Inducing hydrodynamic flow in nematic liquid crystals (NLCs) reorients the symmetry axis of the material—the director, causing changes in the optical properties. The resulting optical gratings have potential use as switchable diffractive optical elements (DOEs). In this study, surface acoustic waves (SAWs) are applied to an NLC device to induce periodic vortices through hydrodynamic instabilities. We show a linear relationship between the wavelength of the applied SAW and induced grating period, where the coefficient is determined by the ratio of the speed of sound in the substrate to that in the NLC. This relationship is further used to design a novel device, where the period of the hydrodynamic grating can be continuously varied from 90 μm to 260 μm by utilizing a broadband (chirped) SAW transducer. These devices present great potential for creating a new class of continuously variable DOEs, overcoming current technological limitations.