thirsty, parched, yearn, pine
渴 centers on a strong, urgent lack of water: being thirsty or parched. The extended senses of yearning or pining grow naturally from that same feeling of intense, unmet need.
渴 combines 氵 (water) with 曷, which likely contributes the sound and the idea of stopping or ceasing, suggesting a lack of water. The exact historical development of 曷 is uncertain.
The water radical 氵 beside 曷 looks like a person gasping under the sun 日 with a container 勹, desperate for water. Picture someone parched, yearning for a drink.
For カツ, imagine a thirsty person gulping down a whole cut of watermelon: cut -> カツ, and the water quenches the thirst.