Tomoaki Itano

Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?

We have examined bursting processes observed in turbulent channel flow by direct numerical simulation of the incompressible Navier-Stokes equations in a minimal flow unit. A traveling wave solution (TWS) is obtained by a shooting method. The TWS corresponds to a saddle point in a two-dimensional phase space. A low-dimensional dynamics confined to the near-wall region is proposed in terms of the TWS and its manifolds. The characteristics of the coherent structures constituting the TWS are investigated dynamically and statistically in detail. The dynamics well describes an elementary process of intermittent turbulent regeneration in wall turbulence.The instability of a streak and its nonlinear evolution are investigated by direct numerical simulation (DNS) for plane Poiseuille flow at Re=3000. It is suggested that there exists a traveling-wave solution (TWS). The TWS is localized around one of the two walls and notably resemble to the coherent structures observed in experiments and DNS so far. The phase space structure around this TWS is similar to a saddle point. Since the stable manifold of this TWS is extended close to the quasi two dimensional (Q2D) energy axis, the approaching process toward the TWS along the stable manifold is approximately described as the instability of the streak (Q2D flow) and the succeeding nonlinear evolution. Bursting corresponds to the escape from the TWS along the unstable manifold. These manifolds constitute part of basin boundary of the turbulent state.

A periodic-like solution in channel flow

We search channel flow for unsteady solutions for different Reynolds numbers and configurations by extending a shooting method which was previously used to obtain a travelling-wave solution. A general initial condition is considered. A periodic-like solution to the incompressible Navier–Stokes equations in a minimal flow unit is found. One cycle of the solution consists of two typical intervals: a single-streak period and a double-streak period. The solution seems to be periodic; however, it cannot be distinguished from a heteroclinic cycle which consists of two heteroclinic orbits connecting two single-streak solutions, because the solution is tracked only for one and half periods.

Interaction between a large-scale structure and near-wall structures in channel flow

Direct numerical simulation of a turbulent channel flow in a periodic domain of relatively wide spanwise extent, but minimal streamwise length, is carried out at Reynolds numbers

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft

\Rey_\tau\,{=}\,137

Electrical charge effect on osmotic flow through pores

and 349. The large-scale structures previously observed in studies of turbulent channel flow using huge computational domains are also shown to exist even in the streamwise-minimal channels of the present study. Moreover, the limitation of the streamwise length of the domain enforces the interaction between large-scale structures and near-wall structures, which consequently makes it tractable to extract a simple cycle of processes sustaining the structures in the present channel flow. It is shown that the large-scale structures are generated by the collective behaviour of near-wall structures and that the generation of the latter is in turn enhanced by the large-scale structures. Hence, near-wall and large-scale structures interact in a co-supporting cycle.

Effects of electric charge on osmotic flow across periodically arranged circular cylinders

A mathematical model is presented for steady fluid flow across microvessel walls through a serial pathway consisting of the endothelial surface glycocalyx and the intercellular cleft between adjacent endothelial cells, with junction strands and their discontinuous gaps. The three-dimensional flow through the pathway from the vessel lumen to the tissue space has been computed numerically based on a Brinkman equation with appropriate values of the Darcy permeability. The predicted values of the hydraulic conductivity Lp, defined as the ratio of the flow rate per unit surface area of the vessel wall to the pressure drop across it, are close to experimental measurements for rat mesentery microvessels. If the values of the Darcy permeability for the surface glycocalyx are determined based on the regular arrangements of fibres with 6nm radius and 8nm spacing proposed recently from the detailed structural measurements, then the present study suggests that the surface glycocalyx could be much less resistant to flow compared to previous estimates by the one-dimensional flow analyses, and the intercellular cleft could be a major determinant of the hydraulic conductivity of the microvessel wall.

Co-Supporting Cycle: Sustaining Mechanism of Large-Scale Structures and Near-Wall Structures in Channel Flow Turbulence

An electrostatic model for osmotic flow through circular cylindrical pores is developed to describe the reflection coefficient for the membrane transport in the presence of surface charges on the pore wall and the solute. For a spherical solute placed at an arbitrary radial position in the pore, the electrical potential was computed by a spectral element method applied to the Poisson-Boltzmann equation together with the condition of electrical neutrality. The interaction energy between the surface charges was used to estimate the osmotic reflection coefficient. The proposed model predicts that even for a small Debye length compared to the pore radius, the repulsive electrostatic interaction between the surface charges could significantly increase the osmotic flow through the pore.

Spiral Roll State in Heat Convection between Nonrotating Concentric Double Spherical Boundaries

An electrostatic model is developed for osmotic flow across a layer consisting of identical circular cylinders with a fixed surface charge, aligned parallel to each other so as to form an ordered hexagonal arrangement. The expression of the osmotic reflection coefficient is derived for spherical solutes with a fixed surface charge suspended in an electrolyte, based on low-Reynolds-number hydrodynamics and a continuum, point-charge description of the electric double layers. The repulsive electrostatic interaction between the surface charges with the same sign on the solute and the cylinders is shown to increase the exclusion region of solute from the cylinder surface, which enhances the osmotic flow. Applying the present model to the study of osmotic flow across the endothelial surface glycocalyx of capillary walls has revealed that this electrostatic model could account well for the reflection coefficients measured for charged macromolecules, such as albumin, in the physiological range of charge density and ion concentration.

Symmetry of coherent vortices in plane couette flow

Direct numerical simulation of a turbulent channel flow in a periodic domain of relatively wide spanwise extent, but minimal streamwise length, is carried out at Reynolds numbers Reτ = 137 and 349. The large-scale structures previously observed in studies of turbulent channel flow using huge computational domains are also shown to exist even in the streamwise-minimal channel of the present work. In the system, it is also clearly observed how the large-scale structures and the near-wall structures affect each other. While the collective behavior of near-wall structures enhance a large-scale structure, the resulting large-scale structure in turn activates the generation and drift of the latter. Hence near-wall and large-scale structures interact in a co-supporting cycle. The preliminary numerical results suggesting the existence of traveling wave solutions that correspond to large-scale structures are reported.

ON THE POSSIBLE EXISTENCE OF A CO-SUPPORTING CYCLE OF LARGE-SCALE AND NEAR-WALL STRUCTURES IN WALL TURBULENCE

We studied the single-arm spiral roll state in the system of Boussinesq fluid confined between nonrotating double concentric spherical boundaries with an opposing temperature gradient previously reported by Zhang et al. [Phys. Rev. E 66, 055203(R) (2002)]. It was found that the state exists even in a gap thicker than that used in this previous study, as an autonomously rotating wave solution with a finite constant angular velocity in a nonrotating geometry. We further confirmed that individual spiral roll states bifurcate directly from the static state at a number of intersections of the marginal stability curves. The double convective timescales peculiar to the state may involve global mixing through the entire domain albeit at the onset of convection, where a passive tracer geometrically explores through the entire spherical domain for sufficient time beyond a cell that would be formed by the other highly-symmetric steady states bifurcating at the onset.