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Dec 1977

Volume 20, Issue 12, pp. 1967-2157

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Turbulent vortex pairs in neutral surroundings

Jin Wu

Phys. Fluids 20, 1967 (1977); http://dx.doi.org/10.1063/1.861826 (8 pages) | Cited 2 times

Online Publication Date: 26 August 2008

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Experiments were conducted in neutral surroundings on turbulent vortex pairs produced with various initial conditions. A pair was observed to spread linearly along the direction of motion: This is expressed as b=0.26z, where b is one half its maximum width and z is the elevation of its leading extremity. The advance of the pair was found to follow Z/b0=2.3(Tw0/b0)1/3, where Z and T are elevation and time, respectively, with respect to the virtual origin; and b0 and w0 are the initial size and velocity of the pair. These results appear to indicate that the motion of the pair follows the similarity solution and relates only to the initial momentum and the entrainment coefficient, regardless of the conditions of its generation. An additional experiment was conducted with polymer solutions to illustrate the influence of turbulent mixing inside the pair on its spreading behavior.
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47.27.T- Turbulent transport processes

Calculations of turbulent boundary layer flows with drag reducing polymer additives

F. Durst and A. K. Rastogi

Phys. Fluids 20, 1975 (1977); http://dx.doi.org/10.1063/1.861827 (11 pages) | Cited 10 times

Online Publication Date: 26 August 2008

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Results of investigations into numerical predictions of turbulent flows in plane two‐dimensional channels and circular pipes with and without polymer additives are presented. These predictions are based on an available computer program for two‐dimensional boundary layer flows and on the k‐ϵ turbulence model. The model takes into account the low Reynolds number effects in the immediate vicinity of the wall and is modified to take into account the influence of the polymer additives in smooth as well as rough conduits in accordance with experimental results available in the literature. Results of the predictions are presented and compared with experiments. Based on the reliability of the present predictions and the uncertainty in the available measurements, a practical approach is outlined to study turbulent flows with drag reducing polymer additives. Degradation of polymer molecules is predictable with the described theoretical model.
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47.27.nb Boundary layer turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems

Skewness of temperature derivatives in turbulent shear flows

K. R. Sreenivasan and R. A. Antonia

Phys. Fluids 20, 1986 (1977); http://dx.doi.org/10.1063/1.861828 (3 pages) | Cited 29 times

Online Publication Date: 26 August 2008

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The nonzero value of the measured skewness of the streamwise temperature derivative is not necessarily inconsistent with the concept of local isotropy of small scale turbulence, and may be estimated adequately from a ramp‐like model for the large scale structure of temperature.
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47.27.nb Boundary layer turbulence

Pressure gradient‐velocity correlations for flows with two‐and three‐dimensional turbulence

Rishi Raj

Phys. Fluids 20, 1989 (1977); http://dx.doi.org/10.1063/1.861829 (4 pages) | Cited 3 times

Online Publication Date: 26 August 2008

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The pressure gradient‐velocity correlations as applied to curved and rotating turbulent flows are developed. A problem is raised for modeling pressure gradient‐velocity correlations for two‐dimensional turbulence. It is interesting to note how the behavior of the pressure gradient‐velocity correlations differs for the cases of two‐ and three‐dimensional turbulence near and away from the boundary. An explicit dependence of pressure gradient‐velocity correlations on rotation is shown to exist in the case of rotating flows.
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47.27.-i Turbulent flows
47.32.Ef Rotating and swirling flows
92.60.hk Convection, turbulence, and diffusion

Steady‐state convection with melting at a boundary

William B. Heard

Phys. Fluids 20, 1993 (1977); http://dx.doi.org/10.1063/1.861830 (7 pages)

Online Publication Date: 26 August 2008

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A fluid is heated from below and cooled from above in such a way that a frozen layer overlies a convecting layer. The lower boundary of the fluid is maintained at a constant temperature while the upper boundary of the ice transfers heat to an ambient atmosphere according to Newton’s law of cooling. The Boussinesq equations for convection are used in the mean field approximation and with a one‐mode, two‐dimensional representation to determine the steady state of the system in the limit of very large Rayleigh number. The fluid‐ice interface is corrugated and is a free boundary of the problem. The convective steady states are likely to bifurcate discontinuously from the conductive steady states. Analytical and numerical results are given for the temperature at the upper boundary of the ice, the mean depth of the fluid, and the amplitude of the corrugations.
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44.25.+f Natural convection

