As one kind of submesoscale instability, symmetric instability (SI) of the ocean surface mixed layer (SML) plays a significant role in modulating the SML energetics and material transport. The small spatial scales of SI, O(10 m ~ 1 km), are not resolved by current climate ocean models and most regional models. This paper describes comparisons in an idealized configuration of the SI parameterization scheme proposed by Bachman et al. (2017) (SI-parameterized) versus the K-Profile Parameterization (KPP) scheme (SI-neglected run) as compared to a SI-permitting model; all variants use the Coastal and Regional Ocean Community Model version of the Regional Ocean Modeling System (CROCO-ROMS) and this paper also serves to introduce the SI parameterization in that model. In both the SI-parameterized and SI-permitting model, the geostrophic shear production is enhanced and anticyclonic potential vorticity is reduced versus the SI-neglected model. A comprehensive comparison about the energetics (geostrophic shear production, vertical buoyancy flux), mixed layer thickness, potential vorticity, and tracer redistribution indicates that all these variables in the SI-parameterized case have structures closer to the SI-permitting case in contrast to the SI-neglected one, demonstrating that the SI scheme has a positive improvement to capture the impacts of SI. This work builds toward applying the SI scheme in a regional or climate model.