammatic techniques, we construct the first-order smoothing and direct-interaction approximations for the perturbation dynamics. It is argued that the effective viscosity for the isotropic flow is always positive, and approaches a value independent of the molecular viscosity in the high-Reynolds-number limit; this flow is thus stable to long-wavelength disturbances. The anisotropic flow has negative effective viscosity for some orientations of the disturbance, and is therefore unstable, when its Reynolds number exceeds √2 .
A theory is presented for Pierrehumbert's three-dimensional short-wave inviscid instability of the simple two-dimensional elliptical flow with velocity field u(x,y,z)=Ω(−Ey,E−1x,0). The fundamental modes, which a...
A theory is presented for Pierrehumbert's three-dimensional short-wave inviscid instability of the simple two-dimensional elliptical flow with velocity field u(x,y,z)=Ω(−Ey,E−1x,0). The fundamental modes, which are also exact solutions of the nonlinear equations, are plane waves whose wave vector rotates elliptically around the z axis with period 2πΩ. The growth rates are the exponents of a matrix Floquet problem, and agree with those calculated by Pierrehumbert.
"This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynami...
详细信息
ISBN:
(数字)9781461211402
ISBN:
(纸本)9780387908199;9781461270201
"This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #;#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #;#2
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