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Dec 1990

Volume 2, Issue 12, pp. 2085-2254


The permeability of a random medium: Comparison of simulation with theory

Antonio Cancelliere, Celeste Chang, Enrico Foti, Daniel H. Rothman, and Sauro Succi

Phys. Fluids A 2, 2085 (1990); http://dx.doi.org/10.1063/1.857793 (4 pages) | Cited 73 times

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The results of numerical simulations of the lattice‐Boltzmann equation in three‐dimensional porous geometries constructed by the random positioning of penetrable spheres of equal radii are presented. Numerical calculations of the permeability are compared with previously established rigorous variational upper bounds. The numerical calculations approach the variational bounds from below at low solid fractions and are always within one order of magnitude of the best upper bound at high solid fractions ranging up to 0.98. At solid fractions less than 0.2 the calculated permeabilities compare well with the predictions of Brinkman’s effective‐medium theory, whereas at higher solid fractions a good fit is obtained with a Kozeny–Carman equation.
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02.60.-x Numerical approximation and analysis

Three‐dimensional instability of rotating flows with oscillating axial strain

Nagi N. Mansour and Thomas S. Lundgren

Phys. Fluids A 2, 2089 (1990); http://dx.doi.org/10.1063/1.857794 (3 pages) | Cited 10 times

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The equations of motion for perturbed uniformly rotating flows with uniform axial‐time periodic strain, are derived from the Navier–Stokes equations in the low Mach number limit. The perturbation equations admit exponentially growing three‐dimensional solutions for which the amplification factors per period are computed for a range of compression and swirl ratios. It is found that for a given compression ratio, the flow is stable for low swirl ratios, but at high swirl ratios the flow is unstable with the amplification factor dependent on wave angle but independent of wavelength. For an unstable swirl ratio, higher compression ratios yield larger amplification factors.
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47.20.-k Flow instabilities
47.32.Ef Rotating and swirling flows
47.40.-x Compressible flows; shock waves
47.10.-g General theory in fluid dynamics

The average rotation rate of a fiber in the linear flow of a semidilute suspension

Donald L. Koch and Eric S. G. Shaqfeh

Phys. Fluids A 2, 2093 (1990); http://dx.doi.org/10.1063/1.857795 (10 pages) | Cited 20 times

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Shaqfeh and Fredrickson [Phys. Fluids A 2, 7 (1990)] renormalized the multiple reflection expansion for hydrodynamic fiber interactions in a semidilute suspension, nl3≫1 and ϕ≪1, where ϕ is the fiber volume fraction, n is the number of fibers per unit volume, and l is the fiber half‐length. We use the results of Shaqfeh and Fredrickson to obtain the average rotation rate of a fiber in linear shear flows of a semidilute suspension. Specific results are obtained for the case where most of the fibers are oriented in a preferred direction, as occurs in simple shear and extensional flows. The correction to the O(γ) Jeffrey rotation rate [Proc. R. Soc. London Ser. A 102, 161 (1922); J. Fluid Mech. 14, 284 (1962)] due to hydrodynamic interactions is shown to be O[γ/ln(1/ϕ)], where γ is the shear rate.
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47.15.-x Laminar flows
47.15.G- Low-Reynolds-number (creeping) flows
05.20.Dd Kinetic theory

An experimental investigation on the stability of viscous drops translating through a quiescent fluid

C. J. Koh and L. G. Leal

Phys. Fluids A 2, 2103 (1990); http://dx.doi.org/10.1063/1.857796 (7 pages) | Cited 16 times

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The evolution of the shape of an initially nonspherical drop translating at low Reynolds number through a quiescent fluid is investigated experimentally. It is found that the drop reverts to a spherical shape when the degree of initial deformation is small enough. However, drops that are highly deformed initially are shown to deform continuously. Specifically, a prolate drop breaks up into multiple droplets as it rises, while an oblate drop deforms into a double‐emulsion drop as it translates. The experimental results agree well with results obtained earlier from numerical simulations [Phys. Fluids A 1, 1309 (1989)].
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47.15.G- Low-Reynolds-number (creeping) flows
47.20.-k Flow instabilities

Some influences of particle shape on drag and heat transfer

H. A. Dwyer and D. S. Dandy

Phys. Fluids A 2, 2110 (1990); http://dx.doi.org/10.1063/1.857797 (9 pages) | Cited 5 times

