run, go, quick, tend towards
趨 centers on swift, directed movement: running, going quickly, or tending toward a goal. The idea of tending toward something is a natural extension of moving rapidly in a direction.
趨 combines 走 (run) with 芻, which likely contributes the sound and may relate to quick, hurried movement. The exact historical role of 芻 is uncertain.
The running radical 走 surrounds 芻, which looks like a bundle of grass being carried swiftly. Picture someone running with a bundle, moving quickly toward a destination.
For スウ, imagine running so fast you create a swoosh sound: swoosh -> スウ, as you tend quickly toward the finish line.