A semi-infinite domain eigenvalue problem describing turbulent velocity fluctuations

This paper discusses the formulation and approximate solution of an eigenvalue problem that provides estimates for fully turbulent velocity fluctuations. The fluctuating velocity model is derived by splitting the Reynolds decomposed (but not averaged) Navier–Stokes equations into mean and fluctuating expressions. The linear fluctuating portion of the equations (normally lost to averaging) poses a semi-infinite domain eigenvalue problem. Approximate analytical solutions are derived that suggest a qualitatively physically plausible solution. The derivation and use of these expressions are not known in the literature implying that a qualitative scoping study of this nature is appropriate. This type of analysis provides support for the practical application of these equations to estimate structural loadings due to the presence of turbulent velocity and pressure fluctuations.