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.

An asymptotic analysis for one dimensional stress wave propagation in damaged viscoelastic media

A regular perturbation technique is suggested to deal with the problem of one dimensional stress wave propagation in viscoelastic media with damage. Based upon the first order asymptotic solution obtained, the characteristics of wave attenuation are studied. In fact, there exist three different time-dependent phenomena featuring the dynamic response of the materials, the first expressing the characteristics of wave propagation, the second indicating the innate effect of visco-elastic matrix and the third coming from the time dependent damage. The comparision of first order asymptotic solution with the numerical results calculated by a finite difference procedure shows that the perturbation expansion technique may offer a useful approach to the problem concerned.

Some theoretical aspects of the simplified Navier-Stokes(SNS) equations

This study deals with the formulation, mathematical property and physical meaning of the simplified Navier-Stokes (SNS) equations. The tensorial SNS equations proposed is the simplest in form and is applicable to flow fields with arbitrary body boundaries. The zones of influence and dependence of the SNS equations, which are of primary importance to numerical solutions, are expounded for the first time from the viewpoint of subcharacteristics. Besides, a detailed analysis of the diffusion process in flow fields shows that the diffusion effect has an influence zone globally windward and an upwind propagation greatly depressed by convection. The maximum upwind influential distance of the viscous effect and the relative importance of the viscous effect in the flow direction to that in the direction normal to the flow are represented by the Reynolds number, which illustrates the conversion of the complete Navier-Stokes (NS) equations to the SNS equations for flows with large Reynolds number.

Optimization of tried wave-function in quantum monte-carlo method

A method for optimizing tried wave functions in quantum Monte Carlo method has been found and used to calculate the energies of molecules, such as H-2, Li-2, H-3+, H-3 and H-4. Good results were obtained.

Standing wave of finite-amplitude in an circular basin with uneven bottom

The effect of the particle cover over the density interface between two layers of fluids and of the suspended solid particles in the upper turbulcnt layer on the turbulent entrainment has been studied experimentally. The entrainment distance D is a function of the time of power: D=kt, where =0.200-0.130p. For suspended particles in the upper layer and pure 2-layer fluid is equal to 0.200, but the value of k for the suspended particles is smaller than that for the pure 2-layer fluid. The non-dimensional entrainment velocity is E=KRiln, where n=1.50+0.93 p. It is shown that the particle cover over the interface changes the power of Ril in the entrainment and hinders the turbulent entrainment. The variation rule of E for the suspended particles is the same as that for the pure 2-layer fluid, but the K value of the former is smaller than that of the latter. The turbulent mixing mechanism has been discussed.

Hierarchal structure of the simplified Navier-Stokes equations (SNSE) and its mechanical connotation and application

The hierarchial structure and mathematical property of the simplified Navier-Stokesequations (SNSE) are studied for viscous flow over a sphere and a jet of compressible flu-id. All kinds of the hierarchial SNSE can be divided into three types according to theirmathematical property and also into five groups according to their physical content. Amultilayers structure model for viscous shear flow with a main stream direction is pre-sented. For the example of viscous incompressible flow over a flat plate there existthree layers for both the separated flow and the attached flow; the character of thetransition from the three layers of attached flow to those of separated flow is elucidated.A concept of transition layer being situated between the viscous layer and inviscidlayer is introduced. The transition layer features the interaction between viscous flow andinviscid flow. The inner-outer-layers-matched SNSE proposed by the present author inthe past is developed into the layers matched (LsM)-SNSE.

Fission of solitary wave in stratified fluid

In this paper, we study the fission of a solitary wave in the stratified fluid with a free surface. It has been discovered that there is no difference between the fissions of the internal solitary waves in odd or even modes, and the effect of the stratification on the fission of a surface solitary wave can almost be neglected

Simplified Navier-Stokes equations (SNSE)

Ten kinds of the simplified Navier-Stokes equations (SNSE) are reviewed and also used to calculate the Jeffery-Hamel flow as well as to analyze briefly the seven kinds of flows to which the exact solutions of the complete Navier-Stokes equations (CNSE) have been found. Analysis shows that the actual differences among the solutions of the different SNSE can go beyond the range of the order of magnitude of Re-1/2 and result even in different flow patterns, therefore, how to choose the viscous terms included in the SNSE is worthy of notice where Re=S∞u∞ L/μ∞ is the Reynolds numbers. For the aforesaid eight kinds of flows, the solutions to the inner-outer-layer-matched SNSE and to the thin-layer-2-order SNSE agree completely with the exact solutions to CNSE. But the solutions to all the other SNSE are not completely consistent with the exact solutions to CNSE and not a few of them are actually the solutions of the classical boundary layer theory. The innerouter-layer-matched SNSE contains the shear stress causing angular displacement of the inormal axis with respect to the streamwise axis and the normal stress causing expansion-contraction in the direction of the normal axis and the viscous terms being of the order of magnitude of the normal stress; and it can also reasonably treat the inertial terms as well as the relation between the viscous and inertial terms. Therefore, it seems promising in respects of both mechanics and mathematics.

Effect of current on the evolution of a solitary wave

In this paper, the effect of current on the evolution of a solitary wave is studied. The governing equation in the far field, KdV equation with variable coefficients, is derived. A solitary wave solution is obtained. The fission of a solitary wave is discussed, and the fissible region on the Q～h2-plane and the criterion of the number of the solitary waves after fission are found.

Naive asymptotic expansion of the water wave generated by a slowly moving body

It is pointed out that the naive asymptotic expansion does not satisfy all the body boundary condition. A nonhomogeneous body boundary condition is obtained from this expansion. It is this condition that the additional wave term must satisfy. Moreover, because of this condition, the wave term must appear. It is pointed out that the zeroth approximation in the naive asymptotic expansion has weak singularity and the singularities become still stronger in the subsequent approximations.

T.E. wave in inhomogeneous magnetized plasma-filled cylindrical waveguide

The T. E. wave in cylindrical wavegulde filled with inhomogeneous plasma immersed in the external uniform longitudinal magnetic field is investigated. The analytic solution expressed in polynomial formed by cutting the confluent hypergeometric function is obtained. Furthermore the eigenfrequency of T. E. wave is obtained.

The wave model of mesothermal plasma near wakes and Korteweg-de Vries equation

The stationary two-dimensional (x, z) near wakes behind a flat-based projectile which moves at a constant mesothermal speed (V∞) along a z-axis in a rarefied, fully ionized, plasma is studied using the wave model previously proposed by one of the authors (VCL). One-fluid theory is used to depict the free expansion of ambient plasma into the vacuum produced behind a fast-moving projectile. This nonstationary, one-dimensional (x, t) flow which is approximated by the K-dV equation can be transformed, through substitution, t=z/V∞, into a stationary two-dimensional (x, z) near wake flow seen by an observer moving with the body velocity (V∞). The initial value problem of the K-dV equation in (x, t) variables is solved by a specially devised numerical method. Comparisons of the present numerical solution for the asymptotically small and large times with available analytical solutions are made and found in satisfactory agreements.