The Lamb dipole is a steady translating structure in 2D ideal fluid flow with opposite-sign vorticity of compact support in a circular disk. Previous studies have shown that when viscosity is present, the resulting viscous Lamb dipole develops a head-tail structure in which the head expands in size, while a tail of low amplitude vorticity is left behind as the head moves forward; in addition, the maximum vorticity and total circulation on each side of the dipole decay in time. Here we examine these decay properties by comparing numerical solutions of the Navier–Stokes equation (NSE) and diffusion equation (DE) in the Reynolds number range using the inviscid Lamb dipole as initial condition; this enables us to compare the combined effects of convection and diffusion in the NSE with the sole effect of diffusion in the DE. The results show that for a given Re, the vortex core size, shape, and maximum vorticity are nearly the same for the NSE and DE, indicating that convection has little effect on these properties. Nonetheless, compared to the DE, convection in the NSE inhibits circulation decay at low Re, while it enhances circulation decay at high Re, and the lateral separation of the vortex cores is a critical factor in this transition.

兰姆偶极子是2D理想流体流动中的稳定平移结构，圆盘中紧密支撑的涡旋性相反。先前的研究表明，当存在粘度时，所产生的粘性兰姆偶极子会形成一个头尾结构，其中头的大小会扩大，而随着头向前的移动，会留下低振幅涡旋的尾巴。此外，偶极子两边的最大涡度和总循环随时间衰减。在这里，我们通过比较雷诺数范围内的Navier–Stokes方程（NSE）和扩散方程（DE）的数值解来检查这些衰减特性使用无粘性的羔羊偶极子作为初始条件；这使我们能够将NSE中对流和扩散的综合效应与DE中扩散的唯一效应进行比较。结果表明，对于给定的Re，NSE和DE的涡流核心尺寸，形状和最大涡度几乎相同，这表明对流对这些特性的影响很小。尽管如此，与DE相比，NSE中的对流抑制了低Re时的循环衰减，而它却增强了高Re时的循环衰减，涡芯的横向分离是该过渡过程中的关键因素。