The analysis of complex flow fields based on the notion of organized motions of flow field features with spatial and temporal coherence, the so-called coherent structures, is one of the principal methods in the development of advanced analysis tools in fluid mechanics. For decades the focus of research was on vortex structures as the only coherent structure of interest, caused by the significan...

Recent numerical studies in the area of transition to turbulence discovered that the classical plane Couette flow, plane Poiseuille flow, and pipe Poiseuille flow share some universal 3D steady coherent structure in the form of a “streak-roll-critical layer”. As the Reynolds number approaches infinity, the steady coherent structure approaches a 3D limiting shear of the form (U(y, z), 0, 0) in v...

In recent years, Lagrangian Coherent Structures (LCS) have been characterized using the Finite-Time Lyapunov Exponent, following the advection of a dense set of particles into a corresponding flow field. The large amount of particles needed to sufficiently map a flow field has been a non-trivial computational burden in the application of LCS. By seeding a minimal amount of particles into the fl...

We present a simple, intuitive algorithm for visualizing time-varying flow fields that can reveal complex flow structures with minimal user intervention. We apply this technique to a variety of biological systems, including the swimming currents of invertebrates and the collective motion of swarms of insects. We compare our results with more experimentally difficult and mathematically sophistic...

The stochastic coherent adaptive large eddy simulation (SCALES) method [1] exploits a wavelet thresholding filter-based dynamic grid adaptation strategy to solve for the energetic “coherent” eddies in a turbulent flow field. The effect of the residual less energetic flow structures is modeled by supplying the simulation with a suitable subgrid-scale (SGS) model. The SCALES approach was successf...

We present direct numerical simulations of two-dimensional decaying turbulence at initial Reynolds number 5 x 10(4) in a circular container with no-slip boundary conditions. Starting with random initial conditions the flow rapidly exhibits self-organization into coherent vortices. We study their formation and the role of the viscous boundary layer on the production and decay of integral quantit...

Three-dimensional travelling wave solutions are found for pressure-driven fluid flow through a circular pipe. They consist of three well-defined flow features streamwise rolls and streaks which dominate and streamwise-dependent wavy structures. The travelling waves can be classified by the m-fold rotational symmetry they possess about the pipe axis with m = 1, 2, 3, 4, 5 and 6 solutions identif...

There is a fundamental nonlinearity that governs the coherent and cuasiorganised flows in magnetized plasma, high power laser-produced plasmas and planetary atmosphere. It consists of the convection of a vector field by its own velocity field. Unfolding the complexity of this self-interaction is only possible in few, nongeneric cases. However a new conceptual approach is possible if we provide ...

Different approaches are discussed of variational principles characterizing coherent vortex structures in two-dimensional flows. Turbulent flows seem to form ordered structures in the large scales of the motion and the self-organization principle predicts asymptotic states realizing an extremal value of the energy or a minimum of enstruphy. On the other hand the small scales take care of the in...

Observations indicate that the magnetotail convection is turbulent and bi-modal, consisting of fast bursty bulk flows (BBF) and a nearly stagnant background. We demonstrate that this observed phenomenon may be understood in terms of the intermittent interactions, dynamic mergings and preferential accelerations of coherent magnetic structures under the influence of a background magnetic field ge...