Boundary layer dynamics of a decaying vortex core

The rapid transient motions within a decaying axi-symmetric vortex boundary layer are analyzed for various “local” Rossby and Reynolds numbers. Both laminar (no-slip) and turbulent (slip) boundary conditions are considered for flows over rotating and stationary surfaces. Similarity transformations are performed by expanding the velocity components in powers of a ratio of dimensionless radius to time. The zeroth-order system described by two nonlinear second-order ordinary differential equations is solved by Newton's iterative method. Comparisons are made with Hatton (1975) for the special case of laminar flow over a stationary surface. For the first order system, asymptotic solutions representing the flow far above the lower surface are obtained.

For laminar flow our results indicate that the vertical velocity is either only downward, both upward and downward thus indicating the possibility of a stagnation point in the latter case or only upward motion depending on the value of the Rossby (Reynolds) number. Turbulent conditions are shown to produce only negative (downward) vertical velocities. The presence of an axial stagnation point and the value of the Reynolds number for which the axial motion (laminar, zeroth order) becomes completely downward corresponds with the findings of Hatton (1975). The addition of mass as simulated by blowing is shown to effectively delay the decay process.