Stochastically driven instability in rotating shear flows

The origin of hydrodynamic turbulence in rotating shear flows is investigated, with particular emphasis on the flows whose angular velocity decreases but whose specific angular momentum increases with the increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain the observed data. Such a mismatch between the linear theory and the observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and then the corresponding turbulence therein is ruled out. This work explores the effect of stochastic noise on such hydrodynamic flows. We essentially concentrate on a small section of such a flow, which is nothing but a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disc. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities and hence large energy dissipations of perturbation, which presumably generate the instability. A range of angular velocity (Omega) profiles of the background flow, starting from that of a constant specific angular momentum (lambda = Omega r(2); r being the radial coordinate) to a constant circular velocity (v(phi) = Omega r), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of their perturbations, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand the origin of instability and turbulence in three-dimensional Rayleigh stable rotating shear flows by introducing additive noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion discs.

Effect of compressibility on the velocity gradient tensor at free shear flow boundaries

Analyses of the invariants of the velocity gradient ten- sor were performed on flow fields obtained by DNS of compressible plane mixing layers at convective Mach num- bers Mc=0:15 and 1.1. Joint pdfs of the 2nd and 3rd invariants were examined at turbulent/nonturbulent (T/NT) boundaries—defined as surfaces where the local vorticity first exceeds a threshold fraction of the maximum of the mean vorticity. By increasing the threshold from very small lev-els, the boundary points were moved closer into the turbulent region, and the effects on the pdfs of the invariants were ob-served. Generally, T/NT boundaries are in sheet-like regions at both Mach numbers. At the higher Mach number a distinct lobe appears in the joint pdf isolines which has not been ob-served/reported before. A connection to the delayed entrain-ment and reduced growth rate of the higher Mach number flow is proposed.

Visualization of coherent structures in turbulent subsonic jet using planar laser induced fluorescence of acetone

In this paper, we present the molecular density distribution measurement in turbulent nitrogen jet (Re approximate to 3 x 10(3)), using acetone as molecular tracer. The tracer was seeded in the nitrogen jet by purging through the liquid acetone at ambient temperature. Planar laser sheet of 266 nm wavelength from frequency quadrupled, Q-switched, Nd:YAG laser was used as an excitation source. Emitted fluorescence images of jet flow field were recorded on CMOS camera. The dependence of planar laser induced fluorescence (PLIF) intensity on acetone vapor density was used to convert PLIF image of nitrogen jet into the density image on pixel-by-pixel basis. Instantaneous quantitative density image of nitrogen jet, seeded with acetone, was obtained. The arrowhead-shaped coherent turbulent structures were observed in the present work. It was found that coherent structures were non-overlapping with separate boundaries. Breaking of coherent structures into turbulence was clearly observed above four times jet width.

Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box 0, L](3) is addressed through four sets of numerical simulations that calculate a new set of variables defined by D-m(t) = (pi(-1)(0) Omega(m))(alpha m) for 1 <= m <= infinity where alpha(m) = 2m/(4m - 3) and Omega(m)(t)](2m) = L-3 integral(v) vertical bar omega vertical bar(2m) dV with pi(0) = vL(-2). All four simulations unexpectedly show that the D-m are ordered for m = 1,..., 9 such that Dm+1 < D-m. Moreover, the D-m squeeze together such that Dm+1/D-m NE arrow 1 as m increases. The values of D-1 lie far above the values of the rest of the D-m, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier-Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of 4096(3).

