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This investigation analyses special papers and doctoral theses that treat transitions of pipe flows as a resonance phenomenon of wave frequencies. These frequencies are natural frequencies of pipe flows, of components of the test section and of vortex ring formations. Resonance conditions are derived that show how the critical Reynolds number, Rec, depends on the volume of the plenum chamber, the pipe diameter, the pipe length, etc. The derived resonance relations were verified experimentally using the experimental data of the third author, yielding $ R{e_c} \sim 1/\sqrt {{V_{ple}}} $ R e c ∼ 1 / V ple , $ R{e_c}\sim 1/\left({\sqrt L D} \right) $ R e c ∼ 1 / (L D) and other interesting results. These findings suggest that the laminar-to-turbulent transition has various modes and transitive dependences. To understand this fully, it is necessary to take all components of the test section involved into account. The test section considered in this paper consists of a mass flow controller to supply the airflow and a plenum chamber, followed by the actual pipe of interest. It is shown that all the components can contribute to the measured value of the critical Reynolds number of pipe flow transition. [ABSTRACT FROM AUTHOR]

Regional flood frequency analysis is still an important area of hydrology research as there are many ungauged catchments. The majority of hydrological methods in regional flood frequency analysis involve complex non‐linear relationships between predictor variables and flood characteristics. In the past, dimensionality reduction techniques based on linear methods such as canonical correlation analysis (CCA) were used in regional flood frequency analysis to delineate hydrological clusters. Non‐linear dimensionality reduction techniques, such as KCCA and multidimensional scaling (MDS), have been used in several fields of science, but not explicitly in regional flood frequency analysis. To determine hydrologically similar clusters, the approaches considered in this article use CCA, KCCA, and MDS as dimensionality reduction techniques in conjunction with Gaussian mixture models (GMM). Log‐linear regression and generalized additive models are then applied to the hydrological clusters to evaluate regional flood frequency analysis. A comparison of linear and non‐linear (NL) methods is performed using data from Victoria, Australia, to demonstrate the benefit of these methods. It has been found that the non‐linear frameworks of multi‐dimensional scaling with Gaussian mixture model‐non‐linear (MDSGMM‐NL) and KCCA with Gaussian mixture model‐non‐linear (KCCAGMM‐NL), as well as the mixed frameworks (i.e. KCCA and Gaussian mixture model‐non‐linear [CCAGMM‐NL]), can be used to represent the non‐linear complexities of hydrological processes in regional flood frequency analysis. [ABSTRACT FROM AUTHOR]