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Oct 1988

Volume 31, Issue 10, pp. 2739-3158

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Gravity flow of a viscous liquid down a slope with injection

Leonard W. Schwartz and Efstathios E. Michaelides

Phys. Fluids 31, 2739 (1988); http://dx.doi.org/10.1063/1.866977 (3 pages) | Cited 9 times

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The free‐surface lubrication equations are solved numerically for the time‐dependent three‐dimensional flow down an inclined plane produced by continuous injection through a circular orifice in the plane. The flow pattern ultimately becomes steady with stream depth and width scaling as the − (1)/(7) th power and (3)/(7) th power of the downslope distance from the orifice, in agreement with a known similarity solution. The predicted stream width gives partial agreement with a recent experimental result, even though significant thermal effects were present in the experiment. The physical prototype is flow of lava.
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47.10.-g General theory in fluid dynamics
47.50.-d Non-Newtonian fluid flows
47.27.-i Turbulent flows

Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder

C. H. K. Williamson

Phys. Fluids 31, 2742 (1988); http://dx.doi.org/10.1063/1.866978 (3 pages) | Cited 131 times

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The existence of a discontinuity in the Strouhal–Reynolds number relationship for the laminar vortex shedding of a cylinder is found to be caused by a change in the mode of oblique shedding. By ‘‘inducing’’ parallel shedding (from manipulating end conditions) the resulting Strouhal curve becomes completely continuous and agrees very well with the oblique‐shedding data, if it is transformed by S0=Sθ/cos θ (where Sθ is the Strouhal number corresponding with the oblique‐shedding angle θ). The curve also agrees with data from a completely different facility. This provides evidence that this Strouhal curve (S0) is universal (for a circular cylinder).
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47.27.W- Boundary-free shear flow turbulence

Viscous modulation of the Lamb dipole vortex

G. E. Swaters

Phys. Fluids 31, 2745 (1988); http://dx.doi.org/10.1063/1.866979 (3 pages) | Cited 10 times

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A simple analytical singular perturbation theory is developed to describe the viscous adiabatic decay of the two‐dimensional Lamb dipole vortex. The vortex parameters (translation speed, radius, and wavenumber) evolve so as to satisfy leading‐order globally averaged energy and enstrophy balances. These transport equations are shown to be solvability conditions for the asymptotic expansion. Extensions of the asymptotic procedure to other isolated vortex problems are discussed.
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47.20.-k Flow instabilities
47.32.Ef Rotating and swirling flows
47.15.ki Inviscid flows with vorticity

Analysis of energy transfer in direct numerical simulations of isotropic turbulence

J. Andrzej Domaradzki

Phys. Fluids 31, 2747 (1988); http://dx.doi.org/10.1063/1.866980 (3 pages) | Cited 26 times

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The energy transfer between wavenumber bands is calculated from the results of direct numerical simulations of isotropic, decaying turbulence. The results are consistent with the notion of the energy cascade induced by the interactions among wavenumbers of comparable lengths. The nonlocal interactions are also present and give rise to the inverse energy cascade.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.10.-g General theory in fluid dynamics
47.35.-i Hydrodynamic waves

‘‘Flicker’’ in small scale laser–plasma self‐focusing

S. V. Coggeshall, W. C. Mead, and R. D. Jones

Phys. Fluids 31, 2750 (1988); http://dx.doi.org/10.1063/1.866981 (3 pages) | Cited 14 times

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Small amplitude, short wavelength ion acoustic waves in laser‐produced plasmas cause fluctuations in the trajectories of light rays that can lead to time‐dependent, self‐sustaining shifting of focal spots and a somewhat random redistribution of the light near the critical surface. This flickering is seen in simulations involving small scale beam inhomogeneities over a uniform background laser profile, which model the center of a realistic laser beam. The effect can cause significant intensity multiplication in long scale length high‐Z plasmas with only modest beam imperfections.
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52.38.-r Laser-plasma interactions
52.35.Dm Sound waves
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.65.-y Plasma simulation

Electron–ion hybrid mode due to transverse velocity shear

G. Ganguli, Y. C. Lee, and P. J. Palmadesso

Phys. Fluids 31, 2753 (1988); http://dx.doi.org/10.1063/1.866982 (4 pages) | Cited 32 times

