Riblets reduce skin-friction drag until their viscous-scaled size becomes large enough for turbulence to approach the wall, leading to the breakdown of drag-reduction. In order to investigate inertial-flow mechanisms that are responsible for the breakdown, we employ the minimal-span channel concept for cost-efficient direct numerical simulation (DNS) of rough-wall flows (MacDonald et al. in J Fluid Mech 816: 5–42, 2017). This allows us to investigate six different riblet shapes and various viscous-scaled sizes for a total of 21 configurations. We verify that the small numerical domains capture all relevant physics by varying the box size and by comparing to reference data from full-span channel flow. Specifically, we find that, close to the wall in the spectral region occupied by drag-increasing Kelvin–Helmholtz rollers (Garcia-Mayoral and Jimenez in J Fluid Mech 678: 317–347, 2011), the energy-difference relative to smooth-wall flow is not affected by the narrow domain, even though these structures have large spanwise extents. This allows us to evaluate the influence of the Kelvin–Helmholtz instability by comparing fluctuations of wall-normal and streamwise velocity, pressure and a passive scalar over riblets of different shapes and viscous-scaled sizes to those over a smooth wall. We observe that triangular riblets with a tip angle $$\alpha =30^{\circ }$$ and blades appear to support the instability, whereas triangular riblets with $$\alpha =60^{\circ }$$ – $$90^{\circ }$$ and trapezoidal riblets with $$\alpha =30^{\circ }$$ show little to no evidence of Kelvin–Helmholtz rollers.

中文翻译：

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最小跨度通道中各种形状的湍流的直接数值模拟

Riblets 减少皮肤摩擦阻力，直到它们的粘性尺寸变得足够大，湍流接近壁面，导致减阻失效。为了研究导致击穿的惯性流动机制，我们采用最小跨度通道概念对粗糙壁流动进行经济高效的直接数值模拟 (DNS)（MacDonald 等人，J Fluid Mech 816: 5 –42, 2017)。这使我们能够研究总共 21 种配置的六种不同的肋条形状和各种粘性尺寸。我们通过改变盒子大小并与来自全跨度通道流的参考数据进行比较来验证小数值域捕获所有相关物理。具体来说，我们发现，靠近由增加阻力的开尔文-亥姆霍兹滚子占据的光谱区域中的壁（Garcia-Mayoral 和 Jimenez in J Fluid Mech 678: 317-347, 2011），相对于光滑壁流的能量差不受窄域，即使这些结构具有很大的展向范围。这使我们能够通过比较壁法向和流向速度、压力和不同形状和粘性尺度尺寸的肋条上的被动标量与光滑壁上的那些波动来评估开尔文-亥姆霍兹不稳定性的影响。我们观察到具有尖端角 $$\alpha =30^{\circ }$$ 的三角形肋条和叶片似乎支持不稳定性，