Assessing the White-in-Time Stochastic Forcing in Resolvent Prediction of Velocity and Pressure for Turbulent Channel Flow

Research on the frequency spectra of velocity and pressure fluctuations in turbulent channel flow is central to applications in petroleum engineering, including pipeline transport efficiency, erosion prediction, and flow-induced vibration in wellbores and surface facilities. Direct numerical simulation at high Reynolds numbers remains prohibitively expensive, motivating the use of resolvent analysis as a computationally efficient alternative. The resolvent analysis, formulated from the linearized Navier–Stokes equations, relies on appropriate modeling of stochastic forcing. In this work, we demonstrate that the conventional white-in-time stochastic forcing model exhibits fundamental deficiencies in predicting velocity and pressure statistics. Specifically, it fails to reproduce the correct two-point correlation of the wall-normal velocity, leading to inaccurate predictions of the rapid pressure spectrum. Moreover, it does not capture the correct wall-normal distribution of the forcing divergence, resulting in erroneous predictions of the slow pressure component. More fundamentally, we rigorously show that a linear convection–diffusion system driven by white-in-time stochastic forcing possesses an infinite frequency bandwidth, which implies unphysical vanishing Taylor time microscales for velocity fluctuations. These results highlight intrinsic limitations of white-in-time forcing and demonstrate the necessity of adopting colored-in-time stochastic forcing models to obtain physically consistent spectral predictions.