This study focuses on the investigation of the nonlinear flow behaviour along rough-walled fractures with contact areas in the framework of the lattice Boltzmann method. The numerical results indicate that the fracture surface roughness controls both the advective aperture and the eddy aperture in the analysis of pressure, velocity, and vorticity fields. The eddy volume fraction increases from 28% to 40% with the increase in the fractal dimension from $D=2.0$ to $D=2.4$. The parametric analysis based on Forchheimer’s equation further demonstrates that the enhancement in the vorticity field contributes to the strengthened nonlinear flow behaviour. The two competing roles of fractal dimension and contact area greatly impact the non-Darcy flow patterns. The fractal dimension is the main factor affecting flow nonlinearity at a low contact ratio, while the contact area dominates the nonlinear flow behaviour at a high contact ratio. The increase in the contact ratio strengthens the boundary effect, and thus greatly increases the volume of the eddy region and enhances the nonlinearity of the flow field. These observations provide a promising pathway to analyse the flow behaviour along the fracture based on vorticity analysis, and enlighten the understanding of the competing mechanism between fractal dimensions and contact areas for the influence of nonlinear flow behaviours.

本研究的重点是在格子 Boltzmann 方法的框架内研究沿具有接触区域的粗糙壁裂缝的非线性流动行为。数值结果表明，在压力场、速度场和涡量场分析中，断面粗糙度同时控制平流孔径和涡流孔径。随着分形维数的增加，涡体积分数从 28% 增加到 40%$D=2.0$至$D=2.4$. 基于 Forchheimer 方程的参数分析进一步证明了涡量场的增强有助于增强非线性流动行为。分形维数和接触面积这两个相互竞争的角色极大地影响了非达西流动模式。分形维数是影响低接触比下流动非线性的主要因素，而接触面积主导着高接触比下的非线性流动行为。接触比的增加加强了边界效应，从而大大增加了涡流区的体积，增强了流场的非线性。这些观察结果为基于涡度分析分析沿裂缝的流动行为提供了一条有希望的途径，