Index of content:
Volume 25, Issue 11, November 1982

The touching pair of equal and opposite uniform vortices
View Description Hide DescriptionThe shape and speed of a pair of touching finite area vortices are calculated and an error in previous work corrected.

The interaction between topography and a nonlinearly stratified rotating fluid
View Description Hide DescriptionLaboratory experiments have been conducted in which a spherical solid obstacle has been towed steadily through a thermally stratified rotating fluid in order to determine the effects of the density‐profile shape upon the attenuation with height of the disturbance produced by the obstacle. The existence of a cutoff level in the fluid beyond which the disturbance is not detected is illustrated, and the dependence of this level upon local variations in density profile is studied. Measurements of velocity above and behind the obstacle are reported.

An energy loss coefficient in fluid buckling
View Description Hide DescriptionA jet of viscous fluid falling against a flat plate may become unstable and buckle. The buckling process is postulated as a discontinuity, and a simple model is developed that indicates a loss of energy in the fluid buckling. Experimental values of the energy loss coefficient are presented.

Subharmonic generation by resonant three‐wave interaction of deep‐water capillary waves
View Description Hide DescriptionSubharmonic generation has been observed during the propagation of deep‐water capillary waves. The observations are shown to be in agreement with the theory of degenerate resonant noncollinear three‐wave interaction in a nonlinear, dispersive medium.

Anomalous frequency spectrum of inertial waves in a finite, rotating, sectored cylinder
View Description Hide DescriptionIt is shown that an inviscid, incompressible liquid completely filling a finite, sectored, rapidly rotating cylinder, possesses a continuous inertial wave frequency spectrum rather than the usual denumerably infinite set of frequencies! A physical argument for this unusual phenomenon is presented along with reference to some confirmatory experiments.

The velocity field induced by a helical vortex filament
View Description Hide DescriptionAn exact analytical solution for the velocity field, both interior and exterior, induced by an infinite right‐handed helical vortex filament is derived. Due to the way the variables combine in this solution, the paper also shows that it is possible to derive a stream function for this nonaxisymmetric flow. Sample calculations of these expressions are included.

The stability of swirling flows at large Reynolds number when subjected to disturbances with large azimuthal wavenumber
View Description Hide DescriptionAn asymptotic theory is developed to describe the stability characteristics of a swirling axial flow at high Reynolds number R when subject to disturbances with a large azimuthal wavenumber n. It is based on an earlier study by Leibovich and Stewartson of the corresponding inviscid problem. The essence of the theory is to exploit the fact that the disturbance is concentrated on a narrow band at a finite distance from the axis decaying exponentially on either side. As an example to illustrate the theory, the stability characteristics of a trailing vortex is examined. A comparison with computed values of the neutral curves for n=1,2,3 shows that even at such low values of n the theory is generally qualitatively correct and in some respects is remarkably accurate. UFoff

Continuous temporal eigenvalue spectrum of an Ekman boundary layer
View Description Hide DescriptionIt is demonstrated that the perturbation equation governing small disturbances in an Ekman boundary layer possesses a double branched, continuous spectrum of temporal eigenvalues. The nature of these eigenvalues and their associated eigenfunctions is discussed and compared with that of the temporal spectrum of the Blasius boundary layer.

Similarity solutions and experiment for turbulent wakes
View Description Hide DescriptionAvailable data for the turbulent wake of unheated and heated cylinders are compared to far‐wake solutions obtained from the relevant equations prior to application of any closure assumption. It is found that such comparisons require a new determination of the virtual origin significantly different from traditional values and at the same time provide a sensitive criterion to decide if the stations at which data are collected are sufficiently far downstream for far‐wake solutions to apply.

The boundary layer behind the blast wave generated by a very intense explosion on a flat ground
View Description Hide DescriptionA strong explosion occurring on a flat ground generates a blast wave behind which an unsteady boundary layer sets in. It is shown that when the ground is insulated the boundary layer develops a self‐similar structure and its thickness does not depend directly on time to the first approximation.

A bimodal Maxwellian distribution as the equilibrium solution of the two‐particle regime
View Description Hide DescriptionThe Maxwellian distribution known as the one‐particle equilibrium solution is generalized to the two‐particle regime where homogeneous macroscopic fluctuations in the density, the velocity, and the temperature prevail. The equilibrium distribution has the form of a bimodal Maxwellian, namely, the average of two Maxwellians with thermodynamic parameters greater and smaller than the mean values by the root‐mean‐squared fluctuations. This result is shown to hold for monatomic gases with arbitrary intermolecular potentials. Turbulent reaction rate calculated with this distribution can be by the order of magnitude large compared with the Arrhenius law, in other words, far beyond the first order smallness of the temperature fluctuation if the activation energy is sufficiently high.

Kinetic analysis of evaporation and condensation in a vapor‐gas mixture
View Description Hide DescriptionEvaporation and condensation of vapor‐gas mixture is studied on the basis of the kinetic BGK–Morse model equation. The linearized kinetic model equation is solved using the half‐range Hermite polynomials and various slip coefficients are obtained. The obtained slip coefficient of vapor pressure is insensitive to the variation in concentration of a noncondensable gas. When the mean concentration of noncondensable gas is very small, an exponential distribution of noncondensable gas is obtained and a set of nonlinear equations is transformed to that of linear equations for pure vapor. It is found from the linear and nonlinear solutions that the impedance of mass flux in the two‐surface problem is composed of surface and induced resistances and that the latter is proportional to the total amount of the noncondensable gas rather than the mean concentration of it.

