  Symmetric instability (SI) is a frontal instability arising from the
interaction of rotation with lateral and vertical shear of a frontal jet and is
a generalization of shear, centrifugal, and gravitational instabilities. While
the onset of SI has been studied in numerous observations and models, intuition
about its growth in physical ocean comes primarily from constant-viscosity
linear instability analysis and large eddy simulation (LES). A forward cascade
arising from SI in the real ocean, where numerous fine-to-microscale processes
interact with growing SI velocity cells, is less understood. While many
instances of symmetrically unstable flow have been observed, observations of
enhanced turbulent kinetic energy (TKE) dissipation ($\epsilon$) at these sites
are less common. We use numerical instability analysis of an idealized
geostrophic jet to show that viscous-diffusive effects of preexisting
turbulence from other turbulent processes (e.g., competing instabilities,
internal wave processes, or boundary layer processes) can suppress the growth
of SI in the real ocean. For example, a moderate level of ambient turbulence,
represented by uniform diffusivity and viscosity of $\kappa =\nu = 10^{-4}
m^2/s$, restricts the wavelength range of SI's fastest-growing mode from
$\mathcal{O}(10-100)$m to $\mathcal{O}(100)$m and elongates its e-folding
timescale by $\mathcal{O}(1-10)$ hrs; suggesting the net viscous-diffusive
effects of preexisting turbulence can damp the growth of SI. Viscous damping is
one possible explanation for the rarity of SI structures in the real ocean, and
our results motivate the inclusion of dependence on previous-timestep
$\epsilon$ or $\kappa$ when parameterizing SI in regional models.
