We study solutions of the surface quasi-geostrophic (SQG) equation which are locally constant outside a thin neighbourhood of a curve that evolves with time. To such an SQG solution we associate a distinguished curve (the 'spine'). If the above thin neighbourhood has thickness δ, then we prove that the spine satisfies its own evolution equation (equal to the sharp-front equation) modulo errors O(δ 2|logδ|).
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics