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Register a new userGeometrical and topological description of chirality-relevant flow structures
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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.
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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 dimensional pseudo-Euclidean spaces, with different signatures of the bulk, we investigate the existence of a topological difference in the immersed brane-world. In particular the Schwarzschilds brane-world and its Kruskal (or Fronsdal) brane-world extension are examined from point of view of the immersion formalism. We prove that there is a change of signature of the bulk when we consider a local isometric immersion and different topologies of a brane-world in that bulk.
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 demonstrate that an energy cascade in wave turbulence can be bi-directional, that is, can simultaneously flow towards large and small wavelength scales from the pumping scales at which it is injected. This observation is in sharp contrast to existing experiments and wave turbulence theory where the energy flux only flows in one direction. We demonstrate that the bi-directional energy cascade changes the energy budget in the system and leads to formation of large-scale, large-amplitude waves similar to oceanic rogue waves. To study surface wave turbulence, we took advantage of capillary waves on a free, weakly charged surface of superfluid helium He-II at temperature 1.7K. Although He-II demonstrates non-classical thermomechanical effects and quantized vorticity, waves on its surface are identical to those on a classical Newtonian fluid with extremely low viscosity. The possibility of directly driving a charged surface by an oscillating electric field and the low viscosity of He-II have allowed us to isolate the surface dynamics and study nonlinear surface waves in a range of frequencies much wider than in experiments with classical fluids.
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 observed in the recent numerical experiments [D.S. Agafontsev et al, Phys. Fluids 27, 085102 (2015)]. We study the process of pancakes development in terms of the vortex line representation (VLR), which represents a partial integration of the Euler equations with respect to conservation of the Cauchy invariants and describes compressible dynamics of continuously distributed vortex lines. We present, for the first time, the numerical simulations of the VLR equations with high accuracy, which we perform in adaptive anisotropic grids of up to $1536^3$ nodes. With these simulations, we show that the vorticity growth is connected with the compressibility of the vortex lines and find geometric properties responsible for the observed scaling $omega_{max}simell^{-2/3}$.
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, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulations and theoretical analysis, we demonstrate and quantify combined effects of wettability and hierarchical geometry on displacement patterns, showing a transition from fingering to compact mode. Our results suggest that with a higher porosity of the 2nd-order porous structure, the displacement can keep compact across a wider range of wettability conditions. Combined with our previous work on viscous fingering in such media, we can provide a complete insight into the fluid-fluid displacement control in hierarchical porous media, across a wide range of flow conditions from capillary- to viscous-dominated modes. The conclusions of this work can benefit the design of microfluidic devices, as well as tailoring porous media for better fluid displacement efficiency at the field scale.
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 fluctuations of two velocity components is higher than a threshold based on the long-time turbulence statistics, in the spirit of the three-dimensional quadrant analysis proposed by Lozano-Duran et al. (J. Fluid Mech., vol. 694, 2012, pp. 100-130). We consider both the direct contribution of the structures to the mean in-plane velocity components and their geometrical properties. The instantaneous phenomena taking place in the turbulent duct are compared with turbulent channel flow at Reynolds numbers of $Re_tau=180$ and $360$, based on friction velocity at the center-plane and channel half height. In the core region of the duct, the fractional contribution of intense events to the wall-normal component of the mean velocity is in very good agreement with that in the channel, despite the presence of the secondary flow in the former. Additionally, the shapes of the three-dimensional objects do not differ significantly in both flows. On the other hand, in the corner region of the duct, the proximity of the walls affects both the geometrical properties of the coherent structures and the contribution to the mean component of the vertical velocity, which is less relevant than that of the complementary portion of the flow not included in such objects. Our results show however that strong Reynolds shear-stress events, despite the differences observed between channel and duct, do not contribute directly to the secondary motion, and thus other phenomena need to be considered instead.
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