JOURNAL OF GEOPHYSICALRESEARCH,VOL. 100, NO. C4, PAGES6743-6759, APRIL 15, 1995 Evolution of the instability of a mixed-layer front R. M. Samelsonand D. C. Chapman Woods Hole OceanographicInstitution, Woods Hole, Massachusetts Abstract. Observations from the FrontalAir-Sea Interaction Experiment (FASINEX), indicatingthe presence of small-scale cold-core features in the North Atlantic Subtropical Convergence Zone, motivated a recentlinear analysis of the instability of a geostrophically balanced mixed-layer front. The results of that analysis suggested that the instability would preferentiallyform small-scale cold-core eddiesat finite amplitude. In the present study, the finite-amplitude evolution of the fastest growingmode of this nongeostrophic baroclinic instability is investigated numerically. The linear prediction of cold-core eddy formation is confirmedby the nonlinear calculation. There are large horizontal and vertical heat and potential vorticity fluxesassociated with the developing disturbance. The heat flux is confinedabove the thermocline, in the region of slopingfrontal isothermsthat providethe energysource for the instability, but the potential vorticity fluxesare maximum 50-75 m deeper and reach into the thermocline. A tongue of low-potential-vorticity fluid is advected50-75 m downwardalong isopycnal surfaces from the cold side of the front into the thermocline at the mixed-layer base. The small-scalepotential vorticity structure has similarities to estimates of the upper ocean potential vorticity field obtained previouslyfrom FASINEX observations.The calculations illustrate the role that frontal instabilities may play in the flux of heat and potential vorticity from the mixed layer into the thermocline. The evolution of the disturbance resembles baroclinic wave life cycles obtained in atmospheric models. 1. Introduction During the Frontal Air-Sea Interaction Experiment (FASINEX), which wascarried out during 1986 in the western North Atlantic Subtropical Convergence Zone [Weller, 1991], several "subfrontal"-scale cold-core fea- tures with velocityand temperature signatures compa- rable to those of the fronts were observed [Weller and $amelson, 1991]. Thesefeatures had horizontal scales of 15-25 km, comparable to or smaller than the widths of the frontal jets. Their presence wasunexpected, but Weller and $amelson [1991] suggested that they could resultfrom instabilities of the baroclinic frontaljets. $amelson [1993]explored this hypothesis by com- puting the linearinstabilities of a geostrophically bal- ancedfrontal jet with vertical and cross-front horizontal densityand velocitystructure representative of fronts observedduring FASINEX. The most unstable lin- ear modeshad e-folding timescales of 2-3 days and alongfront wavelengths near 70 km. The main energy source for the modes was(nongeostrophic) baroclinic instability. Superpositions of the linear modes at fi- nite amplitude on the basic state jet suggested that the instabilities would preferentially form small-scale cold- core eddies and provided indirect evidencethat baro- Copyright 1995by the American Geophysical Union. Paper number 94JC03216. 0148-0227 / 95/ 94JC-03216505.00 clinic instabilityof the frontal jets is a possible source of the cold-core features observed during FASINEX. How- ever,this interpretation depended uponthe extrapola- tion of the linearresults into the nonlinear (finiteam- plitude) regime. In the presentstudy, we consider the nonlinear evolu- tion ofthe fastest growing mode of thefrontal instability studied by $amelson [1993]. This is done by obtaining solutions numerically for a set of initial value problems for the hydrostatic primitive equations, using a hybrid finite-difference and Chebyshev-spectral scheme. We compare the results of the calculations with observa- tions of the cold-core features from FASINEX. In ad- dition, we consider the cross-frontal fluxes of potential vorticity and heat associated with the evolution and equilibrationof the instability. The model is briefly described in section 2. The main results for the initial value problems are presented in section 3. These are compared with observations from FASINEX in section 4. Section 5 contains a summary. 2. Model Equations The model equations are the hydrostatic primitive equations, ut -+- uu• -+- VUy -+- wu• - f v -- -p•:/po + Aa(u•:• + Uyy) + (A,•u•)•, (la) 6743