Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization

We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and coupling-enhancement are provided. We apply these algorithms to the self-organized synchronization of two coupled Lorenz systems. It is found that after a long-time self-organized process, the two coupled chaotic systems can achieve synchronization with almost minimum required coupling-speed ratio.Comment: 4 pages, 5 figure

Momentum and Heat Transfer in a Laminar Boundary Layer with Slip Flow

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77059/1/AIAA-22968-756.pd

The friction factor of two-dimensional rough-boundary turbulent soap film flows

We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.Comment: 4 pages, 3 figure

Laminar Craya-Curtet jets

This Brief Communication investigates laminar Craya-Curtet flows, formed when a jet with moderately large Reynolds number discharges into a coaxial ducted flow of much larger radius. It is seen that the Craya-Curtet number, C=(J/sub c//J/sub j/)/sup 1/2/, defined as the square root of the ratio of the momentum flux of the coflowing stream to that of the central jet, arises as the single governing parameter when the boundary-layer approximation is used to describe the resulting steady slender jet. The numerical integrations show that for C above a critical value C/sub c/ the resulting streamlines remain aligned with the axis, while for C<C/sub c/ the entrainment demands of the jet cannot be satisfied by the coflow, and a toroidal recirculation region forms. The critical Craya-Curtet number is determined for both uniform and parabolic coflow, yielding C/sub c/=0.65 and C/sub c/=0.77, respectively. The streamlines determined numerically are compared with those obtained experimentally by flow visualizations, yielding good agreement in the resulting flow structure and also in the value of C/sub c

On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers

The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies inversely-linear with the distance along the surface $ (U_e(x) = U_\infty x^{-1}). The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. Then, we examenin detail new exact solutions. The analysis shows that solutions exist only for a lateral suction. For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties of solutions depend onthe suction parameter. Furthermore, making use of the fourth--order Runge--Kutta scheme together with the shooting method, numerical solutions are obtained.Comment: 15 page

Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution

Results on the Prandtl-Blasius type kinetic and thermal boundary layer thicknesses in turbulent Rayleigh-B\'enard convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary layer equations, we calculate the ratio of the thermal and kinetic boundary layer thicknesses, which depends on the Prandtl number Pr only. It is approximated as $0.588Pr^{-1/2}$ for $Pr\ll Pr^*$ and as $0.982 Pr^{-1/3}$ for $Pr^*\ll\Pr$, with $Pr^*= 0.046$. Comparison of the Prandtl--Blasius velocity boundary layer thickness with that evaluated in the direct numerical simulations by Stevens, Verzicco, and Lohse (J. Fluid Mech. 643, 495 (2010)) gives very good agreement. Based on the Prandtl--Blasius type considerations, we derive a lower-bound estimate for the minimum number of the computational mesh nodes, required to conduct accurate numerical simulations of moderately high (boundary layer dominated) turbulent Rayleigh-B\'enard convection, in the thermal and kinetic boundary layers close to bottom and top plates. It is shown that the number of required nodes within each boundary layer depends on Nu and Pr and grows with the Rayleigh number Ra not slower than \sim\Ra^{0.15}. This estimate agrees excellently with empirical results, which were based on the convergence of the Nusselt number in numerical simulations