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Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise, is appropriate for a broader spectrum of audiences ranging from students to researchers, thus illustrations of differential forms and relevant basic topological concepts are also offered, followed by the demonstration with formulation of differential forms of the classical Navier-Stokes flow theory and the discussions of recent studies in fundamental fluid mechanics and turbulence.
We study the geometrical and topological properties of the bulk (environment space) when we modify the geometry or topology of a brane-world. Through the characterization of a spherically symmetric space-time as a local brane-world immersed into six
Turbulence in a system of nonlinearly interacting waves is referred to as wave turbulence. It has been known since seminal work by Kolmogorov, that turbulent dynamics is controlled by a directional energy flux through the wavelength scales. We demons
The incompressible three-dimensional Euler equations develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling $omega_{max}simell^{-2/3}$ between the vorticity maximum and the pancake thickness, as was obse
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability,
The aim of the present work is to investigate the role of coherent structures in the generation of the secondary flow in a turbulent square duct. The coherent structures are defined as connected regions of flow where the product of the instantaneous