FLOW AROUND A CYLINDER - istiarto

– 2.24 –
plot of w ��w
�� indicates that it is not exponentially distributed. It is not clearly known
what may cause this deviation of the measured and theoretical distributions of w ��w
��;
other measurements at LRH have also the same phenomenon (see Cellino, 1998;
Yulistiyanto, 1997).
2.4.4 Vertical distribution of the Reynolds shear-stresses
Fig. 2.10 shows the vertical distributions of the Reynolds stresses measured at the six
stations. The transversal component of the Reynolds stress, �v �� w ��,
is always negligible
compared to the longitudinal component, �u �� w ��.
Fig. 2.10 Reynolds shear-stresses of the approach flow.
The Reynolds stress, ��v ��w
��,
can be interpreted as the total shear stress since the viscous
component of the shear stress is negligible compared to the turbulence stress in the most
part of the flow depth. Its vertical distribution is linear with a zero stress at the water
surface and a maximum at the bed. It is given by (Graf and Altinakar, 1998, p. 64):
2
�zx � � �u �� w ���
�o ��1� z h�
� u� �1� z h�
(2.23)
in which the origin of the vertical distance, z = 0, is defined at a level 0.2ks below the
peaks of the bed roughness. The above relation can be used to obtain the bed shear stress,