name of a Chinese river
洙 refers specifically to the name of a Chinese river. It has no broader conceptual center beyond this proper-name usage.
洙 combines the water radical 氵 with the phonetic component 朱, forming a character used as a proper name for a river. The exact historical development is uncertain.
The water radical 氵 on the left and 朱 on the right together suggest a river name. Imagine a vermilion (朱) river flowing with water (氵).
For シュ, picture a shoe floating down the river: shoe -> シュ, and the river carries it away.