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.
Zhu et al. (Tue,) studied this question.