Exponential mixing by orthogonal non-monotonic shears

Non-monotonic velocity profiles are an inherent feature of mixing flows obeying non-slip boundary conditions. There are, however, few known models laminar which incorporate this and have proven properties. Here we present such a model, alternating between two non-monotonic shear act in orthogonal (i.e. perpendicular) directions. Each is defined by independent variable, giving two-dimensional parameter space within prove the property over open subsets. Within these windows, use results from billiards literature to establish exponential rates. Outside find large regions where elliptic islands persist, leading poor mixing. Finally, comment on challenges extending windows potential for non-exponential rate at particular values.