Abstract Submesoscale fronts with large horizontal buoyancy gradients and $O(1)$ Rossby numbers are common in the upper ocean. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability (SI) – a form of stratified inertial instability which can occur when the potential vorticity is of the opposite sign to the Coriolis parameter. Here, we use a weakly nonlinear stability analysis to study SI in an idealised frontal zone with a uniform horizontal buoyancy gradient in thermal wind balance. We find that the structure and energetics of SI strongly depend on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Vertically bounded non-hydrostatic SI modes can grow by extracting potential or kinetic energy from the balanced front and the relative importance of these energy reservoirs depends on the front strength and vertical stratification. We describe two limiting behaviours as ‘slantwise convection’ and ‘slantwise inertial instability’ where the largest energy source is the buoyancy flux and geostrophic shear production, respectively. The growing linear SI modes eventually break down through a secondary shear instability, and in the process transport considerable geostrophic momentum. The resulting breakdown of thermal wind balance generates vertically sheared inertial oscillations and we estimate the amplitude of these oscillations from the stability analysis. We finally discuss broader implications of these results in the context of current parameterisations of SI. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability (SI) – a form of stratified inertial instability which can occur when the potential vorticity is of the opposite sign to the Coriolis parameter. Here, we use a weakly nonlinear stability analysis to study SI in an idealised frontal zone with a uniform horizontal buoyancy gradient in thermal wind balance. We find that the structure and energetics of SI strongly depend on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Vertically bounded non-hydrostatic SI modes can grow by extracting potential or kinetic energy from the balanced front and the relative importance of these energy reservoirs depends on the front strength and vertical stratification. We describe two limiting behaviours as ‘slantwise convection’ and ‘slantwise inertial instability’ where the largest energy source is the buoyancy flux and geostrophic shear production, respectively. The growing linear SI modes eventually break down through a secondary shear instability, and in the process transport considerable geostrophic momentum. Baroclinic instability releases the potential energy stored in the horizontal density gradient, rather than extracting it from the thermal wind shear (Charney 1947; Stone 1972), and is a major mechanism behind the generation of submesoscale eddies (e.g. Boccaletti, Ferrari & Fox-Kemper 2007; Fox-Kemper, Ferrari & Hallberg 2008; Callies et al. 2016). Symmetric instability (SI) is an ageostrophic instability that can develop in frontal regions when the Ertel potential vorticity (PV) q ≡ ( f ˆz + ∇ × u) ·∇ b, (1.1) (defined with the velocity, u, and buoyancy, b ≡− gρ/ρ0) is of the opposite sign to the Coriolis parameter, f (Hoskins 1974). The destabilising contributions of a balanced flow are evident if we decompose the PV into a vortical and baroclinic component, respectively q = (ωz + f)N2 − M4/f, (1.2) where ωz is the vertical component of the relative vorticity and M2 ≡ ∂x ¯b (as above) is the horizontal analogue to the buoyancy frequency, N2 ≡ ∂z ¯b. A negative PV does not necessarily imply SI, however. In the absence of a frontal buoyancy gradient (i.e. M2 = 0) ‘gravitational instability’ occurs when N2 < 0a n dωz + f > 0 whereas ‘inertial instability’ occurs when N2 > 0a n d ωz + f < 0. Therefore SI only occurs when (ωz + f)N2 > 0 but M4/f is sufficiently large so that fq < 0. perpendicular to the horizontal buoyancy gradient), grow faster than baroclinic modes (independent of the cross-front direction) for Ri < 0.95, where Ri ≡ N2f 2/M4 is the balanced Richardson number. Stone (1971) considered the non-hydrostatic contributions to symmetric and baroclinic instabilities in the ageostrophic Eady model, showing that the vertical inertia suppresses both baroclinic and symmetric instabilities. Viscous contributions to the bounded non-hydrostatic SI problem were then included by Weber (1980) and approximated by a viscosity acting on a vertically unbounded normal mode. Beyond the Eady model other types of We do this by introducing the energy production ratio, B B + Pg = λ1 + λ2 2kxΓ , (4.4) as plotted in figure 7, where B is the buoyancy flux, Pg is the geostrophic shear production and λ1 and λ2 describe the vertical mode structure ( 2.11) and depend on Ri and Γ (details of which are given in Appendix B.2). The production ratio suggests the expected character of SI. For strong fronts with weak vertical stratification, SI extracts energy from shear production, and so we refer to this flavour of SI as ‘slantwise inertial instability ’. We have characterised the two limiting behaviours of SI distinguished by the dominant 926 A6-16 https://doi.org/10.1017/jfm.2021.680 Published online by Cambridge University Press The influence of front strength on SI energy source: ‘slantwise convective instability’ extracts energy from the background potential energy via buoyancy production with modes tending along absolute momentum surfaces, while ‘slantwise inertial instability’ is energised by shear production and has more upright modes nearly along isopycnals. This finding provides context to the work by Grisouard ( 2018)o nm i x e d‘ inertial–symmetric instability’.