Journal of Fluid Mechanics

Axisymmetric turbulent boundary layer along a circular cylinder at constant pressure

Noor  Afzal a1 and R.  Narasimha a2
a1 Department of Mechanical Engineering, Aligarh Muslim University, Aligarh, India
a2 Department of Aeronautical Engineering, Indian Institute of Science, Bangalore, India

Article author query
afzal n   [Google Scholar] 
narasimha r   [Google Scholar] 


A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate.

(Published Online March 29 2006)
(Received July 17 1974)
(Revised September 16 1975)