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A study has been carried out on some of the influences of particle shape and orientation on the drag, lift, and heat transfer characteristics of nonspherical particles at intermediate Reynolds numbers, 10≤Re≤66. The geometry that has been employed in the investigation has been an ellipsoid of revolution with variation in angle of attack, and the aspect ratio (ratio of the major to the minor axis) has been varied by a factor of 3. The method of solution consists of a second‐order, finite volume formulation of the Navier–Stokes equations, which is capable of being extended to time‐dependent and variable density low Mach number flows. For relatively small increases in the ratio of major to minor axis the behavior of the pressure and skin friction distributions becomes substantially different in both qualitative and quantitative ways. The skin friction distribution as well as the heat flux to the particle surface exhibit a maxima near the major axis of the ellipsoid regardless of orientation, and the total friction drag and the total particle heat transfer exhibit a strong correlation. The total drag coefficient and the lift coefficient behave in a much different manner and they are strongly influenced by the Reynolds number, aspect ratio, and angle of attack. It appears that the total drag and lift force depend strongly on the particle shape, and it appears difficult to develop simple correlation schemes. The numerical methods that have been used performed well and they will be extended to more complex problems in the future.
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82.33.Vx Reactions in flames, combustion, and explosions
44.90.+c Other topics in heat transfer (restricted to new topics in section 44)
05.60.-k Transport processes
02.60.-x Numerical approximation and analysis

The migration of a compound drop due to thermocapillarity

David S. Morton, R. Shankar Subramanian, and R. Balasubramaniam

Phys. Fluids A 2, 2119 (1990); http://dx.doi.org/10.1063/1.857798 (15 pages) | Cited 9 times

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The quasistatic thermocapillary motion of a compound drop in an unbounded fluid possessing a uniform temperature gradient is analyzed. For completeness, gravitational effects are included in the treatment. The general model is formulated, and the equations for the concentric case are solved using spherical polar coordinates, while the eccentric case is handled using bispherical coordinates. Results are given for the velocity of the drop as well as that of the droplet with respect to the drop, along with useful approximations. Illustrative results are presented graphically for the thermocapillary migration of a compound drop in the special case when the droplet is a gas bubble. In addition to the velocities of the drop and the bubble, representative isotherms and streamlines also are presented which display interesting qualitative features.
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47.55.Kf Particle-laden flows
44.30.+v Heat flow in porous media
47.15.G- Low-Reynolds-number (creeping) flows

Breakup of a liquid jet in a swirling gas

Z. W. Lian and S. P. Lin

Phys. Fluids A 2, 2134 (1990); http://dx.doi.org/10.1063/1.857799 (6 pages) | Cited 11 times

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The convective instability of a viscous liquid jet emanating into a inviscid gas with a swirl is investigated. Contrary to the known case of a swirling liquid jet in a quiescent gas, the swirl in the ambient gas is shown to have a stabilizing effect. The inertia force in the gas is shown to play dual roles of both stabilization and destabilization. The gas inertia associated with the swirl has a stabilizing influence, but that associated with the interfacial pressure fluctuation has a destabilizing effect. A physical explanation of the mechanism of stabilization by the gas swirl is given.
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47.27.W- Boundary-free shear flow turbulence
47.32.Ef Rotating and swirling flows
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)
51.90.+r Other topics in the physics of gases (restricted to new topics in section 51)

Local shear stress measurements on an axisymmetric body in a microbubble modified flow field

S. Deutsch and S. Pal

Phys. Fluids A 2, 2140 (1990); http://dx.doi.org/10.1063/1.857800 (7 pages) | Cited 3 times

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An array of flush‐mounted hot film probes has been used to measure the local shear stress reduction as a result of microbubble injection over an axisymmetric body at the four discrete, free‐stream speeds of 4.6, 10.7, 13.2, and 16.8 m/sec. Visualization of the bubble flow pattern supplement these results at intermediate free‐stream speeds. At speeds of 10.7 m/sec and above, a circumferential gradient in skin friction, with skin friction reduction larger at the top than at the bottom of the model occurs at some distance downstream of injection. For these speeds, the gradient is stronger at the lower speeds and higher gas injection conditions. Higher speeds tend to drive the axial location of the gradient farther from the injection location. At speeds below 10.7 m/sec, the flow is dominated by a double vortex structure that entrains the bubbles at the bottom and sides of the model and transports them to the top. At sufficiently high gas flow rates a cavity, large enough to be observed visually, is formed just upstream of the vortices, centered near the body midline. The axial position of the cavity is roughly independent of flow speed and gas flow conditions. The transport of bubbles by the vortices, to the top of the body, is the cause of the poor skin friction reduction performance of microbubble injection at low speeds on an axisymmetric shape. Integration of the current local skin friction results gives good agreement with earlier drag balance measurements. The persistence of the drag reduction phenomenon with axial distance as well as the statistics of the shear stress fluctuations are quite similar to what was observed earlier on flat plates.
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47.55.Kf Particle-laden flows
47.27.N- Wall-bounded shear flow turbulence
47.32.Ef Rotating and swirling flows
51.20.+d Viscosity, diffusion, and thermal conductivity

