Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetr...Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.展开更多
This paper generalizes the contour dynamics for single ring vortices to that for multiple ring vortices,wherein sixsets of numerical computation are performed.The phenomenon of the counterclockwise loop of a moving vo...This paper generalizes the contour dynamics for single ring vortices to that for multiple ring vortices,wherein sixsets of numerical computation are performed.The phenomenon of the counterclockwise loop of a moving vortex is clearly shown in the computational results and the asymmetric change with time of the vortex structure may serve as a pre-cursor for the phenomenon.Besides,we also discuss the dependence of the motion direction of a vortex upon the degreeof its contour denseness,and the dependence of the westward component of vortex motion upon its asymmetricstructure.The results are fairly consistent with those of previous dynamical analyses and numerical experiments.展开更多
Detennining the sequence of document production and stamping is one of the most important issues in the field of questioned document identification.In China,whether a contract or a document is legal or not,highly depe...Detennining the sequence of document production and stamping is one of the most important issues in the field of questioned document identification.In China,whether a contract or a document is legal or not,highly depends on the relationship between the generation time of the document?s content and its stamping.Usually,a formal(legal)document would become effective once a seal is affixed,and normally,the content of the document is generated first and then subsequently stamped after being approved by the relevant personnel.Therefore,correctly identifying the sequence used to produce a document is necessary to detennine whether it is authentic or whether it may have been forged.However,because of the interference of many factors,the identification of such kind of forged documents has long been considered one of the most difficult technical issues in the field of questioned document identification.In this work,four nondestructive approaches to determine the order of photocopying and stamping were investigated:The stereomicroscope method,fluorescence microscopy,the three-dimensional pseudo-color method,and the contour ring method.Each method is associated with its own advantages and disadvantages,but all have been shown to produce some useful results relevant for determining the sequence of photocopying and stamping.展开更多
基金The project supported by The National Education Commission of China and NASA under cooperative grant agreement # NCC5-34
文摘Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.
基金This work is supported by the National Natural Science Foundation of China.
文摘This paper generalizes the contour dynamics for single ring vortices to that for multiple ring vortices,wherein sixsets of numerical computation are performed.The phenomenon of the counterclockwise loop of a moving vortex is clearly shown in the computational results and the asymmetric change with time of the vortex structure may serve as a pre-cursor for the phenomenon.Besides,we also discuss the dependence of the motion direction of a vortex upon the degreeof its contour denseness,and the dependence of the westward component of vortex motion upon its asymmetricstructure.The results are fairly consistent with those of previous dynamical analyses and numerical experiments.
文摘Detennining the sequence of document production and stamping is one of the most important issues in the field of questioned document identification.In China,whether a contract or a document is legal or not,highly depends on the relationship between the generation time of the document?s content and its stamping.Usually,a formal(legal)document would become effective once a seal is affixed,and normally,the content of the document is generated first and then subsequently stamped after being approved by the relevant personnel.Therefore,correctly identifying the sequence used to produce a document is necessary to detennine whether it is authentic or whether it may have been forged.However,because of the interference of many factors,the identification of such kind of forged documents has long been considered one of the most difficult technical issues in the field of questioned document identification.In this work,four nondestructive approaches to determine the order of photocopying and stamping were investigated:The stereomicroscope method,fluorescence microscopy,the three-dimensional pseudo-color method,and the contour ring method.Each method is associated with its own advantages and disadvantages,but all have been shown to produce some useful results relevant for determining the sequence of photocopying and stamping.
