A “metastable solution” to a differential equation typically refers to a family of solutions for which nearby initial data converges to the family much faster than evolution along the family. Metastable families have been observed both experimentally and numerically in various contexts; they are believed to be particularly relevant for organizing the dynamics of fluid flows. In this work we pro...

We study the clustering properties of advected, noninteracting, passive scalar particles in a Burgers fluid with noise, a problem which maps to that of passive sliding particles moving under gravity on a surface evolving through the Kardar-Parisi-Zhang equation. Numerical simulations show that both the density-density correlation function and the single-site mass distribution scale with system ...

Kolmogorov's phenomenological theory for the energy spectrum in a turbulent fluid in three dimensions is perhaps the single most successful theoretical attempt to comprehend fully developed turbulence. (1) Nevertheless it fails to account for certain fluctuation effects (" intermittency ") that are seen experimentally in three dimensions3 2) Furthermore, it is formulated in such general terms t...

We present theoretical results on spontaneous stratiication of sedimenting suspensions and colloids caused by a lateral temperature gradient. Fluid motion is treated in the Stokes approximation, and motion of suspended particles is described by Burgers equation with convection. The internal structure and interaction of shocks at convection roll boundaries is studied numerically using a reduced ...

Ralph Pohl, Claas Willem Visser, Gert-Willem Römer, Detlef Lohse, Chao Sun, and Bert Huis in ’t Veld Chair of Applied Laser Technology, Faculty of Engineering Technology, University of Twente, Netherlands Physics of Fluids Group, Faculty of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, University of Twente, Netherlands (Received 18 July 2014; revised manuscript received 21 Oc...

This article concerns the dressing method for solving of multidimensional nonlinear Partial Differential Equations. In particular, we join hierarchy of matrix Burgers type equation with hierarchies of equations integrable by the Inverse Spectral Transform (IST). Example of resonance interaction of wave packets in (3+1)-dimensions is given.