Research Article

New Theories on Boundary Layer Transition and Turbulence Formation

Table 2

Comparison of classical theory and our DNS observation.

TopicClassical or existing theoryObservation of our DNS

Turbulence generationBy “vortex breakdown”Not by “vortex breakdown” but by shear layer instability
First-ring generationSelf-induced, deformed, inclined, and pinched-offBy counter-rotated vortices interaction, circular, perpendicular, no pinch-off
Multiple-ring structure“Crow theory” or breakdown and then reconnectedNo breakdown, not “Crow theory” but momentum deficit caused by ejection, vorticity conservation
Multiple-level high shearsNo reportBy multiple-level sweeps and ejections
Energy transfer channel, turbulence sustenanceEnergy transfers from larger vortices to smaller one through “vortex breakdown” without dissipation until viscosityFrom inviscid flow down to bottom by multilevel sweeps
U-shaped vortexHead wave, secondary vortex, by second sweep, newly formed, breakdownNot head wave, tertiary vortex, by secondary vortex, existing from beginning, never breakdown
RandomizationBackground noise, starting from the top ring and then going down to the bottomInternal property, starting from second level rings in the middle, affects bottom and then up to affect top rings. Loss of symmetry maybe caused by C-K shift
Coefficients of frictionTurbulent flow has large friction due to strong boundary layer mixingDepending only on velocity profile changes in laminar sublayer, no matter turbulent or laminar
Richardson eddy cascadeClassical theoryNot observed
Vortex breakdownClassical theoryNot observed
Kolmogorov scaleClassical theorySmallest length scale should be determined by minimum shear layer instability