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as E-f, the fibroblast resting-membrane potential, the fibroblast conductance G(f), and the MF gap-junctional coupling G(gap). Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as G(gap), G(f), and E-f, and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity CV decreases as a function of G(gap), for zero-sided and one-sided couplings; however, for two-sided coupling, CV decreases initially and then increases as a function of G(gap), and, eventually, we observe that conduction failure occurs for low values of G(gap). In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling G(gap) or E-f. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

Scaling of turbulent flame speed for expanding flames with Markstein diffusion considerations

In this paper we clarify the role of Markstein diffusivity, which is the product of the planar laminar flame speed and the Markstein length, on the turbulent flame speed and its scaling, based on experimental measurements on constant-pressure expanding turbulent flames. Turbulent flame propagation data are presented for premixed flames of mixtures of hydrogen, methane, ethylene, n-butane, and dimethyl ether with air, in near-isotropic turbulence in a dual-chamber, fan-stirred vessel. For each individual fuel-air mixture presented in this work and the recently published iso-octane data from Leeds, normalized turbulent flame speed data of individual fuel-air mixtures approximately follow a Re-T,f(0.5) scaling, for which the average radius is the length scale and thermal diffusivity is the transport property of the turbulence Reynolds number. At a given Re-T,Re-f, it is experimentally observed that the normalized turbulent flame speed decreases with increasing Markstein number, which could be explained by considering Markstein diffusivity as the leading dissipation mechanism for the large wave number flame surface fluctuations. Consequently, by replacing thermal diffusivity with the Markstein diffusivity in the turbulence Reynolds number definition above, it is found that normalized turbulent flame speeds could be scaled by Re-T,M(0.5) irrespective of the fuel, equivalence ratio, pressure, and turbulence intensity for positive Markstein number flames.

Effect of side confining walls on the growth rate of compressible mixing layers

Model free simulations are performed to study the effect of the presence of side wall in compressible mixing of two parallel dissimilar gaseous streams with significant temperature difference. The turbulence statistics shows the three dimensional nature of the flow with and without the presence of side walls. The presence of side wall neither makes the flow field two dimensional, nor suppresses three dimensional disturbances. However, the comparison of shear layer growth rate and wall pressures reveal a better match with the two dimensional simulation results. This better match is explained on the basis of formation of oblique structures due to the presence of side walls which also suppress the distribution of momentum in third direction making the pressures to be higher as compared with the case without side walls. (C) 2013 Elsevier Ltd. All rights reserved.

Effect of Inlet Jet injection angle on a calandria based reactor-An investigation with numerical analysis of heat and mass transfer for an optimum reactor design

Heat and mass transfer studies in a calandria based reactor is quite complex both due to geometry and due to the complex mixing flow. It is challenging to devise optimum operating conditions with efficient but safe working range for such a complex configuration. Numerical study known to be very effective is taken up for investigation. In the present study a 3D RANS code with turbulence model has been used to compute the flow fields and to get the heat transfer characteristics to understand certain design parameters of engineering importance. The angle of injection and of the coolant liquid has a large effect on the heat transfer within the reactor.

Scaling of pressure spectrum in turbulent boundary layers

Scaling of pressure spectrum in zero-pressure-gradient turbulent boundary layers is discussed. Spatial DNS data of boundary layer at one time instant (Re-theta = 4500) are used for the analysis. It is observed that in the outer regions the pressure spectra tends towards the -7/3 law predicted by Kolmogorov's theory of small-scale turbulence. The slope in the pressure spectra varies from -1 close to the wall to a value close to -7/3 in the outer region. The streamwise velocity spectra also show a -5/3 trend in the outer region of the flow. The exercise carried out to study the amplitude modulation effect of the large scales on the smaller ones in the near-wall region reveals a strong modulation effect for the streamwise velocity, but not for the pressure fluctuations. The skewness of the pressure follows the same trend as the amplitude modulation coefficient, as is the case for the velocity. In the inner region, pressure spectra were seen to collapse better when normalized with the local Reynolds stress (-(u'v') over bar) than when scaled with the local turbulent kinetic energy (q(2) = (u'(2)) over bar + (v'(2)) over bar + (w'(2)) over bar)

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNPO4 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity theta and the wavelength lambda of a plane wave; we show that PD leads to a periodic, spatial modulation of theta and a temporally periodic modulation of lambda; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNPO4 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNPO4 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a ``cold'' accretion flow at 3000Kis too ``hot'' in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Active Viscoelastic Matter: From Bacterial Drag Reduction to Turbulent Solids

A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time-reversal symmetry. In practice, active fluids may have not only liquid-crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding a polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontaneous flow along a pipe (a ``drag-reduction'' effect). Remarkably, active turbulence can also arise after switching on activity in a sufficiently soft elastomeric solid.

