In this study, a white-noise stochastic forcing model is proposed for the eddy-viscosity-based linearized Navier-Stokes equations of turbulent channel flow. The white-noise stochastic forcing is first optimized by minimizing the relative errors of the generated energy profiles of velocities compared to the direct numerical simulation results with ${\text{Re}}_{\tau }=186$ to 934. For different tested eddy-viscosity models, the optimized forcing energy profiles all show self-similar properties in the near-wall region, where the optimized forcing profiles with different flow scales show a good collapse when the wall-normal coordinate is normalized by the spanwise wavelength ${\lambda }_z$. For higher regions beyond the maximum points of the optimized forcing energy profiles, their values all decrease by more than $75\%$ at the centerline of the channel compared to their maxima. Based on the optimized results, a stochastic forcing model is proposed by describing the modeled forcing energy profile with squared mean-quantity-based eddy-viscosity profiles in the near-wall region after scaling and linearly decaying profiles in the higher region beyond the maximum points. The proposed white-noise forcing model is validated for its predictions of the covariance of velocity fluctuations. For different eddy-viscosity models, the prediction errors of the covariance tensor are reduced by $35.3\%$ to $86.4\%$ when adopting the forcing model compared to the results with spatially uniform white-noise forcing. Moreover, the forcing model is also applied to predict the coherent structures specified as the proper orthogonal decomposition (POD) modes, which provides rational results for both the shapes and energy distributions of the leading three pairs of POD modes. Finally, the new model is applied to evaluate the transfer functions for estimations of large-scale structures, which exhibit notable improvements compared to the results based on spatially uniform white-noise forcing, with a reduction in relative estimation error by more than $80\%$.

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• Turbulence modeling
• Turbulence simulations
• Turbulent boundary layers