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It has been established that electrostatic ion‐cyclotron‐like and Kelvin–Helmholtz modes can be sustained by a transverse velocity shear for L>ρi, where L is the velocity shear scale length and ρi is the ion gyroradius. Here it is shown that if ρe<L≪ρi, where ρe is the electron gyroradius, then a short wavelength electron–ion hybrid mode can be excited around the lower hybrid frequency. Like the Kelvin–Helmholtz instability, an explicit dependence on the second derivative of the dc electric field is essential for the growth of this mode.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
94.30.cq MHD waves, plasma waves, and instabilities

A microscopic model of electrorheology

Paul M. Adriani and Alice P. Gast

Phys. Fluids 31, 2757 (1988); http://dx.doi.org/10.1063/1.866983 (12 pages) | Cited 73 times

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An electrorheological fluid is modeled as a concentrated suspension of hard spheres with aligned field‐induced electric dipole moments. The presence of dipole moments causes clustering of the particles into an anisotropic suspension characterized by a particle probability distribution function. The elastic shear modulus and the dynamic viscosity are calculated from a perturbation to the particle distribution as a result of a small amplitude, high frequency, oscillatory flow. The high frequency elastic shear modulus and the dynamic viscosity are shown as a function of particle concentration and electric dipole strength. Both the modulus and the viscosity increase strongly with particle concentration. Dynamic viscosity is insensitive to dipole strength, but elastic shear modulus increases strongly with dipole strength indicating the relative importance of the particle distribution to elastic properties. The results of these calculations provide insight into the relationship between the macroscopic properties of an electrorheological fluid and microscopic structural changes.
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62.10.+s Mechanical properties of liquids
47.65.-d Magnetohydrodynamics and electrohydrodynamics
51.10.+y Kinetic and transport theory of gases

The combined effects of hydrodynamic interactions and Brownian motion on the orientation of particles flowing through fixed beds

Eric S. G. Shaqfeh and Donald L. Koch

Phys. Fluids 31, 2769 (1988); http://dx.doi.org/10.1063/1.866984 (12 pages) | Cited 13 times

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In a previous publication [Phys. Fluids 31, 728 (1988)], the evolution of the orientation distribution in a dilute suspension of axisymmetric ‘‘tracer’’ particles flowing through a bed of fixed fibers or spheres was determined under conditions in which hydrodynamic interactions played a dominant role in determining particle orientation. In this paper, the previous results are extended to account for the effects of Brownian motion on the tracer particles and for different configuration statistics of the force in the fixed bed. In the former case, orientational evolution equations are developed and solutions obtained that are valid for large values of the rotary Peclet number (the parameter regime of greatest interest). In the latter case, it is demonstrated that, when the disturbance flow ceases to have fore–aft symmetry, a small orientational drift and dispersion are introduced into the resulting evolution equations. The latter effects are particularly important since they will occur in all fixed beds because of interactions between bed particles.
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47.15.-x Laminar flows
47.56.+r Flows through porous media

The measurement of shear‐induced diffusion in concentrated suspensions with a Couette device

Ali Nadim

Phys. Fluids 31, 2781 (1988); http://dx.doi.org/10.1063/1.866985 (5 pages) | Cited 5 times

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A novel theoretical scheme is presented, which permits measurements of the so‐called shear‐induced diffusivity in concentrated suspensions to be made based upon long‐time data collected in a two‐cylinder Couette device. For this purpose the motion of a single (labeled) suspended particle is analyzed as the suspension, which fills the region between the two concentric cylinders, is sheared by rotating the outer cylinder. As the particle samples all radial coordinates as a result of its lateral self‐diffusivity caused by collisions with other suspended particles, its azimuthal coordinate increases. For long times, a Taylor–Aris‐type dispersion analysis shows that both the mean angular position 〈θ〉 and the mean square deviation 〈(θ−〈θ〉)2〉 of the labeled particle grow linearly in time. The two coefficients that govern these linear growths are the mean angular velocity Ω∗ and twice the mean angular dispersivity math@B|θ, which are calculated herein as functions of the cylinder radii, particle size, rotation speed, and the shear‐induced diffusivity. Measurements of the latter of these, based upon the outlined long‐time data, can thus be made more accurately than those previously possible on the basis of short‐time analyses that neglected the presence of the walls of the Couette device and its curved geometry.
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47.55.Kf Particle-laden flows
82.70.Kj Emulsions and suspensions