Unstable normal mode for Rayleigh–Taylor instability in viscous fluids

R. Menikoff, R. C. Mjolsness, D. H. Sharp, and C. Zemach

Phys. Fluids 20, 2000 (1977); http://dx.doi.org/10.1063/1.861831 (5 pages) | Cited 25 times

Online Publication Date: 26 August 2008

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The character of the growth rates of the normal modes for Rayleigh–Taylor instability of superposed incompressible, viscous fluids is analyzed in terms of appropriately scaled dimensionless parameters and a particularly simple representation of the Rayleigh–Taylor dispersion relation. The chief feature that emerges is that the scaled growth rate is remarkably insensitive to the values of fluid densities and viscosities. To within a few percent, the physical growth rate depends only on the surface tension, the density‐weighted average viscosity, and the effective acceleration. Approximate formulae for the most unstable wavenumber and the corresponding maximum growth rate are given.
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47.20.-k Flow instabilities

Stability of a liquid film with respect to initially finite three‐dimensional disturbances

S. P. Lin and M. V. G. Krishna

Phys. Fluids 20, 2005 (1977); http://dx.doi.org/10.1063/1.861832 (7 pages) | Cited 7 times

Online Publication Date: 26 August 2008

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The nonlinear stability of a viscous liquid film flowing steadily down an inclined plane is studied in the phase plane. Explicit expressions of the critical points of the governing differential system are obtained. The nature of the critical points and the integral curves corresponding to various flow parameters, initial conditions, and disturbance characteristics are determined numerically. Based on the phase plane analysis and the numerical results, the following conclusions are reached: The film which is unstable according to linear theory may be stable with respect to a finite three‐dimensional disturbance if the initial amplitude and the side‐band width are sufficiently small. The particular values of the initial amplitude and the side‐band width beyond which the film becomes unstable depend on the relevant flow parameters. The film which is stable according to linear theory is also shown to be stable with respect to three‐dimensional small finite amplitude disturbances with finite bandwidths.
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47.20.-k Flow instabilities

Platelet aggregate formation in a region of separated blood flow

E. Marc Parmentier, William A. Morton, and Harry E. Petschek

Phys. Fluids 20, 2012 (1977); http://dx.doi.org/10.1063/1.861833 (10 pages) | Cited 7 times

Online Publication Date: 26 August 2008

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Microscopic observations of the flow of fresh canine blood in a separated region formed by a step in a polyurethane surface have been made. These observations show the formation of large clumps of freely floating aggregates of platelets. These clumps can easily leave the region and may be representative of disorders occurring in the distal circulation when artificial devices are used in the bloodstream. Measurements of the growth rate of these aggregates are compared with a theoretical analysis of the rate of platelet collisions. Some criteria defining conditions under which such free floating aggregates occur are also suggested.
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87.19.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)

Kinetic theory boundary conditions for discrete velocity gases

R. Gatignol

Phys. Fluids 20, 2022 (1977); http://dx.doi.org/10.1063/1.861834 (9 pages) | Cited 23 times

Online Publication Date: 26 August 2008

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Boundary conditions are investigated for a model gas composed of identical particles with velocities restricted to a given finite set of vectors. A possible model of the gas surface interaction is given and an H theorem for a gas in a vessel is obtained. Then, the steady Couette flow between two parallel plates is studied. The model with four coplanar velocities is used and the velocity set has arbitrary orientation. The exact kinetic solution is compared with the solutions of the associated Navier–Stokes problems.
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51.10.+y Kinetic and transport theory of gases
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)

Inverse problem in transport theory. III

K. M. Case

Phys. Fluids 20, 2031 (1977); http://dx.doi.org/10.1063/1.861835 (6 pages) | Cited 1 time

Online Publication Date: 26 August 2008

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Two explicit solutions of the inverse problem of one velocity transport theory are given. The first involves quantities K (n, n) obtained from a Gelfand–Levitan equation. The second involves quantities A (n, n) obtained from a Marchenko equation. These solutions are complementary. The first is most convenient to find the coefficients of the low order Legendre polynomials in the expansion of the scattering function. The second is efficient for calculating high order coefficients. The explicit relations between the A (n, n) and K (n, n) are given. Since most of the special results needed to obtain these solutions have been published elsewhere, proofs are at most sketched. Appropriate references provide any further details desired.
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05.60.-k Transport processes

