摘要:

Experiments on steady fingers and their stability in Hele–Shaw cells, are reported. It is shown that the shape of steady fingers scales with a modified capillary number, Ca’, as suggested by McLean and Saffman [J. Fluid. Mech.102, 455 (1981) and our previous analysis [J. Fluid Mech.139, 291 (1984)]. The behavior at large Ca’is investigated by using a wide Hele–Shaw cell. It is observed that such fingers are unstable for Ca’>100, in agreement with the prediction by Taylor and Saffman (second symposium on naval hydrodynamics, 1958, p. 277) of instability as Ca’→∞. The mechanism is identified as one of tip‐splitting, which occurs periodically in the weakly supercritical regime, and in a more complex fashion for large Ca’.

ISSN:0031-9171    

DOI:10.1063/1.864947

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

The ideal magnetohydrodynamic instability of a symmetricq=1 magnetic island is studied by using an initial value method for a pressureless cylindrical tokamak plasma. It is shown that the island is unstable to a half‐coalescence motion which destroys the up–down symmetry of the magnetic configuration. The mode characteristics are qualitatively similar to those predicted by Bussacetal. [Phys. Lett.105A, 51 (1984)].

ISSN:0031-9171    

DOI:10.1063/1.864948

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

A new nonflute form of theE×Bshear‐driven trapped particle mode is obtained for a simplified square well equilibrium model of a tandem mirror. The mode is more unstable for a larger passing density in contrast to the curvature‐driven trapped particle mode. Under some circumstances this mode can avoid the stabilizing effect of strong anchor curvature by isolating to the center cell and can do so without paying the magnetohydrodynamic (MHD) penalty for bending the field lines, thus requiring a large center cell ion gyroradius for stabilization.

ISSN:0031-9171    

DOI:10.1063/1.864949

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

Time‐, frequency‐, and wavenumber‐resolved Thomson scattering techniques have been used to identify electron plasma waves driven at the quarter‐critical surface by a CO2laser in a preformed plasma. The clear signature of absolute stimulated Raman scattering was observed, namely &ohgr;p≊&ohgr;0/2 andkp≊k0. In addition, some plasma waves with larger wavenumber were seen, perhaps corresponding to coupling with ion waves produced by stimulated Brillouin scattering. The level of &ohgr;0/2 scattered light, calculated from the observed level of plasma waves, should have been several orders of magnitude above the detection threshold, yet no such emission was seen.

ISSN:0031-9171    

DOI:10.1063/1.864950

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

The marked divergence of experimentally observed plasma instability phenomena from the predictions of ideal magnetohydrodynamics led in the early 1960’s to the formulation of finite‐resistivity stability theory. Beginning in the 1970’s, advanced plasma diagnostics have served to establish a detailed correspondence between the predictions of the finite‐resistivity theory and experimental plasma behavior—particularly in the case of the resistive kink mode and the tokamak plasma. Nonlinear resistive‐kink phenomena have been found to govern the transport of magnetic flux and plasma energy in the reversed‐field pinch. The other predicted finite‐resistivity instability modes have been more difficult to identify directly, and their implications for toroidal confinement are still unresolved.

ISSN:0031-9171    

DOI:10.1063/1.864951

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

The stability of the interface between two viscous fluids is considered when the depth of the lower fluid is much less than the depth of the upper fluid. A long wavelength perturbation scheme is used to solve the linear stability problem and the equation governing the nonlinear evolution of the interface is deduced. The exact dispersion relation is derived for arbitrary values of wavelength and then simplified for large wavelength values. It is found that the flow is always linearly unstable when the lower fluid is also the more viscous fluid.

ISSN:0031-9171    

DOI:10.1063/1.864952

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

The contour dynamics numerical technique is used to study the coalescence of two equal uniform vortices in the presence of an externally applied stretching strain field. Plane three‐dimensional stretching is found to substantially inhibit vortex coalescence when the plane of the vortex axes is initially perpendicular to the plane of the straining motion. This behavior is interpreted qualitatively in terms of a purely two‐dimensional flow fully equivalent to the stretching configuration.

ISSN:0031-9171    

DOI:10.1063/1.864953

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

Numerical solutions are presented for forced spatially developing axisymmetric and two‐dimensional mixing layers. The numerical scheme employs quadratic upwind differencing for convection and a Leith type of temporal differencing in order to solve the incompressible Navier–Stokes and continuity equations. The applied forcing function is derived from linear inviscid stability theory. The resulting large‐scale vortex dynamics is visualized by means of streakline and isovorticity contour plots. It is seen that the vortex merging behavior in both types of mixing layers is determined by the subharmonics present in the forcing function. Manipulation of the vortex dynamics in a predictable fashion is possible through alterations in the frequency content of this applied forcing. Reynolds number is shown to be of only minor importance.

ISSN:0031-9171    

DOI:10.1063/1.864954

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

Periodic solutions of a nonlinear dispersive equation involving both growth and damping mechanisms are investigated numerically and theoretically. General features of equilibrium periodic states for a strongly dispersive case are found to be well explained by means of a perturbation analysis of the cnoidal wave solutions.

ISSN:0031-9171    

DOI:10.1063/1.864955

出版商:AIP    

年代:1985

数据来源: AIP

摘要:

First a small time analysis is developed for the first and second moments of the velocity (W) and displacement (Z) in one direction of particles marked at a given point in an inhomogeneous unsteady turbulent flow, in terms of the local energy dissipation rate, and the local derivatives of the second and third moments of the vertical component of the velocity field, ∂∼(u23)/∂zand ∼(∂u33)/∂z. Then the appropriate form of a Langevin equation in inhomogeneous turbulence is suggested, namely,dW=(−W/TL+a1)dt+a1/22d&ohgr;twherea1,a2, andTLare functions of the particle position and time, andd&ohgr;tis a random Gaussian velocity increment with ∼(d&ohgr;t)=0 and ∼((d&ohgr;t))2=dt. For simplicity, only one component of the particle motion,W(t), is considered. The functionsa1anda2are determined by relating the random walk model to the Eulerian conservation equations for the mass of the contaminant and volume of the flow (i.e., the continuity equation), using the Fokker–Planck equation and the Eulerian equations for the moments of a vertical velocity. The coefficientsa1anda2reduce to the same form as that obtained by the statistical analysis, namelya1=∂∼(u23)/∂z, (≊dW¯/dt, whent → 0) anda2=2∼(u23)/TL+d∼(u23)/dt(≊2∼(W’2)/TL+d∼(W’2)/dt, whent → 0).It is shown that the random walk model has the correct behavior ast/TL → 0. The theory is shown to agree reasonably well with the measurements of mean height and mean vertical displacement of particles released in a convective boundary layer [Q. J. R. Meteorol. Soc.102, 427 (1976)]. Yaglom’s [Isv. Atmos. Oceanic Phys.8, 333 (1972)] surface similarity result is recovered as a special case. Fort ≫ TL, and in a zero‐skewness steady turbulence, the random walk model reduces to the familiarK‐diffusion equation. Some examples are presented to show that mean and mean square particle displacements from the random walk model are virtually identical to those obtained from the analytical solution of the corresponding Eulerian moment equations. Careful analysis is still required when concentration distributions in turbulent flows near a boundary are evaluated using random walk models.

ISSN:0031-9171    

DOI:10.1063/1.864956

出版商:AIP    

年代:1985

数据来源: AIP