Nonlinear diffusion of test particles in the presence of an external conservative force
View Description Hide DescriptionThe diffusion of certain test particles that in the presence of an external constant conservative force, undergo collisions against the field particles of an infinite homogeneous host medium as well as between themselves, is studied on the basis of an integral reformulation of the relevant stationary spatially‐independent nonlinear integrodifferential Boltzmann equation. The existence and uniqueness of the solution for the distribution function of the test particles considered is investigated by an application of the contracting mapping principle for both the general nonlinear case and for the linearized one as resulting through an appropriate decomposition of the sought distribution function. Also, the case when the scattering probability is represented as a factorized expansion of finite rank is discussed in some detail.

Elementary derivation of Poisson structures for fluid dynamics and electrodynamics
View Description Hide DescriptionThe canonical Poisson structure of the microscopic Lagrangian is used to deduce the noncanonical Poisson structure for the macroscopic Hamiltonian dynamics of a compressible neutral fluid and of fluid electrodynamics.

Stability of a thick two‐dimensional quasineutral sheet
View Description Hide DescriptionThe stability of a two‐dimensional magnetic model of a thick quasineutral sheet including a small but finite normal magnetic field component is studied in a collisionless plasma. Such a magnetic configuration allows an adiabatic motion for electrons which are trapped in good agreement with the thick sheet model. A detailed kinetic study of the energy balance shows that the ion linear tearing mode instability is suppressed by the interaction between the perturbed electromagnetic field and the adiabatic electron motion; this interaction leads to a ‘‘compressibility’’ effect which prevents the instability onset. The connection with the magnetohydrodynamic energy principle for stability is demonstrated. A general formalism is developed for any magnetic configuration and applied to a parabolic and a magnetic island topology. Some conclusions concerning the nonlinear tearing mode behavior (explosive phase) are drawn.

Suppression of the drift‐cyclotron instability by lower‐hybrid‐drift turbulence
View Description Hide DescriptionThe nonlinear interaction of the drift cyclotron and lower‐hybrid‐drift modes is examined. A renormalized equation for the drift cyclotron ion response is derived and solved. Lower‐hybrid‐drift modes comprise the turbulent background. For levels of lower‐hybrid‐drift turbulence of eΦ/T _{ i }∼(m _{ e }/m _{ i })^{1/2}(ρ_{ i }/L)^{3/4}, the growth rate of the drift cyclotron mode begins to be reduced by ion cyclotron resonance broadening, which is the dominant nonlinear effect.

The nonlinear filamentation of lower‐hybrid waves by ion‐ion hybrid perturbations
View Description Hide DescriptionThe problem of the nonlinear filamentation of lower‐hybrid waves in a two‐ion species magnetized plasma has been investigated. The dominant nonlinear effect comes from the existence of two ion species if the concentration of second ion species is larger than (m _{ e }/m _{ i })^{ s−1} (with 1<s<3/2). The nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation describing the nonlinear self‐distortion of the propagation cones of lower‐hybrid waves due to the interaction with low‐frequency ion‐ion hybrid perturbations are derived for the case of fast phase variation. In the case of slow phase variation the nonlinear self‐distortion of the propagation cones of lower‐hybrid waves is described by the modified Korteweg–deVries equation when the ion‐ion wave is at the Buschbaum frequency. The nonlinear equation which governs the asymptotic state of filamentation admits an exact solution, describing solitons, envelope solitons, or cusped envelope solitons for the electric field. These solitons represent the nonlinear stage of the evolution of the purely growing mode which appears in the parametric analysis.

The stability of flute modes in the ELMO Bumpy Torus
View Description Hide DescriptionA radial normal mode analysis is carried out to study the stability of fluidlike flute modes in a simplified model of the ELMO Bumpy Torus. The corresponding stability conditions are obtained.

Analytic bumpy torus equilibrium
View Description Hide DescriptionThe equilibrium magnetic field of a bumpy torus confinement system is analyzed by expansion in the inverse aspect ratio. Decomposition of the plasma volume into low‐beta and high‐beta regions permits the derivation of relatively explicit formulas, which should be useful in bumpy torus transport and stability studies. In the low‐beta regions, which typically occupy most of the plasma volume, the magnetic field is computed through first order in the inverse aspect ratio, including plasma pressure correction terms. The high‐beta region is treated in a scalar pressure, thin‐ring approximation, without toroidal corrections; connection formulas for the change in flux‐surface geometry across the high‐beta annulus are obtained, together with an expression for the field inside the annulus. The analysis of both regions is completely general with respect to bump amplitude and bump shape.

Electron radial transport in tandem mirrors in the low collision frequency limit
View Description Hide DescriptionA variational principle formulation is used to calculate the electron radial transport coefficients in a nonaxisymmetric tandem mirror, in the low collisionality regime. Explicit analytical estimates are given for two important classes of electrons. The implications of symmetry, end currents, and ambipolarity are discussed in detail in order to demonstrate their potentially important effect on the radial particle loss rates.