take walk, stroll
遛 centers on moving slowly and casually on foot: taking a walk or strolling without hurry.
遛 combines 辶 (movement) with 留, which likely contributes the sound and the idea of lingering or staying, suggesting a leisurely walk.
The movement radical 辶 wraps around 留 (to stay or detain). Picture someone who stays in motion but moves slowly, taking a stroll without going far.
For リュウ, imagine a leisurely stroll by a flowing river: the sound of the river (流, りゅう) cues リュウ while you walk along.
—