The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became more viscous at the boundary. For certain viscous flows the boundary vorticity can be determined via the dynamical equation up to bounded errors for all time, without the need of knowing the details of the main stream flows. We then validate the dynamical equation by carrying out stochastic direct numerical simulations (i.e. the random vortex method for wall-bounded incompressible viscous flows) by two different means of updating the boundary vorticity, one using mollifiers of the Biot-Savart singular integral kernel, another using the dynamical equations.

翻译：边界涡量的动力学方程已被推导，该方程表明固体壁面处的粘性效应增强至原有两倍，犹如流体在边界处变得更具粘性。对于特定粘性流，可通过该动力学方程在所有时间尺度上确定边界涡量（误差有界），且无需掌握主流流动的细节。我们随后通过两种不同方式更新边界涡量——一种采用Biot-Savart奇异积分核的磨光算子，另一种直接应用动力学方程——来实施随机直接数值模拟（即壁面约束不可压缩粘性流的随机涡方法），从而验证了动力学方程的有效性。