The influence of a ‘‘nonscale invariant’’ forcing is investigated in the renormalization group theory of stirred fluids. It is shown that such forcings introduce a free parameter in the theory. However, the difficulties inherent in the use of the ε expansion remain when the results are applied to real turbulence.

Numerical evidence is presented that the motion of a solid body through incompressible, inviscid fluid, moving irrotationally and otherwise at rest, is chaotic.

Two‐ and three‐dimensional models of the fluid motion through a junction are described for Stokes flow. It is found that for both models separation of the streamlines can occur on the branch of the outer channel wall with smaller flow rate. The relevance of the results for flow at higher Reynolds numbers is also described.

Wave formation in the gravity‐driven low‐Reynolds number flow of two liquid films down an inclined plane is studied by a linear stability analysis. Wavy motion can appear due to an instability of either the fluid–fluid interface or the fluid‐air free surface. It is shown that the flow is always unstable and wavy motion can occur when the less viscous layer is in the region next to the wall for any

Experiments were carried out to study the sedimentation of a two‐dimensional particle cloud. When a large number of particles (glass beads) of uniform size are released from a two‐dimensional opening into a column of fresh water, the mixture initially descends as a thermal; however, after some time, the particles start settling individually, thus leaving the parent fluid behind. For a given type of

This paper uses a fluid‐mechanical model of a granular medium to calculate the hydrodynamic modes of a spatially uniform basic state. These modes are the granular analogs of the heat, sound, and shear modes of the standard fluid. Attention is focused on the possibility of an unstable mode that might result in the spontaneous development of inhomogeneities in density. Two cases are considered: the cooling

The steady perturbation caused in a longshore flow by a bottom undulation is considered. The bedforms are assumed to be alongshore periodic, with crests in the cross‐shore direction and with a small amplitude in order for linear theory to be applicable. The inviscid shallow‐water equations are considered in order to investigate topographic resonance, that is, the condition under which the perturbation

A shear layer formed by two unidirectional gas streams of different velocities with a multisize (polydisperse) spray of evaporating droplets suspended in one of the gas streams is considered here. Similarity solutions are presented for the evolution in droplet size distributions across the shear layer and the effects of various initial droplet size distributions on the profiles of vapor concentrations

The two‐dimensional unsteady incompressible Navier–Stokes equations, solved by a fractional time‐step method, were used to investigate separation due to the application of an adverse pressure gradient to a low‐Reynolds number boundary layer flow. The inviscid pressure distribution of Gaster [AGARD CP 4, 813 (1966)] was applied in the present computations to study the development of a laminar separation

The spatial stability of multiple solutions for fully developed laminar flow through a curved tube and through a straight tube in the presence of buoyant effects was studied using a three‐dimensional numerical representation of the fully elliptic Navier–Stokes and energy equations. Several recent numerical studies have reported the existence of multiple solutions for fully developed laminar flow in

Very small amounts of swirl are shown to strongly destabilize a round jet flow to large n inertial modes, where (k,n) are, respectively, the axial and azimuthal wave numbers of the disturbance. This mechanism is operative if the scale of the small swirl, ε, is O(n−1) for k=O(1). Further, viscosity is shown to exert a stabilizing influence on these modes if the Reynolds number is no larger than O(n3)

The stability of a circular Couette flow with internal heat generation is studied in the region between two coaxial cylinders. The inner cylinder is rotating with constant velocity while the outer one is kept at rest. The investigation is carried out for wide ranges of the Prandtl number and radius ratio R, for the axisymmetric mode (n=0) and the first two asymmetric modes (n=1,2), respectively. For

A stochastic formulation is introduced to study the large amplitude and high‐frequency components of residual accelerations found in a typical microgravity environment (or g‐jitter). The linear response of a fluid surface to such residual accelerations is discussed in detail. The analysis of the stability of a free fluid surface can be reduced in the underdamped limit to studying the equation of the

In Marangoni–Bénard convection with mass transfer from the air to the liquid, an experimental exploration of reflections of solitary waves at walls has been carried out. Mach stems are observed for small enough incident angles. Upon increasing the incident angle the stem disappears thus leading to regular reflections with, however, the angle of reflection being generally larger than the incident angle

There is increasing awareness that even in fully turbulent boundary layers, large‐scale structures in the form of hairpin vortices abound. Although their implications are not all that clear at the present time, they seem to play an important role in turbulent flows. Due to the inherent unpredictability of hairpin vortices in their natural state, in the past effort has been made to generate synthetic

Taylor–Dean vortices are considered in channels whose thickness and curvature vary slowly on a scale 1/δ. The effect of divergence of the channel is shown to be destabilizing and of convergence to be stabilizing. Results for neutral curves are presented for a class of particular channels, and a method of computing such curves for more general channels is given.

