The propagation of Rossby waves on the Earth’s δ-surface is discussed in a reference frame propagation with the zonal phase speed of the wave.In this reference frame,trajectories and streamlines coincide;the propaga...The propagation of Rossby waves on the Earth’s δ-surface is discussed in a reference frame propagation with the zonal phase speed of the wave.In this reference frame,trajectories and streamlines coincide;the propagation of Rossby waves has a different interpretation than in a reference frame fixed on the ground;and the mechanism for the propagation of Rossby waves depends not only on the different positions of the wave relative to the basic current,but also the variation ofβwith latitude(called theδ-effect).展开更多
A novel approach of iso-scallop trajectory generation for smooth manifold surfaces has been developed. Firstly,by defining homeomorphism mapping relations and differentiable structures,the smooth manifold surface is m...A novel approach of iso-scallop trajectory generation for smooth manifold surfaces has been developed. Firstly,by defining homeomorphism mapping relations and differentiable structures,the smooth manifold surface is mapped into several Euclidean planes,thus its trajectory generation can be decomposed into planar curve-filling tasks. Secondly,in the generation of direction-parallel trajectories,the calculation of the cutting interval and the curvature is given,depending on the generation of the first curve in the projection view. Thirdly,after automatic adherences of inverse projection curves,the filled curves are mapped into the original surface inversely to form trajectories. Although the required trajectories are iso-scallop,the trajectory intervals are variable according to the curvature changes at the projection point,which is advantageous to improving the trajectory quality. The proposed approach has appealing merits of dimensionality reduction,which decreases the algorithm complexity. Finally,numerical and machining examples are given to illustrate its feasibility and validity.展开更多
基金supported by the National Natural Science Foundation of China [grant numbers 11362012,11562014,41465002,and 41765004]the High School Science Research Project of the Inner Mongolia Autonomous Region[grant number NJZY16096]the Natural Science Foundation of Inner Mongolia[grant number 2018LH04005]
文摘The propagation of Rossby waves on the Earth’s δ-surface is discussed in a reference frame propagation with the zonal phase speed of the wave.In this reference frame,trajectories and streamlines coincide;the propagation of Rossby waves has a different interpretation than in a reference frame fixed on the ground;and the mechanism for the propagation of Rossby waves depends not only on the different positions of the wave relative to the basic current,but also the variation ofβwith latitude(called theδ-effect).
基金supported by the National Natural Science Foundation of China (Grant Nos.50835004,50905131)the Natural Science Foundation of Hubei Province (Grant No.2009CDB251)
文摘A novel approach of iso-scallop trajectory generation for smooth manifold surfaces has been developed. Firstly,by defining homeomorphism mapping relations and differentiable structures,the smooth manifold surface is mapped into several Euclidean planes,thus its trajectory generation can be decomposed into planar curve-filling tasks. Secondly,in the generation of direction-parallel trajectories,the calculation of the cutting interval and the curvature is given,depending on the generation of the first curve in the projection view. Thirdly,after automatic adherences of inverse projection curves,the filled curves are mapped into the original surface inversely to form trajectories. Although the required trajectories are iso-scallop,the trajectory intervals are variable according to the curvature changes at the projection point,which is advantageous to improving the trajectory quality. The proposed approach has appealing merits of dimensionality reduction,which decreases the algorithm complexity. Finally,numerical and machining examples are given to illustrate its feasibility and validity.