Stabilization of Taylor–Couette flow due to time‐periodic outer cylinder oscillation

B. T. Murray, G. B. McFadden, and S. R. Coriell

Phys. Fluids A 2, 2147 (1990); http://dx.doi.org/10.1063/1.857801 (10 pages) | Cited 4 times

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The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly [Phys. Rev. Lett. 60, 700 (1988)]. The critical Reynolds numbers calculated from linear stability theory agree with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: (1) a truncated Fourier series representation in time and (2) a fundamental solution matrix based on a Chebyshev‐pseudospectral representation in space. For large‐amplitude, low‐frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent interval followed by rapid change in the perturbed flow velocities.
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47.20.-k Flow instabilities
47.15.Cb Laminar boundary layers
02.60.-x Numerical approximation and analysis

Transition to hard turbulence in thermal convection at infinite Prandtl number

Ulrich Hansen, David A. Yuen, and Sherri E. Kroening

Phys. Fluids A 2, 2157 (1990); http://dx.doi.org/10.1063/1.857802 (7 pages) | Cited 35 times

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Direct numerical simulations of two‐dimensional high Rayleigh (Ra) number, base‐heated thermal convection in large aspect‐ratio boxes are presented for infinite Prandtl number fluids, as applied to the Earth’s mantle. A transition is characterized in the flow structures in the neighborhood of Ra between 107 and 108. These high Ra flows consist of large‐scale cells with strong intermittent, boundary‐layer instabilities. For Ra exceeding 107 it is found that the heat‐transfer mechanism changes from one characterized by mushroom‐like plumes to one consisting of disconnected ascending instabilities, which do not carry with them all the thermal anomaly from the bottom boundary layer. Plume–plume collisions become much more prominent in high Ra situations and have a tendency of generating a pulse‐like behavior in the fixed plume. This type of instability represents a distinct mode of heat transfer in the hard turbulent regime. Predictions of this model can be used to address certain issues concerning the mode of time‐dependent convection in the Earth’s mantle.
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47.27.-i Turbulent flows
47.20.-k Flow instabilities
91.35.Dc Heat flow; geothermy

Mixed convection flow in a heated curved pipe with core

G. T. Karahalios

Phys. Fluids A 2, 2164 (1990); http://dx.doi.org/10.1063/1.857803 (12 pages) | Cited 11 times

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Mixed convection flow in a heated pipe with a heated inner core is examined. Analytic solutions are derived in power series of the Dean number and the product of Reynolds and Rayleigh numbers. The results are compared with flows in the absence of an axial core. The core modifies the flow and the fluid temperature distribution.
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44.25.+f Natural convection
28.41.Fr Reactor coolants, reactor cooling, and heat recovery

Experimental investigation of fluctuating forces exerted on a cylindrical tube (Reynolds numbers from 3000 to 30 000)

H. Tadrist, R. Martin, L. Tadrist, and P. Seguin

Phys. Fluids A 2, 2176 (1990); http://dx.doi.org/10.1063/1.857804 (7 pages) | Cited 2 times

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In this paper, an experimental investigation of variations of the global lift coefficient as a function of the Reynolds number is discussed. The experimental unit was capable of measuring the lift coefficient at Reynolds numbers ranging from 3000 to 30 000. Since the intensity of the unsteady lift forces was of the order of few millinewtons, a sensor and signal‐conditioning circuit was specially designed for measurement. The velocity field and the flow turbulence rate were measured upstream from the cylinder using laser‐Doppler anemometry. Tube aspect ratio, blockage, and ends effects are discussed. The evolution of the Strouhal number was observed as the Reynolds number passed from 3000 to 30 000. When measured as a function of the Reynolds number, the global lift coefficient displayed considerable variation for Reynolds numbers between 3000 and 10 000.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)

