摘要:

The cascade model of Desnyansky and Novikov is extended to include energy flow inward as well as outward from a givenk‐space shell. The stationary solutions for the energy spectrum are of the 1941 Kolmogoroff form, &egr;2/3k−5/3f(k/kd), but the scaling functionf(x) has a nonanalytic dependence on a parameterCof the model which represents the relative strength of inward and outward energy flow inkspace. ForC<1,f(0) is finite, and the energy dissipation rate &egr; is nonzero in the limit of zero viscosity. ForC≳1,f(x) behaves asx−&zgr;for smallxwith &zgr;=2 logC/log 2. This leads to an inertial range exponent for the energy spectrum of 5/3+&zgr;, and to an &egr; (&ngr;) which goes slowly to zero as the viscosity, &ngr;, goes to zero. The model may play the role of a mean field theory for strong turbulence in which fluctuations leading to intermittency are neglected. The parameterCwould then be a smooth function of the spatial dimensionality. A comparison with other recent work indicates that the crossover phenomenon whenC=1 occurs between two and three dimensions.

ISSN:0031-9171    

DOI:10.1063/1.861896

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

The joint probability density distributions,p(u,v), of theuandvturbulence components are presented for nine positions across a fully developed turbulent channel flow. These distributions were determined by using 512 000 pairs ofuandvvalues at each position and thus enable comparison of the relative character between the distributions. To show the contribution to the Reynolds stress, −&rgr;uv¯at each point in theu‐vplane, the distributions ofuvp(u,v) were determined. These distributions show the relative contributions touv¯as a function of position across the channel. Finally, the distributions ofp(u,v) are compared with those ofuvp(u,v). The most probable pairs of velocities do not produce the largest contribution touv¯.

ISSN:0031-9171    

DOI:10.1063/1.861897

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

A system ofNtwo‐dimensional vortices interacting in a bounded region can be described by the statistics of the coordinates of the vortices or by the statistics of the Fourier coefficients of the vorticity field. It is shown that both descriptions give equivalent results. A high energy expression for the probability distribution function of the Fourier coefficients is derived and shown to be non‐Gaussian; it has at least two, and in some cases a continuum of, equal height maximum points corresponding to distinct, but equally probable, equilibrium states. Other stationary points previously thought to be metastable states are shown to be saddle points of the distribution function and hence unstable.

ISSN:0031-9171    

DOI:10.1063/1.861874

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

The behavior of linear perturbations in an incompressible fluid undergoing acceleration by radiation pressure is examined. A general formalism is developed, and explicit results are given for several examples in which the equilibrium density is a constant. In that case, the sign of the derivative of the local radiative acceleration by the optical depth determines the stability of the short wavelength normal modes. Long wavelength perturbations can be overstable independent of the shorter wavelength behavior. When an external gravity is introduced, a transition, continuous in the strength of that external gravity, back to the ordinary Rayleigh–Taylor instability appears.

ISSN:0031-9171    

DOI:10.1063/1.861898

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

A theoretical and computational study has been made of plasma phenomena occurring when a hot, dense plasma containing a transverse magnetic field is brought into sudden contact with a cold metal wall; thermal and magnetic boundary layers develop. The time evolution of the plasma temperature, pressure, the charged and neutral particle concentration, magnetic and electric field strengths, and the plasma current density in the neighborhood of the solid surface are investigated. The rate of energy transfer from the plasma to the wall is calculated, and the conditions under which wall surface melting occurs are estimated. The physical conditions previously studied experimentally by Feinberg, are calculated, and the predicted rate of energy transfer from the plasma to the wall is found to be in good agreement.

ISSN:0031-9171    

DOI:10.1063/1.861899

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

The axial flow of a supersonic high density plasma beam into an asymmetric mirror machine has been investigated experimentally. It has been found that in front of the second mirror peak, two supersonic‐subsonic flow transitions and shock formations occur. The subsequent motion upstream, of the first and stronger shock front has been measured by the time‐of‐flight method through diamagnetic loop and electric double probe signals. The shock front speed has been found to be one third the speed of sound in the neighborhood of the sonic transition and decreases to zero ahead of the upstream mirror.

ISSN:0031-9171    

DOI:10.1063/1.861900

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

Based on the approximations of slow time variation and slow axial coordinate variation in an ideal magnetohydrodynamic flow, a simplified set of equations is obtained which applies to the problem of plasma outflow from a theta pinch. The characteristic speed of the flow, the signal speed, is the cusp wave speed. In this model, no high speed Alfve´n waves are present in the low density region. An argument is presented indicating the existence of shocks in the low density outflow region. It is possible that such shocks may permit the analogy of hydrodynamic choking of the flow. A numerical scheme is described for computing a solution of the model equations. A sample computation gives plasma line density profiles and mass flux profiles for one particular case. The computation could not be carried out long enough to see pronounced shock effects in the main body of the plasma. The flow did not appear to approach a steady flow, but it did indicate the great effect of the flow in the throat on the remainder of the flow.

ISSN:0031-9171    

DOI:10.1063/1.861875

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

An analytic study of small amplitude perturbations of a cyclindrical tokamak, using the nonlinear, helically symmetric, reduced magnetohydrodynamic equations of Kadomtsev and Rosenbluth is presented. Results are compared with those of a numerical study of these reduced equations.

ISSN:0031-9171    

DOI:10.1063/1.861901

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

A like particle collision operator is derived for arbitrary values of the product of poloidal wavenumber times gyroradius by employing an ordering in which gyroradius corrections are retained in lowest order and the radial dependence appropriate for sheared magnetic fields is included. In addition, neoclassical, drift, finite &bgr; (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are considered.

ISSN:0031-9171    

DOI:10.1063/1.861902

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

The complete two‐dimensional structure of the dissipative trapped‐electron mode over its full width, which may extend over several mode‐rational surfaces, is discussed. The complete integrodifferential equation is studied in the limitkr&rgr;i<1, where &rgr;iis the ion gyroradius, andkr, the radial wavenumber, is regarded as a differential operator. This is converted into a matrix equation which is then solved by standard numerical methods. Solutions obtained are in reasonably good agreement with one‐dimensional analytic solutions, in the limits where such results are expected to be valid. More significantly, the present approach can readily treat many physically important cases for which purely analytic solutions are difficult to obtain. The results indicate that the differential equation formulation of the eigenmode equation is valid only for long wavelength modes (k&Vthgr;&rgr;i≲0.3, withk&Vthgr;being the poloidal wavenumber). For such cases it is found that shear stabilization estimates obtained from the one‐dimensional radial solution are quite inaccurate for modes overlapping only a small number of mode‐rational surfaces, but become more accurate for modes overlapping many mode‐rational surfaces.

ISSN:0031-9171    

DOI:10.1063/1.861876

出版商:AIP    

年代:1977

数据来源: AIP