A differential equation for the mean velocity u(y) at distance y from the wall in a turbulent boundary layer flow is proposed and solved. It leads to a power law for u(y), followed by a rapid transition to a different power law, in agreement with the results of Barenblatt, Chorin and Prostokishin [Phys. Fluids 12, 2159 (2000)].

1.
G.I.
Barenblatt
,
A.J.
Chorin
, and
V.M.
Prostokishin
, “
A note on the intermediate region in turbulent boundary layers
,”
Phys. Fluids
12
,
2159
(
2000
).
2.
G.I.
Barenblatt
, “
Scaling laws for fully developed shear flows. Part I: Basic hypotheses and analysis
,”
J. Fluid Mech.
248
,
513
(
1993
).
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