Turbulent spots in plane Poiseuille flow — Measurements of the velocity field

Barbro G. B. Klingmann and P. Henrik Alfredsson

Phys. Fluids A 2, 2183 (1990); http://dx.doi.org/10.1063/1.857805 (13 pages) | Cited 4 times

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An experimental study on the development of turbulent spots in plane Poiseuille flow at a Reynolds number of 1600 has been carried out with the aim of achieving a better understanding of the transition to and maintenance of turbulence at low Reynolds numbers. Spots were triggered by a loudspeaker‐induced jet of high velocity. The initial disturbance was found to undergo a first stage of rapid expansion, in which sharp internal shear layers form at locations away from the symmetry plane and precede the transition to turbulence. After this initial stage, a nearly self‐similar structure develops with the typical features of a turbulent spot. The general features, turbulent properties, and spanwise spreading of the spot were investigated and compared both to previous experimental data and to numerical simulations. High‐frequency fluctuations are absent at the front of the spot, whereas the turbulence is apparently self‐sustained at the rear and displays features similar to fully turbulent Poiseuille flow at much higher Reynolds numbers. The waves accompanying the wing tips of the spot extend well within the spot, and reach amplitudes far in excess of those previously found outside the spot. The high level of random fluctuations in this part of the spot indicates that the breakdown of the waves is important for the spanwise propagation of the turbulent region.
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47.15.G- Low-Reynolds-number (creeping) flows
47.27.Cn Transition to turbulence
47.80.-v Instrumentation and measurement methods in fluid dynamics

Numerical study of discrete‐velocity gases

Takaji Inamuro and Bradford Sturtevant

Phys. Fluids A 2, 2196 (1990); http://dx.doi.org/10.1063/1.857825 (8 pages) | Cited 22 times

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A finite‐difference method for solving the discrete Boltzmann equations, which are the governing equations for a model gas in which molecules have many discrete velocities, is developed. The method is applied to three fundamental problems in rarefied gas flow to study the features of discrete‐velocity gases: normal shock wave structure, heat transfer between two parallel plates, and two‐dimensional vapor deposition. Two different discrete‐velocity gas models are used.
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47.45.-n Rarefied gas dynamics
51.10.+y Kinetic and transport theory of gases
44.30.+v Heat flow in porous media
81.10.Bk Growth from vapor

Multigroup solutions of the nonlinear Boltzmann equation

Georg Kügerl and Ferdinand Schürrer

Phys. Fluids A 2, 2204 (1990); http://dx.doi.org/10.1063/1.857806 (7 pages) | Cited 1 time

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The nonlinear Boltzmann equation is solved numerically to examine the Maxwellization of spatially homogeneous gases, using the multigroup method. By applying the Krook–Wu scattering model, an exact solution of the Boltzmann equation (BKW mode) is reproduced with high accuracy. The numerical code is also used for hard‐sphere molecules. Initial distributions are a Maxwellian with tail cutoff and distributions composed of two δ peaks. For the latter class, a strong transient overpopulation of the distribution function is observed, which may amount to several orders of magnitude.
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51.10.+y Kinetic and transport theory of gases
02.60.-x Numerical approximation and analysis

Analysis of molecular mixing and chemical reaction in a vortex pair

B. M. Cetegen and J. P. Aguirre

Phys. Fluids A 2, 2211 (1990); http://dx.doi.org/10.1063/1.857807 (6 pages) | Cited 2 times

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This paper concerns an analytical/numerical study of molecular mixing and infinitely fast chemical reactions in the field of a two‐dimensional vortex pair. Calculations of scalar concentration fields and its mixing statistics are presented for a range of nondimensional vortex strengths, Γ/2πν=10–50, Schmidt numbers, ν/D=1–100, and a time parameter. A measure of molecular mixing ‘‘mixedness,’’ defined as the variance of the spatial concentration field from its well‐mixed value, shows that the augmentation of mixedness resulting from the presence of vortex pair is linearly proportional to the vortex pair strength and time elapse since the inception of the vortex pair.
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47.27.W- Boundary-free shear flow turbulence
47.70.Fw Chemically reactive flows

Plane waves and structures in turbulent channel flow

L. Sirovich, K. S. Ball, and L. R. Keefe

Phys. Fluids A 2, 2217 (1990); http://dx.doi.org/10.1063/1.857808 (10 pages) | Cited 43 times

