Wind speeds measured by the Mars 2020 Perseverance rover in Jezero crater were fitted as a Weibull distribution. InSight wind data acquired in Elysium Planitia were also used to contextualize observations. Jezero winds were found to be much calmer on average than in previous landing sites, despite the intense aeolian activity observed. However, a great influence of turbulence and wave activity was observed in the wind speed variations, thus driving the probability of reaching the highest wind speeds at Jezero, instead of sustained winds driven by local, regional, or large-scale circulation. The power spectral density of wind speed fluctuations follows a power-law, whose slope deviates depending on the time of day from that predicted considering homogeneous and isotropic turbulence. Daytime wave activity is related to convection cells and smaller eddies in the boundary layer, advected over the crater. The signature of convection cells was also found during dust storm conditions, when prevailing winds were consistent with a tidal drive. Nighttime fluctuations were also intense, suggesting strong mechanical turbulence. Convective vortices were usually involved in rapid wind fluctuations and extreme winds, with variations peaking at 9.2 times the background winds. Transient high wind events by vortex-passages, turbulence, and wave activity could be driving aeolian activity at Jezero. We report the detection of a strong dust cloud of 0.75-1.5 km in length passing over the rover. The observed aeolian activity had major implications for instrumentation, with the wind sensor suffering damage throughout the mission, probably due to flying debris advected by winds.