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The problem of a flow with its velocity gradient being of textit{real Schur form} uniformly in a cyclic box is formulated for numerical simulation, and a semi-analytic algorithm is developed from the precise structures. Computations starting from two-component-two-dimensional-coupled-with-one-component-three-dimensional initial velocity fields of the Taylor-Green and Arnold-Beltrami-Childress fashions are carried out, and some discussions related to turbulence are offered for the multi-scale eddies which, though, present precise order and symmetry. Plenty of color pictures of patterns of these completely new flows are presented for general and specific conceptions.
Helicity, as one of only two inviscid invariants in three-dimensional turbulence, plays an important role in the generation and evolution of turbulence. From the traditional viewpoint, there exists only one channel of helicity cascade similar to that
An original experimental setup has been elaborated in order to get a better view of turbulent flows in a von Karman geometry. The availability of a very fast camera allowed to follow in time the evolution of the flows. A surprising finding is that th
We present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smoo
Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. Turbulent flows promote efficient transport and mixing by their inherent randomness. Laminar flows lack such a natural mixing mechanism and efficient trans
Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations in the Blas