论文标题
浮力涡流贴片的运动
Motion of a Buoyant Vortex Patch
论文作者
论文摘要
分析了二维浮力涡流贴片的运动，即具有均匀密度的涡旋贴片与周围流体的均匀密度不同的涡旋贴片，分析了其质心运动的进化方程，其边界的变形及其边界的变形及其涡流的强度，这对于在整个边界上都具有巨大的压力延伸性。质心的方程是通过线性动量分析得出的，并且通过在边界上施加Euler的方程来实现薄板强度，同时研究了边界变形在质心固定框架中。据我们所知，获得了一组复杂的耦合方程组，以前尚未得出。板强度的演变是作为积分方程的。该方程还以消失的大小或浮力涡流的限制的极限进行检查。
The motion of a two-dimensional buoyant vortex patch, i.e. a vortex patch with a uniform density different from the uniform density of the surrounding fluid, is analyzed in terms of evolution equations for the motion of its centroid, deformation of its boundary and the strength of a vortex sheet which is essential to enforce pressure continuity across the boundary. The equations for the centroid are derived by a linear momentum analysis and that for the sheet strength by applying Euler's equations on the boundary, while the boundary deformation is studied in the centroid-fixed frame. A complicated coupled set of equations is obtained which, to the best of our knowledge, has not been derived before. The evolution of the sheet strength is obtained as an integral equation. The equations are also examined in the limit of a patch of vanishing size or a buoyant point vortex.
