In laminar flow shearing force is developed due to viscosity of the fluid,  hence viscous stress exist.  In turbulent flow, fluctuation happens in the direction of  streamwise as well as in direction perpendicular to the flow due to which large Reynolds stress are set up(due to mass interchange of mass in direction perpendicular to the streamline). Viscous effect is dominant only to small region which is very close to the wall.  Hence in turbulent flow viscous stress is much smaller than Reynolds stress.

Turbulent flow over an impervious solid wall

In turbulent flow, the fluid moves in an irregular and chaotic manner, characterized by the presence of eddies and vortices. The flow is highly energetic and exhibits fluctuations in velocity, pressure, and other properties. When this turbulent flow occurs over an impervious solid wall, there are certain characteristics and behaviors that can be observed in terms of viscous stress and Reynolds stress.

Viscous stress at the wall

Viscous stress is a measure of the resistance to flow within a fluid. In the case of turbulent flow over an impervious solid wall, the fluid in direct contact with the wall experiences the maximum viscous stress. This is because the fluid molecules in contact with the wall are brought to a halt due to the no-slip condition, causing a high velocity gradient and thus a high viscous stress. As we move away from the wall, the viscous stress decreases due to the decreasing velocity gradient.

Reynolds stress at the wall

Reynolds stress is a measure of the turbulent fluctuations in the flow. It is caused by the interaction between the fluctuating velocity components and is responsible for the transport of momentum within the fluid. In turbulent flow over an impervious solid wall, the Reynolds stress is not zero at the wall. This is because the turbulent fluctuations in velocity are still present near the wall and contribute to the overall Reynolds stress. However, the magnitude of the Reynolds stress is generally higher compared to the viscous stress at the wall.

Comparison between viscous stress and Reynolds stress

When comparing the viscous stress and Reynolds stress in turbulent flow over an impervious solid wall, it is observed that the Reynolds stress is much larger than the viscous stress. This is due to the highly energetic nature of turbulent flow, which results in significant fluctuations in velocity and thus higher Reynolds stress. On the other hand, the viscous stress is primarily determined by the velocity gradient, which is relatively smaller compared to the turbulent fluctuations. Therefore, the viscous stress is much smaller than the Reynolds stress.

Conclusion

In turbulent flow over an impervious solid wall, the viscous stress is much smaller than the Reynolds stress. This is because the viscous stress is primarily determined by the velocity gradient, while the Reynolds stress is influenced by the turbulent fluctuations in velocity. The highly energetic nature of turbulent flow results in significant turbulent fluctuations, leading to a much larger Reynolds stress compared to the viscous stress at the wall.