The mechanics of spin coating of polymer films

C. J. Lawrence

Phys. Fluids 31, 2786 (1988); http://dx.doi.org/10.1063/1.866986 (10 pages) | Cited 79 times

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The process of spin coating is described, with particular attention to applications in microelectronics. The physical mechanisms involved in the process are discussed and those mechanisms that affect the final state are identified, viz., centrifugal and viscous forces, solute diffusion, and solvent evaporation: A model is proposed that incorporates only the latter mechanisms, with viscosity and diffusivity depending on solute concentration. The evaporation of solvent during spinning causes the solution viscosity to increase and the flow is reduced. The thickness of the final solid film is related to the thickness of a diffusion boundary layer near the free surface. The model predicts the final dry film thickness in terms of the primary process variables, spin speed, and initial polymer concentration. A similarity boundary‐layer analysis leads to a simple approximate result for the final film thickness that is consistent with limited experimental data, hf ∼KC0(ν0D0)1/4/Ω1/2, where K is a number of order unity and the other quantities are, respectively, the initial polymer concentration, the kinematic viscosity, the solute diffusivity, and the spin speed. The dependence on diffusivity has not previously been described theoretically. The total spin time is shown to be proportional to Ω−1, in agreement with experiment. The rate of solvent evaporation is shown to be proportional to Ω, which contradicts previous assumptions.
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68.15.+e Liquid thin films
68.03.Fg Evaporation and condensation of liquids
68.43.Mn Adsorption kinetics

Integrable four vortex motion

Bruno Eckhardt

Phys. Fluids 31, 2796 (1988); http://dx.doi.org/10.1063/1.867025 (6 pages) | Cited 28 times

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It follows from the Poisson brackets between constants of motion that the motion of four vortices of zero net vorticity is integrable if the total momentum vanishes. The phase space motion of this integrable case is analyzed. One stable and several unstable uniformly rotating configurations are identified.
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47.15.ki Inviscid flows with vorticity

Hamiltonian formulation of inviscid flows with free boundaries

Henry D. I. Abarbanel, Reggie Brown, and Yumin M. Yang

Phys. Fluids 31, 2802 (1988); http://dx.doi.org/10.1063/1.866987 (8 pages) | Cited 18 times

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The formulation of the Hamiltonian structures for inviscid fluid flows with material free surfaces is presented in both the Lagrangian specification, where the fundamental Poisson brackets are canonical, and in the Eulerian specification, where the dynamics is given in noncanonical form. The noncanonical Eulerian brackets are derived explicitly from the canonical Lagrangian brackets. The Eulerian brackets are, with the exception of a single term at each material free surface separating flows in different phases, identical to those for isentropic flow of a compressible, inviscid fluid. The dynamics of the free surface is located in the Hamiltonian and in the definition of the Eulerian variables of mass density, ρ(x, t), momentum density, M(x,t) [which is ρ times the fluid velocity v(x,t)], and the specific entropy, σ(x,t). The boundary conditions for the Eulerian variables and the evolution equations for the free surfaces come from the Euler equations of the flow. This construction provides a unified treatment of inviscid flows with any number of free surfaces.
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47.10.-g General theory in fluid dynamics
47.15.ki Inviscid flows with vorticity

Singular vortex systems and weak solutions of the Euler equations

Claude Greengard and Enrique Thomann

Phys. Fluids 31, 2810 (1988); http://dx.doi.org/10.1063/1.866988 (4 pages) | Cited 5 times

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The relationship of point vortex and vorton (and related) systems to weak solutions of the Euler equations is discussed. It is observed that point vortices are more sensible models of fluid flow than are vortons because the latter cannot arise as nice limits of solenoidal vorticity fields.
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47.10.-g General theory in fluid dynamics

The possibility of drag reduction by outer layer manipulators in turbulent boundary layers