Dynamics of a free electron gas interacting with neutral atoms. Two‐dimensional model

Nelly Peyraud

Phys. Fluids 20, 2037 (1977); http://dx.doi.org/10.1063/1.861836 (9 pages) | Cited 3 times

Online Publication Date: 26 August 2008

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The dynamics of a free electron gas interacting with neutral and excited atoms whose populations are assumed fixed is considered. An analytic form of the time dependent electronic distribution function for arbitrary initial conditions, in the case of a two‐dimensional model where interactions are only inelastic and superelastic between two atomic levels, is obtained. It is shown that this electron gas reaches a stationary state. The equilibrium distributions when the elastic collisions between electron and neutral atoms are taken into account is also considered. It is shown that the stationary equilibrium solutions for a three‐dimensional model have the same structure as in the two‐dimensional model.
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05.30.Fk Fermion systems and electron gas
52.20.Fs Electron collisions

Kinetic theory of a chemically reacting polyatomic plasma

J. R. Saraf

Phys. Fluids 20, 2046 (1977); http://dx.doi.org/10.1063/1.861823 (3 pages)

Online Publication Date: 26 August 2008

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A kinetic description is given for a polyatomic plasma consisting of electrons, ions, and atoms, the latter two species possessing internal degrees of freedom. The elastic, internal, and inelastic impact collisions have been modeled such that the system satisfies the conservation of charge, nuclei, mass, momentum, and translational plus rotational energy.
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52.25.Dg Plasma kinetic equations
52.20.-j Elementary processes in plasmas

Parametric instabilities in the presence of space‐time random fluctuations

G. Laval, R. Pellat, D. Pesme, A. Ramani, Marshall N. Rosenbluth, and E. A. Williams

Phys. Fluids 20, 2049 (1977); http://dx.doi.org/10.1063/1.861824 (9 pages) | Cited 54 times

Online Publication Date: 26 August 2008

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The effect of a finite bandwidth driver or of turbulence on the parametric instability is considered. First, exact equations are obtained for special values of the group velocity of the fluctuations V0, with bandwidth modeled by a Kubo–Anderson process. Next, a method which enables one to deal with the space‐time problem for arbitrary V0 is given. For the averaged amplitudes it reduces to the Bourret approximation and for the correlation function it gives the kinetic equation for random phase waves. Convective and absolute instability thresholds are given. It is found that for absolute instabilities the threshold obtained from the averaged intensities is lower than the one obtained from the averaged amplitudes.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
47.27.-i Turbulent flows

Parametric instabilities due to lower‐hybrid radio frequency heating of tokamak plasmas

Miklos Porkolab

Phys. Fluids 20, 2058 (1977); http://dx.doi.org/10.1063/1.861825 (18 pages) | Cited 106 times

Online Publication Date: 26 August 2008

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The linear theory of parametric instabilities relevant to radiofrequency heating near the lower‐hybrid frequency of tokamak‐type plasmas is presented. The dispersion relations are analyzed numerically to all orders of the ion Larmor radius. The complete range of unstable spectra is obtained for 1<ω0/ωlh<5, for both deuterium and hydrogen plasmas. As the pump wave propagates from the edge of the plasma toward its interior, the transition from resonant decay to decay into quasi‐modes is demonstrated. The effects of inhomogeneities upon the threshold for parametric decay, such as density gradients, finite pump width, and magnetic shear, are obtained. The relevance of these results to recent tokamak experiments is discussed briefly.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.50.Gj Plasma heating by particle beams

Quasi‐linear and nonlinear theory of dissipative trapped particle instabilities

David A. Ehst

Phys. Fluids 20, 2076 (1977); http://dx.doi.org/10.1063/1.861837 (12 pages) | Cited 4 times

