sudden, quick, sound of the wind
颯 centers on swift, sudden movement, especially with a rushing sound like wind. It describes things happening quickly or the sound of wind itself.
颯 combines 立 (stand) and 風 (wind), suggesting the sound of wind standing up or a sudden gust. The exact historical development is uncertain, but the component relationship is consistent with the meaning of a quick, windy sound.
Imagine standing (立) in a sudden gust of wind (風) that rushes past with a whoosh. That quick, windy sound is 颯.
For サツ, picture a sudden gust of wind that sounds like a sharp 'satsu' as it whips by. The invented sound 'satsu' cues サツ while the wind rushes suddenly.