Alexander Sahlin, Arne V. Johansson, and P. Henrik Alfredsson

Phys. Fluids 31, 2814 (1988); http://dx.doi.org/10.1063/1.866989 (7 pages) | Cited 5 times

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Experiments were carried out with the aim of investigating the possibility of obtaining a net drag reduction on a finite body by manipulating the outer layer structure of the turbulent boundary layer. The experiments were carried out in a 260 m long towing tank, where large eddy breakup devices (LEBU’s) were used in single and tandem configurations on a large flat plate. The total drag was measured directly by a force gauge, and the geometrical configuration parameters, as well as the chord Reynolds number, were varied over wide ranges. The highest chord Reynolds number tested was 260 000, which is within the range of interest for practical applications. Also, the device drag was measured directly in flight, which enabled evaluation of the performance of the manipulators, as well as determination of the total skin friction reduction. Despite a substantial skin friction reduction for certain configurations (7% averaged over the part downstream from the manipulators) as well as a low device drag, no drag reduction was found. The present results, and a critical evaluation of previously reported data, make any substantial net drag reduction by use of LEBU’s at high Reynolds numbers seem implausible.
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47.27.N- Wall-bounded shear flow turbulence

Space‐time correlations of wall pressure fluctuations in shock‐induced separated turbulent flows

J. P. Bonnet

Phys. Fluids 31, 2821 (1988); http://dx.doi.org/10.1063/1.866990 (13 pages)

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An experimental study of the structure of wall pressure fluctuations is performed in shock‐induced separated supersonic turbulent flows. Two test conditions are studied for external Mach numbers of 2.25 at low Reynolds number and Mach 3.3 at high Reynolds number. Piezoelectric pressure transducers, isolated from the main facility to minimize vibration effects, are used to sense the pressure fluctuations. Pressure fluctuations are given for several locations and analyzed in the frequency domain. The results exhibit the usual behavior. Space‐time correlations are measured and subsequently analyzed using coherence analysis. The results are discussed in terms of structural modifications induced by the shock. Typical results are given for several positions in the incoming boundary layer, at the mean shock location, and in the recirculation region. Some new features concerning the behavior of characteristic scales at the shock traverse are identified, and the results are compared and scaled for both test conditions.
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47.40.Nm Shock wave interactions and shock effects
47.27.N- Wall-bounded shear flow turbulence

Measurements of the free‐stream fluctuations above a turbulent boundary layer

D. H. Wood and R. V. Westphal

Phys. Fluids 31, 2834 (1988); http://dx.doi.org/10.1063/1.866991 (7 pages) | Cited 3 times

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In this paper an investigation of the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure is described. It is assumed that the fluctuations receive contributions from three statistically independent sources: (i) one‐dimensional unsteadiness, (ii) free‐stream turbulence, and (iii) the irrotational motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root‐mean‐square level of the axial velocity fluctuations of about 0.2%. All three velocity components were measured using an X‐wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity fluctuations, measured using two single‐wire probes. The results show that it is possible to separate the contributions to the rms level of the velocity fluctuations without resorting to the dubious technique of high‐pass filtering. This separation could be extended to the spectral densities of the contributions if measurements of sufficient accuracy were available.
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47.27.N- Wall-bounded shear flow turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Relative velocity fluctuations in turbulent flows at moderate Reynolds numbers. I. Experimental

P. Tong and W. I. Goldburg

Phys. Fluids 31, 2841 (1988); http://dx.doi.org/10.1063/1.866992 (8 pages) | Cited 20 times

