Impact of atmospheric cooling on the high-frequency submesoscale vertical heat flux

Recent simulations suggest that submesoscale motions with scales smaller than 30 km and frequencies greater than 1 day$^{-1}$ drive upward vertical heat transport. These simulations have prompted us to revisit the mechanisms that explain high-frequency vertical heat fluxes (VHFs) within the surface mixed layer (ML). Here, an idealized numerical simulation of a re-entrant channel flow with an unbalanced submesoscale thermal front is used to analyze the impact of surface cooling on high-frequency VHFs. Two types of simulations are analyzed: forced and unforced. The VHFs cospectrum analysis shows that surface diurnal cooling increases VHFs, reaching frequencies larger than 1 day$^{-1}$. However, the fastest-growing length scale of ML instabilities limits the extension of positive VHFs toward fine scales. Symmetric and gravitational instabilities are the main conduits producing ageostrophic high-frequency and small-scale structures, which in turn enhance upward VHFs across the diurnal frequency. A comparison between forced-idealized simulations with the KPP scheme and a realistic regional simulation in the frequency-wavenumber space, reveals that the two simulation types reproduce similar VHFs near the diurnal frequency. However, the realistic simulation displays higher VHFs than the forced-idealized simulation. This study emphasizes that surface diurnal cooling significantly impacts high-frequency VHFs. However, this impact is not sufficient to reach the high-frequency VHFs estimated in realistic submesoscale-permitting and tidal-resolving simulations.