摘要:

The stability of a spheromak with an energetic ion ring, carrying a current comparable to the plasma current, to the tilt mode is considered. For small departures from sphericity a perturbative approach is applied to an appropriate energy principle in order to calculate the lowest nontrivial kinetic contribution of the ion ring. An analytic stability criterion is obtained. It is seen that the prolate configuration becomes more stable while the oblate one is less stable than in the absence of the ring. The prolomak becomes stable when the ring kinetic energy exceeds the magnetic energy within the separatrix.

ISSN:0031-9171    

DOI:10.1063/1.866823

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Using a simple model for the layer of the tearing mode, it is demonstrated that toroidally coupled tearing modes with two rational surfaces are most unstable when the &ohgr;*’s of the electrons at the rational surfaces are equal. The onset of instability may then occur because of the tuning of &ohgr;* rather than the passage of &Dgr;’‐like quantities through zero. This mechanism for the onset of instability is sharp since the resonance is narrow. The effect of toroidal rotation is also discussed.

ISSN:0031-9171    

DOI:10.1063/1.867019

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The nonlinear stages of two‐dimensional immiscible displacement processes in Hele–Shaw flows are investigated by means of large scale numerical simulations based on a purely Lagrangian vortex method. The vortex sheet at the interface between the two fluid phases is discretized into circular arcs with a continuous distribution of circulation, which renders our numerical technique highly accurate. A complicated unsteady growth mechanism is observed for the emerging viscous fingers, involving a combination of spreading, shielding, and tip splitting. As the surface tension is further reduced, smaller length scales arise and the fingertip exhibits a new splitting pattern in which three new lobes emerge instead of two. Monitoring the velocity as well as the radius of curvature at the fingertip demonstrates that the instability of the finger evolves in an oscillatory fashion. The two‐lobe and the three‐lobe splitting can thus be explained as different manifestations of the same instability mode. Comparison with experiment shows good qualitative but only fair quantitative agreement. By imposing a constraint on the curvature at the fingertip, experimental results, which show fingers of width considerably smaller than half the cell width and exhibit ‘‘dendritic’’ instability modes, are reproduced.

ISSN:0031-9171    

DOI:10.1063/1.866824

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The penetration of a front of light fluid into a heavy fluid in a Rayleigh–Taylor unstable flow is studied by using a model that simulates the competition among the bubbles formed in the interface when the density ratio of the two fluids is very large. Several different initial conditions have been considered, and it is found that the front moves with constant acceleration. The values obtained for the acceleration of the front are in very good agreement with experimental results obtained by Read [Physica D12, 45 (1984)].

ISSN:0031-9171    

DOI:10.1063/1.866825

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface. The model is compared to solutions of the full Euler equations for compressible two phase flow, using numerical solutions based on the method of front tracking. The front tracking method has the distinguishing feature of being a predominantly Eulerian method in which sharp interfaces are preserved with zero numerical diffusion. Various regimes in the statistical model exhibiting qualitatively distinct behavior are explored.

ISSN:0031-9171    

DOI:10.1063/1.866826

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The fluid flow outside of a stretching cylinder is studied. The problem is governed by a third‐order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier–Stokes equations. Because of algebraic decay, an exponential transform is used to facilitate numerical integration. Asymptotic solutions for large Reynolds numbers compare well with numerical results. The heat transfer is determined.

ISSN:0031-9171    

DOI:10.1063/1.866827

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The onset of chaos in passive advection of particles by flow caused by a pulsed source–sink system is documented. This type of model is of interest in various applications. It is of fundamental interest as the first example of a flow without circulation about any contour at any instant displaying chaotic particle paths. Standard chaos diagnostics such as Poincare´ sections and Lyapunov exponents are studied as are more conventional flow visualization measures such as streaklines. Numerical stirring experiments for various collections of particles are performed and the properties of a certain one‐dimensional map induced by the two‐dimensional flow are examined.

ISSN:0031-9171    

DOI:10.1063/1.866828

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The major flow development in the region within a distanceO((aR)1/2) from the entrance of a curved pipe occurs near the pipe wall, whereais the radius of the pipe cross section, assumed circular, andRis the radius of curvature of the central axis of the pipe. A three‐dimensional boundary‐layer solution is obtained for elucidating the physics of this developing flow; in particular, the effect of nonzero curvature ratio &agr;=a/Ron the geometric similarity of the flow. The numerical results show that the series solution in terms of &agr; is valid only when &agr;≤0.1 ands≤0.1 (aR)1/2, wheresis the distance from the inlet along the pipe axis. The crossover of the axial wall shear is purely a geometric property and its location is a strong function of &agr;. It is also demonstrated that (aR)1/2is the proper length scale by showing that the solution of the first region,s∼O(a), is included in that of the second,s∼O(aR)1/2.

ISSN:0031-9171    

DOI:10.1063/1.866829

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Numerical simulations using a finite volume method with primitive variables formulation are presented for a natural convection flow in the Czochralski melt. In the limit of very small Prandtl numbers it is shown that unsteadiness appears in the form of regular oscillations for sufficiently high values of the Rayleigh number. Such regular oscillations are preceded by a multicell motion structure in the melt, with flow separation at the wall. The critical value of the Rayleigh number for the onset of the oscillations is determined by carrying out a series of time dependent calculations.

ISSN:0031-9171    

DOI:10.1063/1.866830

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The dynamics of a gas in a time‐dependent host medium is studied by means of a generalized Boltzmann equation. Removal and regeneration events, as well as linear external sources, are taken into account. The corresponding continuity equation is solved, and the time evolution of the system is investigated, with particular attention paid to its asymptotic regime.

ISSN:0031-9171    

DOI:10.1063/1.866831

出版商:AIP    

年代:1988

数据来源: AIP