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Register a new userNew Lagrangian diagnostics for characterizing fluid flow mixing
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A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two- (and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is much easier than all other Lagrangian diagnostics known to us and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the Mediterranean Sea.
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We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable scales of fluid motion, due to unresolvable, small, rapid scales of fluid motion.
Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes [C. Nicholson, and S. Hrabv{e}tova, Biophysical Journal, 113(10), 2133(2017)]. However, the exact driving mechanisms are often not known. In this paper, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system (CNS). Different from traditional fluid dynamics problems, flows in biological tissues such as the CNS are coupled with ion transport. It is driven by osmosis created by concentration gradient of ionic solutions, which in term influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al [R.K. Orkand, J.G. Nicholls, S.W. Kuffler, Journal of Neurophysiology, 29(4), 788(1966)]. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.
The most essential characteristic of any fluid is the velocity field v(r) and this is particularly true for macroscopic quantum fluids. Although rapid advances have occurred in quantum fluid v(r) imaging, the velocity field of a charged superfluid - a superconductor - has never been visualized. Here we use superconductive-tip scanning tunneling microscopy to image the electron-pair density r{ho}_S(r) and velocity v_S(r) fields of the flowing electron-pair fluid in superconducting NbSe2. Imaging v_S(r) surrounding a quantized vortex finds speeds reaching 10,000 km/hr. Together with independent imaging of r{ho}_S(r) via Josephson tunneling, we visualize the supercurrent density j_S(r)=r{ho}_S(r)v_S(r), which peaks above 3 x 10^7 A/cm^2. The spatial patterns in electronic fluid flow and magneto-hydrodynamics reveal hexagonal structures co-aligned to the crystal lattice and quasiparticle bound states, as long anticipated. These novel techniques pave the way for electronic fluid flow visualization in many other quantum fluids.
Surface effects become important in microfluidic setups because the surface to volume ratio becomes large. In such setups the surface roughness is not any longer small compared to the length scale of the system and the wetting properties of the wall have an important influence on the flow. However, the knowledge about the interplay of surface roughness and hydrophobic fluid-surface interaction is still very limited because these properties cannot be decoupled easily in experiments. We investigate the problem by means of lattice Boltzmann (LB) simulations of rough microchannels with a tunable fluid-wall interaction. We introduce an ``effective no-slip plane at an intermediate position between peaks and valleys of the surface and observe how the position of the wall may change due to surface roughness and hydrophobic interactions. We find that the position of the effective wall, in the case of a Gaussian distributed roughness depends linearly on the width of the distribution. Further we are able to show that roughness creates a non-linear effect on the slip length for hydrophobic boundaries.
In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of the mean-velocity and Reynolds-stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe in the wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von-K`arm`an and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.
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