There are varying stories of her origins, but all agree that thrice daily…
Your prompt is CHARYBDIS.
From beneath a rock
With a cavernous gullet
She swallows and spits
… she swallows vast amounts of water, and the spits it back out again to form giant whirlpools.
I get it now: "Between Scylla and Charybdis" is another way of saying "Stuck between a rock and a hard place."
Swirling cosmic tides
Ebb and flow through Charybdis channels
Leads less fortunate swept down
Whirlpool ways and means minded by desire.