Symmetric instability (SI) is an important mechanism that contributes to turbulent mixing in a submesoscale front. The presence of ocean surface waves may interact with frontal current shear and lead to Craik-Leibovich type 2 (CL2) instability, which may modulate the development of SI.  In this study, we conduct a linear stability analysis to investigate the impact of surface waves on SI in a viscous submesoscale front. We systematically analyze the development and growth rates of SI and CL2 instability under various combinations of background stratification (Richardson number, Ri), horizontal buoyancy gradient, and surface wave intensity and propagation direction. Our results demonstrate that the surface waves play a dual role in modulating SI. First, they alter the stability of SI by modifying the Ertel potential vorticity (PV). Second, surface waves either suppress or enhance the SI-induced slantwise circulation via the Stokes shear force. While the former effect has been well documented (e.g., Haney et al., 2015), we show that the latter arises from the coupling between Stokes and Eulerian shears, an effect that persists even under cross-front wave conditions. Furthermore, non-linear simulations incorporating surface waves are employed to validate our linear stability results and assess wave-induced impacts on momentum transport. During the early stages, prior to the dominance of non-linear advection, the suppression or enhancement of SI-induced slantwise circulation by the Stokes shear force is clearly seen. Notably, the influence of surface waves on SI-driven momentum transport penetrates throughout the entire mixed layer even though the Stokes shear force is confined near the surface.
 

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