TOPOLOGICAL PHASE TRANSITIONS IV: DYNAMIC THEORY OF BOUNDARY-LAYER SEPARATIONS

• Main Authors: Ma, Tian, Wang, Shouhong
• Other Authors: Sichuan University Chengdu (SCU), Indiana University Bloomington, Indiana University System
• Format: Report
• Language: English
• Published: HAL CCSD 2017
• Subjects: [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS]; [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]; Boundary Point; North Atlantic
• Online Access: https://hal.archives-ouvertes.fr/hal-01672759; https://hal.archives-ouvertes.fr/hal-01672759/document; https://hal.archives-ouvertes.fr/hal-01672759/file/tpt4.pdf

We present in this paper a systematic dynamic theory for boundary-layer separations of fluid flows and its applications to large scale ocean circulations, based on the geometric theory of incompressible flows developed by the authors. First, we derive the separation equations, which provide necessary and sufficient conditions for the flow separation at a boundary point. Second, these separation equations are then further converted to predicable conditions, which can be used to determine precisely when, where, and how a boundary-layer separation occurs. Third, we derive conditions for the formation of vortices from boundary tip points, and conditions for the formation of surface turbulence. Fourth, we derive the mechanism of the formation of the subpolar gyre and the formation of the small scale wind-driven vortex oceanic flows, in the north Atlantic ocean.