标题： 高阶均质肋状边界条件 显示英文标题

标题： Higher-order homogenised riblet boundary conditions

摘要： 肋条和其他减阻装置的描述长期以来一直使用纵向和横向凸起高度的概念，既作为预测减阻本身的方法，也作为通过将肋条的影响转移到虚拟平面上来简化数值模拟的等效边界条件。 这一想法的局限性在于它源于肋条尺寸参数$s^+$的一阶近似，因此无法预测除$s^+$与减阻之间的线性关系以外的内容；换句话说，就是减阻曲线的初始斜率。 在这里，该概念被扩展为使用匹配渐近法的完整渐近展开，这可以一致地提供更高阶的凸起高度和在虚拟平面上的更高阶等效边界条件。 此过程还使我们能够探索纳维-斯托克斯方程的非线性特性及其进入$s^+$展开的方式，结果有些出人意料。 显示英文摘要

摘要： The description of riblets and other drag-reducing devices has long used the concept of longitudinal and transverse protrusion heights, both as a means to predict the drag reduction itself and as equivalent boundary conditions to simplify numerical simulations by transferring the effect of riblets onto a flat virtual boundary. The limitation of this idea is that it stems from a first-order approximation in the riblet-size parameter $s^+$, and as a consequence it cannot predict other than a linear dependence of drag reduction upon $s^+$; in other words, the initial slope of the drag-reduction curve. Here the concept is extended to a full asymptotic expansion using matched asymptotics, which consistently provides higher-order protrusion heights and higher-order equivalent boundary conditions on a virtual flat surface. This procedure also allows us to explore nonlinearities of the Navier-Stokes equations and the way they enter the $s^+$-expansion, with somewhat surprising results.