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Turbulent pipe flow and grid flow have been explored by the scattering of light from small particles suspended in a fluid. Laser Doppler velocimetry and visual observation were used to characterize the gross features of the flows. However, novel information came from the homodyne correlation function g(t), which was measured as a function of the Reynolds number, the photon momentum transfer, and the size of the scattering volume. In terms of these control variables, g(t) was found to be of scaling form. Using such measurements one can deduce from the probability distribution function, P(V,R), that two particles, separated by a distance R, have velocity difference V(R,t). For small‐velocity fluctuations, the scaling behavior of g(t) implies that P(V,R) has the form Q[V/math(R)]/math(R). This self‐similarity in P(V,R) is seen only when Re exceeds a transition Reynolds number Rec. The measured scaling velocity math(R) has the form math(R)∼Rζ, with ζ increasing from 0 at Re=Rec to ∼ (1)/(3) at the maximum attainable levels of turbulence. This scaling behavior was seen in both the grid and pipe flows. By measuring g(t) at very small t, one can also obtain information about the large‐velocity fluctuations. It is found that P(V,R) is well approximated by the product of a Lorentzian and a Gaussian function with characteristic velocities math(R) and u(R), respectively. Here u(R) identifies the large‐velocity fluctuations.
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47.27.Cn Transition to turbulence
42.25.Dd Wave propagation in random media
42.25.Fx Diffraction and scattering
42.25.Ja Polarization

Some special wave solutions in an adiabatic gas in solid‐body rotation

N. Dodgson

Phys. Fluids 31, 2849 (1988); http://dx.doi.org/10.1063/1.866993 (5 pages)

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Waves occurring in a compressible inviscid fluid rotating as a solid body within a circular cylinder are reexamined for the particular case where the disturbance frequency in the rotating system is equal to twice that of the rotating fluid. It is shown that for this frequency there exists a stable wave provided a certain relationship is satisfied between the harmonic m, the axial wavenumber b, and the peripheral Mach number M of the flow. For γ=1.4, where γ is the ratio of the specific heats of the gas, there are solutions for only the first five harmonics and for γ=1 there are solutions for all harmonics. These results are at variance with the conclusions of Gans [J. Fluid Mech. 62, 657 (1974)] and Kerrebrock [AIAA J. 15, 794 (1977)], who suggested that there are no waves for this configuration.
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47.32.Ef Rotating and swirling flows
47.40.-x Compressible flows; shock waves

Heat transfer in rarefied gases: Critical assessments of thermal conductance and accommodation of argon in the transition regime

Lloyd B. Thomas, C. L. Krueger, and S. K. Loyalka

Phys. Fluids 31, 2854 (1988); http://dx.doi.org/10.1063/1.866994 (11 pages)

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Heat transfer measurements from thin filaments to argon gas in cells of cylindrical symmetry are made under extreme clean surface conditions so that known constant values of α, the thermal accommodation coefficient, on the filament pertain over the full range of pressures, 0.01–40 Torr. The results are used in an attempt to assess merit of principal theoretical treatments of heat transfer in the transition regime by extracting α according to each treatment and comparing results with the presumed known value. Before relative merit of the theories can be assigned with confidence, a wider differentiation in the α values obtained is needed. It is expected that this may result when similar experiments for the higher α gases, krypton and xenon, can be completed and critically examined.
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44.30.+v Heat flow in porous media
47.45.-n Rarefied gas dynamics

Cascade model of turbulence

J. Qian

Phys. Fluids 31, 2865 (1988); http://dx.doi.org/10.1063/1.866995 (10 pages)

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A simple low‐order dynamic system is proposed to simulate the energy cascade process of a fully developed hydrodynamic turbulence, and a series of numerical experiments is conducted. The main structural properties of this dynamic system are the same as those of the normalized Navier–Stokes equation. A quick estimation of its first Lyapunov exponent λ1 is made by calculating the chaos index at sampling points on trajectories. The large positive values (20–22) of λ1 indicate that the system is highly chaotic and that it has a strange attractor. After the transient period the dynamic system moves along its strange attractor, and a very wide inertial range is observed, in which the energy flux across the wavenumbers is a constant and equal to the energy dissipation rate. Moreover, the Kolmogorov − (5)/(3) spectrum is obtained as a statistical property of chaotic trajectories along the strange attractor.
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47.27.-i Turbulent flows
05.45.-a Nonlinear dynamics and chaos

Hydrodynamic instability in an ablatively imploded target irradiated by high power green lasers

H. Nishimura, H. Takabe, K. Mima, F. Hattori, H. Hasegawa, H. Azechi, M. Nakai, K. Kondo, T. Norimatsu, Y. Izawa, C. Yamanaka, and S. Nakai

Phys. Fluids 31, 2875 (1988); http://dx.doi.org/10.1063/1.866996 (9 pages) | Cited 23 times

