Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Initial development of microdamage under impact loading

In this paper, the initial development of microdamage in material subjected to impulsive loading was investigated experimentally and analytically with controllable short-load duration. Based on a general solution to the statistical evolution of a one-dimensional system of ideal microcracks, a prerequisite to experimental investigation of nucleation of microcracks was derived. By counting the number of microcracks, the distribution of nucleation of microcracks was studied. The law of the nucleation rate of microcracks can be expressed as a separable function of stress and cracksize. It is roughly linear dependence on loading stress. The normalized number density of microcracks is in agreement with that of a second-phase particle.

Nonequilibrium statistical mechanics of one-dimensional turbulence

The method of statistical mechanics is applied to the study of the one-dimensional model of turbulence proposed in an earlier paper. The closure problem is solved by the variational approach which has been developed for the three-dimensional case, yielding two integral equations for two unknown functions. By solving the two integral equations, the Kolmogorov k−5/3 law is derived and the (one-dimensional) Kolmogorov constant Ko is evaluated, obtaining Ko=0.55, which is in good agreement with the result of numerical experiments on one-dimensional turbulence.

Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

IP Simulation of Micro Gas Flows under 3-D Head Sliders

Gas film lubrication of a three-dimensional flat read-write head slider is calculated using the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method, respectively. The pressure distributions on the head slider surface at different velocities and flying heights obtained by the two methods are in excellent agreement. IP method is also employed to deal with head slider with three-dimensional complex configuration. The pressure distribution on the head slider surface and the net lifting force obtained by the IP method also agree well with those of DSMC method. Much less (of the order about 10(2) less) computational time (the sum of the time used to reach a steady stage and the time used in sampling process) is needed by the IP method than the DSMC method and such an advantage is more remarkable as the gas velocity decreases.

Adiabatic shear localization: occurrence, theories, and applications