A simple argument based on self‐similarity is used to derive a relationship between pointwise energy‐dissipation‐rate moments, 〈εq〉, and inertial‐range volume‐averaged moments, 〈εqr〉, in homogeneous, isotropic and stationary turbulence. These results support the multifractal description of energy dissipation. The moment relationship implies that pointwise and inertial‐range volume‐averaged energy‐dissipation

The dynamic subgrid‐scale eddy viscosity model of Germano et al. [Phys. Fluids A 3, 1760 (1991)] (DSM) is modified by employing the mixed model of Bardina et al. [Ph.D dissertation, Stanford University (1983)] as the base model. The new dynamic mixed model explicitly calculates the modified Leonard term and only models the cross term and the SGS Reynolds stress. It retains the favorable features of

Recent experimental studies on homogeneous curved shear flow have shown that the imposition of strong mean flow curvature can cause a reversal of the turbulent shear stress, giving it the same sign as the gradient of mean velocity. Measurements of the coherence spectrum for these flows has revealed that this reversal is not uniform across all scales, and that eddies of different sizes can have opposite

The expected value Eχ≡E(χ,θ=θ0) of the dissipation rate χ of a passive scalar θ conditioned on the scalar value θ=θ0 has been measured in three varieties of turbulent shear flows: heated wakes, dyed liquid jets, and the atmospheric surface layer. The quantity Eχ depends fairly strongly on θ0 and on the flow. For the wake, Eχ exhibits two peaks—one on the low‐temperature end and the other on the high‐temperature

The turbulent structure in the near field of heated jets was investigated at a Reynolds number of 10 000 for density ratios between 1.0 and 0.5; the corresponding mixing and entrainment of these low density jets was examined. The exit conditions of the jet were carefully controlled using extension tubes to alter the nozzle‐exit boundary layer thickness, as well as using screens to generate turbulent

Thermal plumes in Rayleigh–Bénard convection have been observed to occur with strong vertical component of vorticity, resulting in spiraling hot updrafts and cold downdrafts. Results from two different simulations at Rayleigh numbers 9800 and 33 000 times the critical Rayleigh number close to the boundaries show rapid increase in the conditional averages of vertical velocity and temperature perturbation

The modeling of the turbulent diffusion of quantities such as the turbulent kinetic energy and its dissipation rate in the outer part of wall‐bounded flows is examined with the aid of simulation data. The channel‐flow data of Mansour et al. [J. Fluid Mech. 194, 15 (1988)] and those of Spalart [J. Fluid Mech. 187, 61 (1988)] for a flat‐plate boundary layer with zero pressure gradient are used to examine

Recent analysis of direct numerical simulations of compressible homogeneous shear flow turbulence has unraveled some of the energy transfer mechanisms responsible for the decrease of kinetic energy growth when the flow becomes more compressible. In this complementary study, attention is focused on the rate of strain tensor. A Helmholtz decomposition of the velocity field leads to a consideration of

Equations for the second‐order conditional moments of reactive scalars are derived. For one‐step reaction with equal diffusivity these can be reduced to a single equation for the conditional variance, which is the same for all reactive species. The various terms in the equation have been modeled in light of the experimental data for a turbulent reactive‐scalar mixing layer. In comparison with conventional

The sudden expansion into vacuum of a gas cloud, with initial centrally symmetric density and temperature profiles, is studied theoretically for different values of the specific heat ratio γ. Models treating the expansion are discussed, in particular, a model for isentropic expansion and a model for spatially isothermal expansion. For γ→1, the density of the gas obtained from the former model for late

An electrically insulating layer of a dielectric liquid confined between horizontal conducting electrodes, the upper of which is warmer, becomes unstable with respect to the onset of steady convection when the voltage between the plates reaches a critical value. In a rapidly varying ac field this instability is due to the Kelvin body force which depends on the polarization P and the gradient of the

A measurement method is introduced which can detect steady and unsteady flow in electrically conducting fluids. In this method, the flow region is subjected to an externally applied weak magnetic field B0. The induced magnetic field b generated by fluid flow across the field lines of B0 is used for the flow investigations. It can be measured outside the flow region with the advantage that neither electrical

The time‐dependent drag force on a spherical drop is analyzed for the linear limit of small Reynolds numbers. There is an error in literature on the generalization of the known Basset memory kernel of a rigid sphere to the case of a drop. Correct results are presented here. A new overshooting effect is found if thermocapillarity is driving the drop motion rather than gravity.

