Ocean and atmosphere communicate through exchanges at the air-sea interface, a complex surface in perennial disequilibrium. At large scales, atmospheric dynamics force ocean variability (Gill, 2016) as strong winds enhance surface turbulent heat fluxes and generate upper ocean mixing, reducing sea surface temperature (SST). At finer scales, (100km) , ocean structures influence the atmospheric dynamics (Chelton et al., 2001), impacting air temperature, frictional stress, and the marine atmospheric boundary layer (MABL) stability. The upper ocean and lower atmosphere layers interact through different processes forming a feedback loop (e.g., Strobach et al. (2020)).Ocean thermal structures affect the stability of the air-column and its thermodynamical properties through thermal and dynamical adjustments of the MABL (Small et al., 2008). The resulting small-scale processes, called thermal feedback, have important upscale and remote impacts at seasonal timescales on local surface wind (Chelton et al., 2004), basin-scale atmospheric circulation (Desbiolles et al., 2018), cloud cover, rainfall location over ocean -as shown in long-term average over the Gulf Stream (Minobe et al., 2008) or in composite analyses over Southern Ocean eddies (Frenger et al., 2013) -and climatic variability of heat/ tropical lows inland (Desbiolles et al., 2020). Thus, small-scale air-sea interactions significantly affect the water cycle.Two main mechanisms have been proposed to describe the surface wind response to small-scale variability of SST: the downward momentum mixing (hereafter DM), notably introduced by Hayes et al. (1989), and the pressure adjustment (PA), highlighted by Lindzen and Nigam (1987). The DM mechanism brings into play large eddies within the MABL, stimulated by turbulent fluctuations of momentum, temperature and moisture, that redistribute horizontal momentum in the vertical direction (Small et al., 2008). This process modifies the MABL stability over SST patterns (Businger & Shaw, 1984), entailing, as a net effect, weaker (stronger) surface winds over the cold (warm) flank of an SST gradient (Wallace et al., 1989). As a consequence, a positive correlation emerges between wind divergence and downwind SST gradient (e.g., Chelton