Online Publication Date: 26 August 2008

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An examination of particle linear orbits reveals how charged particles nonresonantly exchange energy with trapped particle modes in the presence of collisions. Phase space diffusion coefficients are constructed which describe the changes in the equilibrium particle distributions and which allow computation of the linear growth rates of the dissipative trapped particle instabilities. Wave‐induced detrapping and resonance broadening are considered as nonlinear modifications of the particle‐wave interaction and found to be ineffective as mechanisms to saturate growth of the dissipative trapped ion mode. Mode coupling with plasma diffusion across the magnetic field is a stronger effect for this and the dissipative trapped electron mode. Final evaluation of plasma diffusion coefficients is complicated by an ignorance of the nonlinear spectral shape.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.20.Dq Particle orbits

Accessibility of equilibria in an electron beam plasma system. II

Alexander Cavalli, John B. Greenly, and J. E. Walsh

Phys. Fluids 20, 2088 (1977); http://dx.doi.org/10.1063/1.861838 (5 pages)

Online Publication Date: 26 August 2008

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Equilibrium analysis of the long time evolution of an electron beam plasma system has demonstrated the accessibility of more than one stable equilibrium. Experimental observations indicate that the plasma finds each of these equilibria depending on the operating parameters and that therefore a knowledge of the overall equilibrium behavior is essential to a complete understanding of the evolution of the system.
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52.40.Mj Particle beam interactions in plasmas
52.25.Gj Fluctuation and chaos phenomena

Test particle study of nonlinear wave‐particle interaction in the magnetosonic mode: Pure sinusoidal wave model

Hiroshi Matsumoto

Phys. Fluids 20, 2093 (1977); http://dx.doi.org/10.1063/1.861839 (11 pages) | Cited 5 times

Online Publication Date: 26 August 2008

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A numerical study of the motions of test particles in a sinusoidal magnetosonic (hydromagnetic fast) wave is presented. The magnetic amplitude of the wave was varied from 1% to 40% of the external magnetic field strength. The motions of 400 particles are calculated in each computer run by time integration of the equation of motion, without the use of the guiding center approximation. The particles are initially distributed uniformly in space with a specified velocity distribution; the space and velocity distributions then evolve in time. For small wave amplitudes, the numerical results agree well with the small amplitude kinetic theory of collisionless Landau damping of hydromagnetic waves. In large amplitude cases, nonlinear effects such as particle trapping, saturation and oscillation characteristics of the average kinetic energy, and the diffusion of particles in velocity space are observed. The physical interpretation of these numerical results is discussed in terms of the guiding center approximation.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
95.30.Qd Magnetohydrodynamics and plasmas

Saturation of the cyclotron decay instability

J. L. Sperling

Phys. Fluids 20, 2104 (1977); http://dx.doi.org/10.1063/1.861840 (9 pages) | Cited 4 times

Online Publication Date: 26 August 2008

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The cyclotron decay instability results from the nonlinear interaction of a magnetosonic wave with two electrostatic ion‐cyclotron waves in a multispecies plasma. A saturation mechanism for the instability is the nonlinear ion‐cyclotron damping process involving the interaction of electrostatic ion‐cyclotron and hydromagnetic‐acoustic turbulence with a nonlinear plasma response near an ion‐cyclotron frequency. Strong nonlinear ion heating can be a consequence of the saturation particularly if electron Landau damping is reduced by quasi‐linear diffusion or trapping.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Collisional effects on trapped electron instabilities

K. T. Tsang, J. D. Callen, and P. J. Catto

Phys. Fluids 20, 2113 (1977); http://dx.doi.org/10.1063/1.861841 (8 pages) | Cited 3 times

Online Publication Date: 26 August 2008

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The effects of collisions on dissipative trapped electron instabilities are evaluated by distinguishing between the perpendicular and parallel electron velocity components when calculating trapped and untrapped electron contributions. The growth rate is obtained for all regimes of collisionality and reduces to previous results in appropriate limits. It is shown that the dominant effect of finite collisionality is to determine the number of trapped and untrapped electrons and that collisional broadening removes the resonant electron response only for collision frequencies greater than or equal to ten times the wave frequency, νe≳10ω. For such large νe/ω, ion‐ion collisions are found to exert a far stronger stabilizing influence than broadening.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Effect of electron‐ion collisions on the nonlinear state of the relativistic two‐stream instability

Lester E. Thode

Phys. Fluids 20, 2121 (1977); http://dx.doi.org/10.1063/1.861842 (7 pages) | Cited 14 times

