摘要:

Laser‐Doppler anemometer measurements upstream and in the wakes of vortex breakdowns of bubble and spiral types are described. Spectral analysis of the data indicates prominent oscillations in the wakes at less than 10 Hz. These oscillations correspond closely to theoretical predictions of the linearly most unstable normal modes of the time‐averaged mean flow profiles. The oscillations are more energetic, and vortex core expansions are greater for flows with a bubble form of vortex breakdown, which is therefore regarded as the stronger form of breakdown.

ISSN:0031-9171    

DOI:10.1063/1.862514

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

Isotropic turbulence is examined for the existence of conditional flow structures by computing estimates of the velocity u(x+r,t) given that the velocity at (x,t) assumes some specified value, u(x,t). In general, the best mean‐square estimate of u(x+r,t) is the conditional average ⟨u(x+r,t) ‖ u(x,t) ⟩. This quantity is approximated in terms of second‐ and third‐order two‐point spatial correlations using nonlinear estimation techniques. The estimate predicts conditional eddies that are vortex rings axisymmetric about the direction of u(x,t). Averaging these estimates over all values of u(x,t) yields two‐point moments that are correct through third order.

ISSN:0031-9171    

DOI:10.1063/1.862515

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

Free oscillations of an incompressible inviscid fluid in a rotating spherical shell are studied by means of the ray method, which is different from the conventional approach. Axisymmetric modes covering the whole sphere and asymmetric modes trapped in equatorial regions bounded by critical circles of constant latitude as well as in regions off the equator bounded by caustics are discovered. The anomalies at poles and critical circles of the ray method expansion are removed by means of uniform asymptotic expansions. The equations for the resonance frequencies of each of the various modes of oscillation are studied numerically.

ISSN:0031-9171    

DOI:10.1063/1.862516

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The stability of a Stokes’ layer of a particle‐fluid mixture is discussed. A set of coupled Orr–Sommerfeld equations governing the evolution of infinitesimal disturbances is derived. For low concentrations of coarse dust, it is found that for sufficiently large values of the particle relaxation time, the flow is unstable. Decreasing the particle relaxation time (by increasing the drag) eventually stabilizes the flow.

ISSN:0031-9171    

DOI:10.1063/1.862517

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The perturbation of Poiseuille pipe flow by nonuniform, axisymmetric magnetic fields with weak axial gradients is treated theoretically for small magnetic Reynolds numbers and finite Hartmann and Reynolds numbers. Numerical examples for pipe flow through a finite length magnet solenoid are given. The results indicate that separated flow may develop in the fringing magnetic fields accompanied by appreciable local static pressure gradients and high local current densities.

ISSN:0031-9171    

DOI:10.1063/1.862518

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

Recent observations of Yuen and Ferguson on the dynamical structure of nonlinearly saturated, spatially periodic solutions of the nonlinear Schro¨dinger equation are given a simple analytical explanation. It is shown that many nonlinear systems can be described as effectively possessing a finite number of degrees of freedom even though the evolution equations formally relate to a continuum. Powerful theorems in general dynamics then lead to the existence of generally recurrent motions which need not, however, be quasi‐periodic or even almost periodic. An explicit example is given to show that a system need not be conservative in order to exhibit recurrence. Explicit estimates of the effective number of degrees of freedom are given for the important nonlinear Schro¨dinger equation and the Korteweg–de Vries equation.

ISSN:0031-9171    

DOI:10.1063/1.862519

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The properties of convective cells and the diffusion resulting from such cells are significantly influenced by an inhomogeneity in the external confining magnetic field, such as that in toroidal plasmas. It is shown, first, that the zero‐frequency convective cell of the homogeneous medium (vortex) is transformed into the interchange flute mode in the presence of the field inhomogeneity. For stable interchange profiles, this has the effect of reducing the step size of the diffusion process. Second, in an inhomogeneous field, convective motions damp by magnetic pumping at a rate typically much faster than perpendicular viscous damping. This reduces the lifetime of the cell. The convective diffusion in the presence of a field inhomogeneity is estimated. For a thermal background, this diffusion is shown to be substantially smaller than classical diffusion. The influence of the field inhomogeneity is also shown to be significant for nonthermal backgrounds.

ISSN:0031-9171    

DOI:10.1063/1.862520

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The cross‐field transport due to the trapping of electrons in a finite amplitude wave (pseudo‐classical transport) is investigated. Both finite wave frequencies and magnetic shear are included. The single particle orbit equations are solved to obtain the trapping criterion as well as the trapped particle orbit width and bounce frequency. Using a random walk model, the scaling of the pseudo‐classical transport coefficients with the parameters of the plasma and wave are deduced. This scaling is employed to extend a previous calculation of the transport coefficients to include magnetic shear which is found to reduce these transport coefficients. Computer simulations of this transport process are presented. The measured transport rates are in very good agreement with the previous kinetic calculation in the absence of magnetic shear and with this extension of pseudo‐classical transport theory which includes magnetic shear.

ISSN:0031-9171    

DOI:10.1063/1.862521

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

Spectrum cascade in drift wave turbulence in a magnetized plasma as well as Rossby wave turbulence in an atmospheric pressure system are studied based on a three‐wave decay process derivable from the model equation applicable to both cases. The decay in the three‐way interaction occurs to smaller and larger values of ‖k‖. In a region of large wavenumbers this leads to the dual cascade; the energy spectrum cascades to smaller ‖k‖ and the enstrophy spectrum to larger ‖k‖, similar to the case of two‐dimensional Navier–Stokes turbulence. In a small wavenumber region a resonant three‐wave decay process dominates the cascade process, and an anisotropic spectrum develops. As a consequence of the cascade, zonal flows in the direction perpendicular to the direction of inhomogeneity appear which presents a potential implication for the particle confinement in a turbulent plasma.

ISSN:0031-9171    

DOI:10.1063/1.862504

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

A general formalism is developed to described the nonlinear evolution associated with the parametric decay of an intense, coherent electromagnetic wave into an electrostatic wave, its second harmonic, and scattered electromagnetic waves in a homogeneous plasma. It is assumed that all waves are coherent, and that the system is in a regime in which pump depletion may be neglected. Two classes of solutions are found. One class is explosively unstable, while the other consists of growing aperiodic oscillations. The evolution of modulational modes is discussed.

ISSN:0031-9171    

DOI:10.1063/1.862505

出版商:AIP    

年代:1979

数据来源: AIP