摘要:

Experimental results are presented describing the buckling type of instability of thin layers of very viscous liquids subjected to linear shear flow. If the dimensionless shear stress in the layer exceeds a critical value, the layer will buckle in a manner similar to the buckling of a thin elastic plate. The stability criteria are obtained as a ratio of the destabilizing viscous stresses relative to the stabilizing surface tension and gravitational forces.

ISSN:0031-9171    

DOI:10.1063/1.863241

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The classical Kelvin–Kirchhoff equations of motion of a rigid body in an inviscid, unbounded fluid are generalized for the case where other fixed boundaries are present. An interesting by‐product of the derivation is a relation, new to the authors, between the direction cosines of the body axes relative to fixed axes and kinematic parameters of the angular motion of the body.

ISSN:0031-9171    

DOI:10.1063/1.863248

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

A density oscillator is studied which consists of two fluids of different density separated by a horizontal wall with the dense fluid at the upper side. A small hole connects the fluids, through which fluid is interchanged with distinct pulses. The pulse time is studied experimentally and a dimensional analysis is performed to find the relevant parameters governing the pulse time.

ISSN:0031-9171    

DOI:10.1063/1.863228

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

A localized wave propagating horizontally at speedcthrough a fluid of arbitrary depthHwhich consists of a lower vertical layer (thicknessL) with a weak‐depth‐dependent density below an upper layer of constant density is considered. The flow is characterized by Long’s equation for the stream function &psgr;. Exact analytic results are obtained for &psgr; throughO[1/(h−1)] and the wave speed through orderO[1/(h−1)2],h=H/L. The terms in &psgr; ofO[1/(h−1)2] are obtained numerically. Using these results the range of validity of such a perturbative approach is examined.

ISSN:0031-9171    

DOI:10.1063/1.863224

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The long‐time behavior of the modulational instability of the nonlinear Schro¨dinger equation is investigated. Linear stability analysis shows that a finite amplitude uniform wave train is unstable to infinitesimal modulational perturbations with sufficiently long wavelengths while it is stable for perturbations with short wavelengths. Near the threshold for instability, the long‐time behavior of the unstable modulation is obtained by means of the multiple time scale technique. As a result, the Fermi–Pasta–Ulam recurrence is rediscovered, in agreement with recent experiments and with a numerical solution of the problem at hand.

ISSN:0031-9171    

DOI:10.1063/1.863242

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Various types of traveling waves may be injected into a tokamak to continuously sustain the toroidal current. Interest in this problem arises from the possibility of operating tokamak reactors in the steady state. The low‐frequency waves most suitable for this task are identified in terms of the power cost for deployment in a reactor. Means of exciting these waves and tradeoffs with design criteria are discussed. A comparison is made with the alternative attractive regime of high‐frequency waves. Conclusions are based, in part, on the numerical solution of the two‐dimensional Fokker–Planck equation with an added quasi‐linear term due to the waves.

ISSN:0031-9171    

DOI:10.1063/1.863243

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

An equation of motion is derived which describes finite‐wavelength (i.e., axial wavelength ∼ plasma radius) oscillations of a Vlasov‐ion, fluid‐electron plasma in a diffuse, near‐&Vthgr; pinch geometry. The equations include simultaneous geometric and ion kinetic effects. For a screw‐pinch geometry, and with isothermal electrons, these equations are shown to be equivalent to the guiding‐center equations. Boundary conditions and a closed‐form solution for the sharp‐profile case are discussed.

ISSN:0031-9171    

DOI:10.1063/1.863244

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Ways have been found to significantly upgrade the resolution of an equilibrium and stability code that is based on the variational principle of ideal magnetohydrodynamics. Nonlinear saturation of ballooning modes for tokamaks has been demonstrated using a revised version of the code. Second stability regions are calculated from the nonlinear dependence of &dgr;Won &bgr;. Anl=2,3 torsatron is described that appears to have no ideal magnetohydrodynamic instabilities for &bgr; as high as 5%.

ISSN:0031-9171    

DOI:10.1063/1.863245

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The space‐time evolution of the drift‐cyclotron instability as influenced by the nonlinear shift in the ion‐cyclotron frequency is studied analytically, numerically, and by computer simulation. The analysis is specialized to the case of a single coherent wave with frequency near both a cyclotron harmonic and the ion diamagnetic frequency. Such an analysis is motivated by observations of large‐amplitude ion‐cyclotron waves in the 2XIIB mirror experiment, which were highly monochromatic and often exhibited these frequency characteristics. A nonlinear dispersion relation describing saturation of the instability is derived by means of a self‐consistent analytical solution of the Vlasov–Poisson equations to third order in the wave amplitude. Solitary wave and self‐similar solutions are obtained that describe nonlinear wave propagation. Numerical solution of a nonlinear evolution equation and particle simulation confirm the analysis.

ISSN:0031-9171    

DOI:10.1063/1.863246

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The time evolution of tearing modes in toroidal geometry is studied in the low‐&bgr; and large aspect ratio limit. An initial value three‐dimensional computer code which numerically advances the reduced set of resistive magnetohydrodynamic equations is employed. Toroidicity has, in general, a destabilizing effect on tearing modes in this limit. A generalization of &Dgr;′ formalism can be used to study the linear regime. The results obtained in this way are in very good agreement with the results from the initial value code. The nonlinear phase of the evolution is also followed numerically. In the case of strong interaction of different helicities, a larger region of stochastic magnetic field lines results than in the cylindrical geometry case.

ISSN:0031-9171    

DOI:10.1063/1.863247

出版商:AIP    

年代:1981

数据来源: AIP