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A fluid mechanic’s analysis of the tea-cup singularity
In 1926 Einstein published a short paper explaining the meandering of
rivers. He famously began the paper by discussing the secondary flow
generated in a stirred tea cup — the flow now widely known to be responsible for the
collection of tea leaves at the center of a stirred cup of tea. In 2014, Luo
and Hou presented detailed numerical evidence of a finite-time
singularity in a rotating, incompressible, inviscid flow. The key driving mechanism of
that singularity is the secondary tea-cup flow. The present work is not aimed at
proving the existence of a singularity in this flow, nor is it aimed at
generating more highly resolved numerical evidence for the singularity than
already exists. Rather, I will assume that the flow simulated by Luo
and Hou genuinely develops a singularity. My goal is to understand, from a
fluid-mechanics perspective, why.