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Time evolution of the ablation front displacement between concave and convex regions of a surface corrugated spherical target was observed by flash x‐ray radiography. The results are compared with calculations based on the linearized fluid equation combined with a one‐dimensional simulation to describe the ambient fluid motion. In the analysis, perturbation of the fluid is scaled up to kδ∼2π (k is the perturbation wavenumber and δ is the perturbation amplitude) for the acceleration phase with perturbation mode numbers of l=20 and 30. The practical perturbation of the target requires a relaxation time to form the nominal eigenstate of the Rayleigh–Taylor instability, which results in time delay of instability growth onset.
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52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
47.20.-k Flow instabilities

Scalings of implosion experiments for high neutron yield

H. Takabe, M. Yamanaka, K. Mima, C. Yamanaka, H. Azechi, N. Miyanaga, M. Nakatsuka, T. Jitsuno, T. Norimatsu, M. Takagi, H. Nishimura, M. Nakai, T. Yabe, T. Sasaki, K. Yoshida, et al.

Phys. Fluids 31, 2884 (1988); http://dx.doi.org/10.1063/1.866997 (10 pages) | Cited 102 times

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A series of experiments focused on high neutron yield has been performed with the Gekko‐XII green laser system [Nucl. Fusion 27, 19 (1987)]. Deuterium–tritium (DT) neutron yield of 1013 and pellet gain of 0.2% have been achieved. Based on the experimental data from more than 70 irradiations, the scaling laws of the neutron yield and the related physical quantities have been studied. Comparison of the experimental neutron yield with that obtained by using a one‐dimensional fluid code has led to the conclusion that most of the neutrons produced in the stagnation phase of the computation are not observed in the experiment because of fuel–pusher mixing, possibly induced by the Rayleigh–Taylor instability. The coupling efficiency and ablation pressure have been calculated using the ion temperature measured experimentally. A coupling efficiency of 5.5% and an ablation pressure of 50 Mbar have been obtained.
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52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.50.Lp Plasma production and heating by shock waves and compression

Renormalized perturbation theory: Vlasov–Poisson system, weak turbulence limit, and gyrokinetics

Y. Z. Zhang and S. M. Mahajan

Phys. Fluids 31, 2894 (1988); http://dx.doi.org/10.1063/1.866998 (10 pages) | Cited 3 times

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The self‐consistency of the renormalized perturbation theory of Zhang and Mahajan [Phys. Rev. 132, 1759 (1985)] is demonstrated by applying it to the Vlasov–Poisson system and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low‐beta gyrokinetic system. Comparison of this theory with other current theories is presented.
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52.35.Ra Plasma turbulence
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.25.Fi Transport properties
52.25.Dg Plasma kinetic equations

A statistical model of electron heating in localized Langmuir fields

W. Rozmus and J. C. Samson

Phys. Fluids 31, 2904 (1988); http://dx.doi.org/10.1063/1.866999 (10 pages) | Cited 6 times

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It is shown that the interaction of charged particles with localized, coherent, electrostatic wave packets can be described by a diffusion model, provided that the modes of each wave packet overlap. A theoretical model for the diffusion coefficient is proposed that takes into account the existence of large adiabatic islands, embedded within stochastic regions of the phase space. The model is based on the observation that particles in the stochastic regions interact independently with each wave packet, and consequently a time‐localized diffusion model can be used. Solutions of the diffusion equation, which use theoretical values for the diffusion coefficient, give very good predictions of the temporal evolution of the particle distribution functions and kinetic energy.
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52.38.-r Laser-plasma interactions
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
05.20.-y Classical statistical mechanics

Association between weakly relativistic ion modulation modes in a collisionless plasma

Yasunori Nejoh

Phys. Fluids 31, 2914 (1988); http://dx.doi.org/10.1063/1.867000 (6 pages) | Cited 11 times

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Association between weakly relativistic ion modulation modes described by the Korteweg–de Vries equation in the small wavenumber region and by the nonlinear Schrödinger equation in the finite wavenumber region is found in a collisionless unmagnetized plasma. It is shown that the stability criterion for the modulation of the ion wave envelope depends on the relativistic effect. The present results may explain the observations obtained in space plasmas.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
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