Damping filter method for obtaining spatially localized solutions

Spatially localized structures are key components of turbulence and other spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not guaranteed. A damping filter method is introduced to obtain variously localized solutions, and adopted into two typical cases. This method introduces a spatially selective damping effect to make a good guess at the exact solution, and we can obtain an exact solution through a continuation with the damping amplitude. First target is a steady solution to Swift-Hohenberg equation, which is a representative of bi-stable systems in which localized solutions coexist, and a model for span-wisely localized cases. Not only solutions belonging to the well-known snaking branches but also those belonging to an isolated branch known as "isolas" are found with a continuation paths between them in phase space extended with the damping amplitude. This indicates that this spatially selective excitation mechanism has an advantage in searching spatially localized solutions. Second target is a spatially localized traveling-wave solution to Kuramoto-Sivashinsky equation, which is a model for stream-wisely localized cases. Since the spatially selective damping effect breaks Galilean and translational invariances, the propagation velocity cannot be determined uniquely while the damping is active, and a singularity arises when these invariances are recovered. We demonstrate that this singularity can be avoided by imposing a simple condition, and a localized traveling-wave solution is obtained with a specific propagation speed.Comment: 9 pages, 13 figure

A class of steady solutions to two-dimensional free convection

We obtained steady solutions to the two-dimensional Boussinesq approximation equations without mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function \mPsi = - Ayf(x), two types of steady solutions are found depending on the boundary conditions. One is kept steady by the balance between the strain of \mPsi and the diffusion. The solution is similar to the Burgers vortex layer solution. The other is done by the balance between vorticity induced by the buoyancy and vorticity flux caused by the external flow. Detailed argument on these two balances is presented for $f(x) = x$. Then two examples other than $f(x) = x$ are shown to have either of the two balancing mechanism. We discuss the relation between these solutions and long-lived fine scale coherent structures observed in direct numerical simulations of two-dimensional free convection turbulence.Comment: REVTeX4, 9 pages, 10 figures, submitted to Phys.Rev.

Non-Kolmogorov scaling for two-particle relative velocity in two-dimensional inverse energy-cascade turbulence

Herein,we numerically examine the relative dispersion of Lagrangian particle pairs in two-dimensional inverse energy-cascade turbulence. Behind the Richardson-Obukhov $t^3$ law of relative separation, we discover that the second-order moment of the relative velocity have a temporal scaling exponent different from the prediction based on the Kolmogorov's phenomenology. The results also indicate that time evolution of the probability distribution function of the relative velocity is self-similar. The findings are obtained by enforcing Richardson-Obukhov law either by considering a special initial separation or by conditional sampling. In particular, we demonstrate that the conditional sampling removes the initial-separation dependence of the statistics of the separation and relative velocity. Furthermore, we demonstrate that the conditional statistics are robust with respect to the change in the parameters involved, and that the number of the removed pairs from the sampling decreases when the Reynolds number increases. We also discuss the insights gained as a result of conditional sampling.Comment: 18 pages, 11 figures Physical Review Fluids, impres

Symmetry of Coherent Vortices in Plane Couette Flow

the 12th EUROMECH European Turbulence Conference, September 10, 2009, Marburg, Germany出典/page.1 Phys. Rev. Lett., 102 の表紙，page.2 Turbulence (Hinze) 教科書より，page.2 J. Fluid Mech. (2000), vol. 422, (by Adrian)，page.3 F. Waleffe, Phys. Fluids 15, 1517　(2003)，page.5,6 T. I. and S.C. Generalis, Phys. Rev. Lett., 102, 114501 (2009

Dynamical aspect of entropy transfer in free convection turbulence

From a dynamical perspective, entropy transfer processes are investigated in two-dimensional free convection turbulence in comparison with an entropy cascade picture based on the coupled dynamics of the T vorticity χ≡(∂yT,-∂xT) and the velocity gradient tensor. Typical entropy transfer processes are observed in direct numerical simulations. For these processes, two characteristic times, the transfer time and the staying time are determined: the former time obeys a Bolgiano-Obukhov (BO) time scaling corresponding to the eddy turnover time in energy cascade. It is suggested that this typical transfer process is not an elementary process of cascade but a dynamical manifestation of intermittency. To examine the meaning of the characteristic times of the typical entropy transfer process, a shell model is constructed based on the entropy cascade picture. By this model, it is shown numerically that typical entropy transfer processes are regarded as the fluctuations satisfying a dynamical similarity. This similarity proved by perturbation analysis requires naturally that the transfer time should obey the BO time scaling