Question

Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?

• A. Nikuradse stresses
• B. Reynolds stresses
• C. Boussinesq stresses
• D. Prandtl stresses

Hint:

In turbulent boundary layers, Reynolds stresses are responsible for the enhancement of fluid mixing and momentum diffusion, which is captured through the concept of eddy viscosity. This is crucial in the study of turbulence and its effects on fluid flow.

Answer 1

The Correct Option is B

In turbulent flow, eddy viscosity is a concept used to model the momentum transfer due to the chaotic fluctuations of the flow. It represents the enhanced diffusion of momentum due to turbulence, and is responsible for the mixing and spreading of fluid layers. The correct answer is Reynolds stresses, which are the main contributors to turbulent viscosity.

Explanation of each option:
- Option (A): Nikuradse stresses: These stresses refer to the frictional forces observed in smooth pipe flow and are related to the resistance due to roughness, but they are not directly responsible for turbulent viscosity.
- Option (B): Reynolds stresses: These are the turbulent stresses that represent the transfer of momentum due to eddy currents in the fluid. These stresses directly affect the effective viscosity in turbulent flow and are used to model turbulent viscosity.
- Option (C): Boussinesq stresses: These stresses are used in the Boussinesq approximation, which models turbulence in terms of an eddy viscosity but does not directly describe the turbulent viscosity itself.
- Option (D): Prandtl stresses: These stresses refer to a different model of turbulence and are not directly responsible for the concept of turbulent viscosity.

Thus, the correct answer is (B) because Reynolds stresses directly contribute to the concept of eddy viscosity in turbulent flows.