Membrane-based deformable mirror: intrinsic aberrations and alignment issues

A deformable mirror (DM) is an important component of an adaptive optics system. It is known that an on-axis spherical/parabolic optical component, placed at an angle to the incident beam introduces defocus as well as astigmatism in the image plane. Although the former can be compensated by changing the focal plane position, the latter cannot be removed by mere optical realignment. Since the DM is to be used to compensate a turbulence-induced curvature term in addition to other aberrations, it is necessary to determine the aberrations induced by such (curved DM surface) an optical element when placed at an angle (other than 0 deg) of incidence in the optical path. To this effect, we estimate to a first order the aberrations introduced by a DM as a function of the incidence angle and deformation of the DM surface. We record images using a simple setup in which the incident beam is reflected by a 37 channel micro-machined membrane deformable mirror for various angles of incidence. It is observed that astigmatism is a dominant aberration, which was determined by measuring the difference between the tangential and sagittal focal planes. We justify our results on the basis of theoretical simulations and discuss the feasibility of using such a system for adaptive optics considering a trade-off between wavefront correction and astigmatism due to deformation. (C) 2015 Optical Society of America

Effect of ultra-fast mixing in a microchannel due to a soft wall on the room temperature synthesis of gold nanoparticles

The room-temperature synthesis of mono-dispersed gold nanoparticles, by the reduction of chlorauric acid (HAuCl4) with tannic acid as the reducing and stabilizing agent, is carried out in a microchannel. The microchannel is fabricated with one soft wall, so that there is a spontaneous transition to turbulence, and thereby enhanced mixing, when the flow Reynolds number increases beyond a critical value. The objective of the study is to examine whether the nanoparticle size and polydispersity can be modified by enhancing the mixing in the microchannel device. The flow rates are varied in order to study nanoparticle formation both in laminar flow and in the chaotic flow after transition, and the molar ratio of the chlorauric acid to tannic acid is also varied to study the effect of molar ratio on nanoparticle size. The formation of gold nanoparticles is examined by UV-visual spectroscopy and the size distribution is determined using scanning electron microscopy. The synthesized nanoparticles size decreases from a parts per thousand yen6 nm to a parts per thousand currency sign4 nm when the molar ratio of chlorauric acid to tannic acid is increased from 1 to 20. It is found that there is no systematic variation of nanoparticle size with flow velocity, and the nanoparticle size is not altered when the flow changes from laminar to turbulent. However, the standard deviation of the size distribution decreases by about 30% after transition, indicating that the enhanced mixing results in uniformity of particle size.

A Full Body Steerable Wind Display for a Locomotion Interface

This paper presents the Treadport Active Wind Tunnel (TPAWT)-a full-body immersive virtual environment for the Treadport locomotion interface designed for generating wind on a user from any frontal direction at speeds up to 20 kph. The goal is to simulate the experience of realistic wind while walking in an outdoor virtual environment. A recirculating-type wind tunnel was created around the pre-existing Treadport installation by adding a large fan, ducting, and enclosure walls. Two sheets of air in a non-intrusive design flow along the side screens of the back-projection CAVE-like visual display, where they impinge and mix at the front screen to redirect towards the user in a full-body cross-section. By varying the flow conditions of the air sheets, the direction and speed of wind at the user are controlled. Design challenges to fit the wind tunnel in the pre-existing facility, and to manage turbulence to achieve stable and steerable flow, were overcome. The controller performance for wind speed and direction is demonstrated experimentally.