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

The correct option is Reynolds stresses .

To understand why, let us break down the concepts of turbulence, momentum transfer, and how eddy viscosity is defined:

1. Laminar vs. Turbulent Flow and Viscosity:
In laminar flow, the shear stress ($\tau$) is governed solely by Newton's law of viscosity:
$\tau =\mu \frac{du}{dy}$
where $\mu$ is the dynamic (molecular) viscosity, which is a fluid property representing resistance to molecular-scale momentum transfer.
In contrast, turbulent flow is characterized by chaotic, fluctuating fluid motion (eddies) that drastically enhances the mixing and transport of momentum across the layers.

2. Reynolds Decomposition and Reynolds Stresses:
To analyze turbulent flow, we decompose the velocity into a time-averaged mean component ($\overline{u}$) and a fluctuating component ($u^{\prime }$):
$u=\overline{u}+u^{\prime }$
Substituting this decomposition into the Navier-Stokes equations and taking the time-average yields the Reynolds-Averaged Navier-Stokes (RANS) equations. During this process, additional convective transport terms arise from the velocity fluctuations, represented as:
${\tau }_{\text{turb}}=-\rho \overline{u^{\prime }{v}^{\prime }}$
These terms ($-\rho \overline{u^{\prime }{v}^{\prime }}$) act as additional shear stresses on the mean flow and are known as Reynolds stresses.

3. Boussinesq Eddy Viscosity Hypothesis:
Because the Reynolds stresses introduce new unknowns into the governing equations (the closure problem), Joseph Boussinesq proposed an analogy to molecular transport. He hypothesized that the turbulent (or Reynolds) shear stress is proportional to the mean velocity gradient:
${\tau }_{\text{turb}}=-\rho \overline{u^{\prime }{v}^{\prime }}={\mu }_t\frac{d\overline{u}}{dy}$
Here, ${\mu }_t$ is the turbulent viscosity (or eddy viscosity).

Conclusion:
The concept of eddy viscosity is a mathematical model introduced specifically to represent the momentum transfer caused by velocity fluctuations. Since these fluctuations generate the Reynolds stresses, it is the Reynolds stresses that are physically responsible for the existence and modeling of eddy viscosity in a turbulent boundary layer.