Warm light water floats on cold, salty, dense water. Build a thermocline and halocline, let a year of heating, cooling and wind mix it, lower a CTD from the ship and send an internal wave along the pycnocline.
Re-runs three years from your current start profile, changing one thing, and reports year 3 (summer minimum and winter maximum of the mixed layer, surface temperature range, strongest N).
The science
Density. Seawater density follows the UNESCO equation of state (Fofonoff and Millard 1983) at surface pressure, so the plotted σθ is potential density (compressibility is ignored). Cold or salty water is denser; at 15 °C one kelvin changes density by about 0.21 kg/m³ and one psu by about 0.78 kg/m³, so a cold polar surface can still float if it is fresh enough.
Buoyancy frequency. A parcel displaced vertically in a stable column oscillates at N² = −(g/ρ0) ∂ρ/∂z. N is largest in the pycnocline (up to roughly 10 cycles per hour here, period about 6 min) and nearly zero in the well-mixed layer. N² < 0 means the column is overturning.
Seasonal mixing. The column obeys ∂T/∂t = ∂/∂z(K ∂T/∂z) + heating and the same for salinity, solved implicitly (stable at any step). Sunlight is absorbed in two exponentials (58 % within 0.35 m, 42 % within 23 m, a clear-water Jerlov-like shape); cooling acts on the top 1 m. Wind raises mixing: K = Kbg + Kw e−z/Dw / (1 + N²/N0²) with Kw and Dw proportional to the wind speed, and strong stratification suppresses it. Any statically unstable pair of layers is mixed instantly (convective adjustment, heat and salt conserved), which is what deepens the mixed layer in winter. The mixed layer depth is where density first exceeds the 10 m value by 0.03 kg/m³ (de Boyer Montégut et al. 2004).
Internal waves. Waves on the pycnocline travel slowly because only the small density contrast restores them. For two layers c = √(g′ h1h2/(h1+h2)) with reduced gravity g′ = gΔρ/ρ0; for a smooth profile the WKB estimate of the first mode is c1 ≈ (1/π) ∫N dz. The animation uses c1 and the mode shape sin(π F(z)) where F is the normalised ∫N dz; its vertical displacement is drawn with the isopycnals. Time in the animation is a looped visual, the true period is shown in the readouts.
What is simplified. One-dimensional: no currents, upwelling, lateral heat or freshwater transport, so the surface salinity is relaxed to a target (0.3 m/day piston velocity) and the annual-mean heat flux is set to zero in the presets. The mixing law, Dw, Kw and N0 are illustrative round numbers tuned to give plausible mixed layers, not a validated turbulence closure. Start profiles are idealised sigmoids; presets are caricatures of ocean regions, not data. Waves are linear and shown only in the cutaway.