The 40th meeting of the Sandbox Series will be held via Webex:
https://stuod.my.webex.com/stuod.my/j.php?MTID=m335d5640370c16b9bf5777cdc03eda93
Fantastical Forces and Where to Find Them
Abstract:
We begin the development of a tensor-based formalism for geophysical fluid dynamics, first defining a generalized time derivative operator that is valid in arbitrarily time-varying, curvilinear coordinates. This operator acts on components of a tensor T and returns components of the total time derivative dT/dt. Using this derivative, we make rigorous the transformation from inertial to accelerating reference frames, systematically deriving apparent forces and sorting them into two classes: the familiar “fictitious” forces arising from rigid transformations, and the unfamiliar “fantastical” forces arising from non-rigid, deforming transformations. Though the coordinate systems chosen in ocean modeling are often deforming, these latter apparent forces are overlooked. This work and companion papers provide a unifying mathematical foundation that improves communication among ocean modelers, permits higher-order, multi-dimensional numerical schemes, and forms a basis for the development of next-generation ocean models and parameterizations.
Schedule
1300-1400: Joel Feske
1400-1500: Discussion & close