HYDRODYNAMICS AND ACOUSTICS

2021 ◊ Volume 2 (92) ◊ Issue 1 ◊ p. 68-93

A. A. Riabenko^*

^* National University of Water and Environmental Engineering, Rivne, Ukraine

Investigation of cnoidal water waves with the allowance for a non-hydrostatics in their initial cross-section

Gidrodin. akust. 2021, 2(1):68-93

https://doi.org/10.15407/jha2021.01.068

TEXT LANGUAGE:Ukrainian

ABSTRACT

The goal of the study is to build the mathematical model of cnoidal waves and other types of near-critical flows, which would adequately reflect the physical nature of these phenomena and take into account possible non-hydrostatics in their initial section. The accumulated information about cnoidal waves is analyzed in detail from the standpoint of a more general theory of near-critical fluid flows. Many shortcomings of the current views on the problem of cnoidal waves have been revealed. Frequently, the cnoidal waves and other types of near-critical fluid flows cannot be uniquely described by only one characteristic parameter, namely, the Froude number in the initial cross-section. The results of experimental research prove this conclusion. A conceptually new mathematical model of wave-like near-critical flows is constructed with explicit allowance for possible non-hydrostatic pressure distribution in their initial sections. Based on the proposed model, the differential equation of the free surface of the two-dimensional flow is derived, and its general solution is in the form of cnoidal waves. The two factors control the conditions for the existence of these waves: the Froude number and the coefficient of non-hydrostaticity in the initial section. As is shown, the periodic cnoidal waves can exist if the Froude numbers in their initial cross-sections are less than, equal to, and greater than unity. In addition, a necessary condition for the existence of the considered waves is the presence of non-hydrostatics in the initial section. At the same time, the curve of the free surface should be concave here, and the non-hydrostatic coefficient should be greater than unity. Extended experimental studies of stationary periodic cnoidal waves were carried out to verify the theoretical results. The obtained data fully confirmed the fundamental correctness of the constructed mathematical model.

KEY WORDS

cnoidal waves, mathematical model, near-critical flows, non-hydrostatic pressure distribution, solitary wave

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