Streamline patterns in experiments of Boyer and Biolley [Philos. Trans. R. Soc. London Ser. A 318, 411 (1986)] on flow past a shallow ridge on the floor of a channel in a rotating, stratified fluid exhibit a clear upstream/downstream asymmetry. In this note this question is considered and also a condition for the existence of an eddy in such flows is derived by examining the mathematical properties

It has been found that vortex shedding can occur from long cylinders at small angles of yaw, i.e. in near‐axial flow. The range of Reynolds number over which this can take place has been determined for yaw angles between 0° and 10°. Results for vortex‐shedding frequencies are also presented, and compared with existing data for larger yaw angles. It is suggested that the phenomenon may be relevant to

The decay of two counter‐rotating point vortices of equal strength in a viscous incompressible fluid is studied by solving the Navier–Stokes equations with a finite‐difference technique. Solutions for Reynolds numbers 10, 50, and 100 are compared with a model presented by Cantwell and Rott. Equivorticity lines and the decay rate of translational velocity and circulation of the half‐plane are presented

A nonequilibrium expression of the turbulent viscosity in the Reynolds stress is proposed with the aid of the results from a two‐scale direct‐interaction approximation. The usual turbulent‐viscosity model based on the turbulent kinetic energy K and its dissipation rate ε is extended to include their nonequilibrium effects DK/Dt and Dε/Dt (D/Dt is the Lagrange derivative based on the mean velocity)

From simulation data it is shown that the difference between the true rate of dissipation of turbulent kinetic energy and the ‘‘isotropic dissipation’’ used by Reynolds‐averaged modelers is less than 2% in a conventional viscous wall region, and negligible elsewhere. The difference is a contribution to viscous diffusion which is a small fraction of the total.

Databases from direct numerical simulations of fully developed turbulent channel flow were used to examine the relation between skin‐friction on the wall and streamwise vortices observed near the wall. It is shown that the wall shear rate correlates with streamwise vortices near the wall and that the maximum correlation occurs downstream and with lateral displacement from the location of skin‐friction

Droplets stretched by electric stresses emit jets from their pointed tips. We observed in the experiment a new tip-streaming phenomenon by applying a radial electric field to a liquid jet. Droplets in the jet are stretched in the radial direction and develop into a disk-like shape. The growth of non-axisymmetric harmonics leads to the formation of tens of Taylor cones evenly distributed at the equator

Non-invasive measurement of pressure drop has great clinical significance for the treatment of coronary artery diseases. The objective of this study is to develop a relationship that can estimate pressure drop in a stenosed coronary artery model as a function of different parameters such as blood viscosity, artery length and diameter, flow rate and flow profile, and shape and degrees of stenosis. Experimental

Guiding active microswimmers by external fields to requested target locations is a promising strategy to realize complex transport on the microscale. For this purpose, one possibility consists of attaching the microswimmers to orientable passive components. Accordingly, we analyze theoretically, using a minimal model, the dynamics of a microswimmer when rigidly attached to a (significantly larger)

Hydrodynamic behavior of two-dimensional tandem-arranged flapping flexible foils in uniform flow is investigated numerically by an immersed boundary-lattice Boltzmann method. The leading edge of the leading foil is forced to undergo both heave and pitch motions, while the leading edge of the trailing foil is forced to undergo heave motion only. Of particular interests are the effects of stream-wise

The ceiling effect on the aerodynamics of flapping wings with an advance ratio is investigated by solving the three-dimensional incompressible Navier–Stokes equations. The aerodynamic forces and flow fields around the model wings flapping in a horizontal plane were simulated at various advance ratios, Reynolds numbers, as well as the distance between the wing and the ceiling. It is found that the ceiling

The wake structures generated by rotating wings are studied numerically to investigate the complex vortex formation and evolution in both near-wake and far-wake regions. Flat rectangular wings with finite aspect ratios (AR = 1–8) that rotate from rest at an angle of attack ranging from 15° to 90° in a low Reynolds number regime (200–1600) are considered. Simulations were carried out using an in-house

The hydrodynamics of a three-dimensional self-propelled flexible plate with a Navier slip surface was explored in an effort to assess its role in the hydrodynamics of a slip boundary that mimics the mucus layer. The Navier slip arises when the component of the tangential velocity at a wall is proportional to the strain. The immersed boundary method was employed to simulate the flow. For comparison

We refine the derivation of the Boltzmann equation by considering that the molecules passing through the interfaces of a volume element of physical space and velocity space exhibit different velocity distribution functions and number densities. The resulting equation has a time parameter close to the relaxation time and degenerates into the conventional Boltzmann equation when this parameter takes

The force between two approaching solids in a liquid medium becomes increasingly large with decreasing separation—a phenomenon that prevents contact between the two solids. This growth in force occurs because of the intervening liquid, and studies of such physical systems constitute the classical discipline of lubrication. Furthermore, when the solid(s) are soft, there are quantitative as well as qualitative