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A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen–Loève procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.
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47.27.Cn Transition to turbulence
47.35.-i Hydrodynamic waves
47.27.N- Wall-bounded shear flow turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems

Spatial effects of removal and creation processes on the dynamics of gases

Damián H. Zanette

Phys. Fluids A 2, 2227 (1990); http://dx.doi.org/10.1063/1.857809 (3 pages) | Cited 1 time

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Exact similarity solutions are presented for the spatial‐dependent McKean–Boltzmann equation, when creation and removal processes are allowed. The effects of such processes on the spatial dynamics of the gas are analyzed through these solutions.
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51.10.+y Kinetic and transport theory of gases
82.30.-b Specific chemical reactions; reaction mechanisms
82.40.Bj Oscillations, chaos, and bifurcations

Creeping flow of a conducting fluid past axisymmetric bodies in the presence of an aligned magnetic field

A. Kyrlidis, R. A. Brown, and J. S. Walker

Phys. Fluids A 2, 2230 (1990); http://dx.doi.org/10.1063/1.857810 (10 pages) | Cited 2 times

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The use of strong magnetic fields for the control of particle settling in metallic systems is investigated in the limit of small inertial and magnetic Reynolds numbers. Finite element calculations of flow around axisymmetric bodies show that the drag increases proportional to the intensity of the magnetic field B or the Hartmann number Ha. The flow field forms boundary layers, which thin with increasing Ha, along surfaces parallel to the flow. For axisymmetric bodies, the boundary layer separates as the poles of the surface are approached and encloses regions of almost stagnant fluid. These regions spread upstream and downstream along the body with increasing Ha, thereby trapping the particle in a column of stagnant fluid. The pressure difference between the leading and trailing fluid columns is responsible for the increased particle drag. Asymptotic analysis with Ha≫1 confirms the scalings from the computations and clarifies the flow structure near the body.
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47.15.G- Low-Reynolds-number (creeping) flows
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.15.-x Laminar flows
81.90.+c Other topics in materials science (restricted to new topics in section 81)

The effect of electromagnetic fields on the stability of a uniformly elongating plastic jet

David L. Littlefield and John D. Powell

Phys. Fluids A 2, 2240 (1990); http://dx.doi.org/10.1063/1.857811 (9 pages) | Cited 13 times

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In this paper the stability characteristics of an infinitely long, uniformly elongating metal jet are investigated. The application to a metallic jet formed from an explosive charge, or shaped‐charge jet, is of particular interest. The effect of an axial electric current on the stability of the jet is determined. The jet is assumed to be perfectly plastic, perfectly conducting, nonswirling, and isothermal. The governing equations are solved to determine the idealized motion of the jet, which is then perturbed by an arbitrary three‐dimensional disturbance. The resulting first‐order equations are solved numerically for the time evolution of this perturbation. For a given initial condition, the growth rate of the disturbance depends on the relative importance of the inertial, electrical, and plastic forces. The details of growth rate characteristics are explained in terms of the appropriate physical principles.
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47.20.-k Flow instabilities
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.50.-d Non-Newtonian fluid flows

Shear flow coherent structures via Karhunen–Loève expansion

Mojtaba Rajaee and Sture K. F. Karlsson

Phys. Fluids A 2, 2249 (1990); http://dx.doi.org/10.1063/1.857812 (3 pages) | Cited 3 times

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The method of snapshots for Karhunen–Loève expansion has been applied to two‐dimensional, two‐component hot‐wire data from the first pairing region of a weakly perturbed free shear layer. Almost 90% of the fluctuation energy is captured by the first four modes. The first and the second modes contain almost equal amounts of energy, as do the third and the fourth, and the time dependence for each pair is very nearly sinusoidal with the odd modes leading in phase by π/2.
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47.27.W- Boundary-free shear flow turbulence
47.10.-g General theory in fluid dynamics

Bulk viscosity of a dilute polyatomic gas

George Emanuel

Phys. Fluids A 2, 2252 (1990); http://dx.doi.org/10.1063/1.857813 (3 pages) | Cited 21 times

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Theoretical and experimental knowledge of the bulk viscosity for a dilute gas is briefly reviewed. Neither area is satisfactory; the lack of experimental data for polyatomic gases over a broad temperature range is particularly acute. There is one circumstance where this deficiency is especially detrimental, namely, high‐speed entry into planetary atmospheres.
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51.20.+d Viscosity, diffusion, and thermal conductivity
95.55.Pe Lunar, planetary, and deep-space probes
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