Online Publication Date: 26 August 2008

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The analysis outlines conditions for the hydrodynamic interaction, including foil scattering and beam self‐magnetic field effects. For the hydrodynamic interaction, the oblique coupling coefficient model is extended to include the effect of a finite electron‐ion collision rate on the nonlinear state. Partial numerical simulation results are found to be in agreement with the model. Limitations due to temperature inhomogeneity along the deposition length and to increased deposition length are also discussed. It is found that an intense relativistic electron beam can couple its energy via the two‐stream instability to a high density 1017–1020 cm−3 plasma. It is required that the plasma be fully ionized, with an initial electron temperature of ≳10 eV for 1017 cm−3, 10–20 eV for 1018 cm−3, 15–50 eV for 1019 cm−3, and ∼100 eV for 1020 cm−3.
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52.40.Mj Particle beam interactions in plasmas
52.50.Gj Plasma heating by particle beams
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.25.Kn Thermodynamics of plasmas

Finite‐gyroradius stabilization of diffuse high beta stellarators

J. P. Freidberg and D. W. Hewett

Phys. Fluids 20, 2128 (1977); http://dx.doi.org/10.1063/1.861843 (11 pages) | Cited 10 times

Online Publication Date: 26 August 2008

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A method is described for estimating the finite gyroradius stabilization of m⩾2 magnetohydrodynamic modes in diffuse high‐β stellarators. The procedure combines both analysis and numerical computation. In particular, the difficult trajectory integrals which arise in the formulation are evaluated by plasma simulation techniques. The method is successfully applied to the m=2 modes in the high‐β, l=1 stellarator configuration. It is found that the stability criterion for diffuse profiles is somewhat more optimistic than earlier estimates based on the sharp boundary model.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)

Theory of the multiple potential well structure created by bipolar injection in spherical geometry

B. E. Cherrington and D. A. Swanson

Phys. Fluids 20, 2139 (1977); http://dx.doi.org/10.1063/1.861844 (6 pages) | Cited 2 times

Online Publication Date: 26 August 2008

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A theoretical analysis has been performed on the potential structure formed when electrons and ions are injected into the interior of a sphere. The solution of Poisson’s equation including spreads in the total energy and the angular energy of the injected particles has predicted a multiple potential structure very similar to that experimentally observed. The inclusion of trapped secondary electrons in the analysis also predicts a ’’triple‐well’’ structure similar to that assumed to have been formed in Hirsch’s original experiments.
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52.40.Mj Particle beam interactions in plasmas

Magnetosonic waves in the presence of a lower hybrid turbulence and plasma heating

Mukul Sinha and B. N. Goswami

Phys. Fluids 20, 2145 (1977); http://dx.doi.org/10.1063/1.861845 (3 pages) | Cited 1 time

Online Publication Date: 26 August 2008

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A theoretical investigation has shown that energy could be fed into a microturbulence from an externally excited low frequency magneto‐acoustic source. A magnetosonic wave, normally undamped in a quiescent plasma, is shown to be damped in the presence of a lower hybrid microturbulence which in turn effectively heats the plasma ions. This process does not require any threshold amplitude of the external pump wave and therefore, very small amplitude waves can deposit their energy into the plasma unlike the usual parametric heating schemes which demand a minimum threshold amplitude.
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52.50.Gj Plasma heating by particle beams
52.35.Dm Sound waves
52.35.Ra Plasma turbulence

Log‐normality of the vorticity at a fluid particle

R. J. Hill

Phys. Fluids 20, 2148 (1977); http://dx.doi.org/10.1063/1.861846 (2 pages) | Cited 1 time

Online Publication Date: 26 August 2008

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It is shown that the magnitude of the vorticity, at a given fluid particle in inviscid turbulent flow, is a log‐normal random function of time.
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47.32.Ef Rotating and swirling flows
47.27.-i Turbulent flows

Energy stability limit for rotation‐modified plane Poiseuille flow

Daniel F. Jankowski and David R. Squire

Phys. Fluids 20, 2149 (1977); http://dx.doi.org/10.1063/1.861847 (2 pages) | Cited 3 times

Online Publication Date: 26 August 2008

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The energy theory of hydrodynamic stability is applied to the flow between two parallel horizontal plates caused by a constant reduced pressure gradient in a system rotating about a vertical axis.
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47.20.-k Flow instabilities
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