We examine the natural convection flow that arises in an electrically conducting nanofluid due to the sinusoidal surface temperature variations along a vertical surface. The effect of thermal radiation is also incorporated. The reduced system of governing equations is solved using an efficient implicit finite difference method which is also known as the Keller box method. The results are presented

This paper reports a parametric study on mixing performance of dean flows in spiral micro-channels using the finite element method. Many important parameters such as the Reynolds number (Re), Peclet number (Pe), flow rate ratio between two species flows (α), and ratio of diffusion coefficient (β) were examined for enhancing mixing efficiency (ηmix). The numerical results matched well with those predicted

Nanopores with various shapes are well developed in unconventional reservoirs, and the transport phenomena of solutions in these reservoir rocks are ubiquitous but have not yet been fully understood. This article investigates the flow characteristics of solutions in hydrophilic slit nanopores through the combination of a modified Poisson–Boltzmann (MPB) model and the modified Navier–Stokes (NS) equation

Despite their remarkable effect on printing accuracy and uniformity, charge migrations that dominate the deformation of ink droplets during electrohydrodynamic jet printing have not been widely investigated. In this work, the large deformation mechanisms of a conductive nanodroplet under a strong electric field are examined from the point of view of charge migrations. It is found that the charge migrations

For a particular printing ink and drop-on-demand piezoelectric inkjet printhead, piezoelectric voltage and temperature of the ink were varied to change the inkjet performance, and the jetting velocity of the inkjet was analyzed under various conditions. The ink was cooled by using a Peltier module, which was attached to the nozzle plate as a heat sink. The inkjet drops were captured by the shadowgraphic

In this work, the decaying laminar inlet swirl flow in a straight circular micro-pipe with wall slip is solved analytically and the solution is verified numerically. Based on a fully developed parabolic axial velocity profile, the swirl velocity equation is solved by the separation of variables technique. The solution is expressed as a function of the flow Reynolds number, the axial distance within

We study the dynamics of moving contact lines and film deposition on a chemically heterogeneous plate withdrawn from a liquid bath. The plate is patterned with vertical stripes characterized by alternating wettabilities. It is assumed that the interfacial slope with respect to the plate is small such that lubrication theory can be employed. The finite element method is used to solve the two-dimensional

We perform the stability analysis for a free surface fluid current modeled as two finite layers of constant vorticity, under the action of gravity and absence of surface tension. In the same spirit as Taylor [“Effect of variation in density on the stability of superposed streams of fluid,” Proc. R. Soc. London, Ser. A 132, 499 (1931)], a geometrical approach to the problem is proposed, which allows

An amphiphilic polymer-based supramolecular system was formulated by exploring the electrostatic interactions between the cationic amphiphilic polymer and polyacid. The effect of aging time on the viscoelastic properties, salt and temperature tolerance, shear resistance, and viscosity recovery of the system was explored by means of rheological measurements. The intrinsic relationship between the viscoelasticity

Three-dimensional numerical simulations of viscoelastic fluids in the Stokes limit with a four-roll mill background force (extended to the third dimension) were performed. Both the Oldroyd-B model and FENE-P model of viscoelastic fluids were used. Different temporal behaviors were observed depending on the Weissenberg number (non-dimensional relaxation time), model, and initial conditions. Temporal

A rheological constitutive model is required to characterize the behavior of a nitrocellulose-based material used as a binder in polymer bonded explosives. The behavior of the binder is extremely important as it heavily influences the mechanical response of the polymer composite; this is due to the binder having stiffness five orders of magnitude lower than the stiffness of the explosive crystals.

Using a parallel-plate rheometer equipped with a partitioned plate and the Sentmanat extensional rheometer fixture, a full rheological characterization of several commercial ionomers (sodium and zinc) and their corresponding parent copolymers has been carried out. Particular emphasis has been placed on the distribution of the relaxation times to identify the characteristic times, such as reptation

This article presents the theoretical analysis of two-dimensional peristaltic transport of two-fluids in a flexible tube under the influence of electro-osmotic force. The flow domain is composed of two regions, namely, the core region and the peripheral region. The Newtonian and the FENE-P models are used to describe the rheology of fluids in the peripheral and the core regions, respectively. Governing

The capillary flow properties of several commercial ionomers (sodium and zinc) were studied to assess their processability in terms of instabilities such as wall slip and melt fracture. Using capillary dies of various diameters and lengths to control capillary extrusion pressure, it was found that the viscosity of these polymers exhibits a relatively small dependence on pressure, more importantly at

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we focus on the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses

The effect of shock waves on the dispersion characteristics of a particle cloud is investigated both numerically and analytically. A one-dimensional analytical model is developed for the estimation of the cloud topology in the wake of a shock wave, as a function of time, space, and characteristic response time τp of the cloud based on the one-way formalism. The model is compared with the results obtained