Insoluble monolayers on water have been patterned at the macroscopic scale (i.e., at the centimeter scale of the flow apparatus) as well as the mesoscopic scale (i.e., down to the micron scale resolvable via optical microscopy). The macroscopic patterning at the air/water interface results from a hydrodynamic instability leading to a steadily precessing flow pattern. The velocity field is measured, and the associated shear stress at the interface is shown to be locally amplified by the flow pattern. The resulting hydrodynamic effects on two different monolayer systems are explored: (1) the pattern in a model monolayer consisting of micron-size, surface-bound particles is visualized to show that the particles are concentrated into isolated regions of converging flow with high shear, and (2) Brewster angle microscopy of a Langmuir monolayer (vitamin K-1) shows not only that the monolayer is patterned at the macroscopic scale but also that the localized high-shear flow further patterns the monolayer at the mesoscale.