Separation of Scales at High Latitudes in Rotating and Stratified Flows

Earth's high latitudes stand to be among the first regions affected by climate change issues due to changes induced by melting ice in the Arctic and Antarctic. The dynamics in the high latitudes is affected by the higher rotation rate as measured by the Rossby number. The smaller the Rossby number, the more important the rotation is to the dynamics. Motivated by gaining fundamental understanding of ocean dynamics at high latitudes we have derived new results, based on the method of multiple scales presented in Embid and Majda (1996, 1998) that address the scale separation between slow-and fast-time scale dynamics in the limit of fast rotation while retaining order one affects due to stratification. We derive new equations and their conservation laws for the slow dynamics and show some numerical results that support the theory.