This paper presents an experimental investigation of the circulation of the horseshoe vortex system within the equilibrium scour hole at a circular pier, with the data measured by an acoustic Doppler velocimeter （ADV...This paper presents an experimental investigation of the circulation of the horseshoe vortex system within the equilibrium scour hole at a circular pier, with the data measured by an acoustic Doppler velocimeter （ADV）. Velocity vector plots and vorticity contours of the flow field on the upstream plane of symmetry （y = 0 cm） and on the planes ：e3 cm away from the plane of symmetry Cv = ~3 cm） are presented. The vorticity and circulation of the horseshoe vortices were determined using the forward difference technique and Stokes theorem, respectively. The results show that the magnitudes of circulations are similar on the planes y = 3 cm and y = -3 cm, which are less than those on the plane y = 0 cm. The circulation decreases with the increase of flow shallowness, and increases with the densimetric Froude number. It also increases with the pier Reynolds number at a constant densimetric Froude number, or at a constant flow shallowness. The relative vortex strength （dimensionless circulation） decreases with the increase of the pier Reynolds number. Some empirical equations are proposed based on the results. The predicted circulation values with these equations match the measured data, which indicates that these equations can be used to estimate the circulation in future studies.展开更多
Comparison and oscillation theorems which relate to the oscillatory behaviors among the members of a class of 'advanced type' difference equations are derived. Among others, these theorems show that oscillati...Comparison and oscillation theorems which relate to the oscillatory behaviors among the members of a class of 'advanced type' difference equations are derived. Among others, these theorems show that oscillation criteria for the standard second order linear difference equation can be applied to these equations. Oscillation criterion for a nonlinear advanced type difference equation is also derived as an application.AMS 1991 Subject classification: 39A10展开更多
Based on the fixed point theory for a Banach space, asymptotically constant solutions are founded for a second order delay system of difference equation.
文摘This paper presents an experimental investigation of the circulation of the horseshoe vortex system within the equilibrium scour hole at a circular pier, with the data measured by an acoustic Doppler velocimeter （ADV）. Velocity vector plots and vorticity contours of the flow field on the upstream plane of symmetry （y = 0 cm） and on the planes ：e3 cm away from the plane of symmetry Cv = ~3 cm） are presented. The vorticity and circulation of the horseshoe vortices were determined using the forward difference technique and Stokes theorem, respectively. The results show that the magnitudes of circulations are similar on the planes y = 3 cm and y = -3 cm, which are less than those on the plane y = 0 cm. The circulation decreases with the increase of flow shallowness, and increases with the densimetric Froude number. It also increases with the pier Reynolds number at a constant densimetric Froude number, or at a constant flow shallowness. The relative vortex strength （dimensionless circulation） decreases with the increase of the pier Reynolds number. Some empirical equations are proposed based on the results. The predicted circulation values with these equations match the measured data, which indicates that these equations can be used to estimate the circulation in future studies.
文摘Comparison and oscillation theorems which relate to the oscillatory behaviors among the members of a class of 'advanced type' difference equations are derived. Among others, these theorems show that oscillation criteria for the standard second order linear difference equation can be applied to these equations. Oscillation criterion for a nonlinear advanced type difference equation is also derived as an application.AMS 1991 Subject classification: 39A10
基金This work is supported by the Distinguished Expert Science Foundation of the Naval Aeronautical Engineering Institute.
文摘Based on the fixed point theory for a Banach space, asymptotically constant solutions are founded for a second order delay system of difference equation.
