Experimental Study of the Formation of Three-Dimensional Waves from a Two-Dimensional Solitary Wave on Vertically Fallin
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EXPERIMENTAL STUDY OF THE FORMATION OF THREE-DIMENSIONAL WAVES FROM A TWO-DIMENSIONAL SOLITARY WAVE ON VERTICALLY FALLING LIQUID FILMS A. V. Bobylev∗ , V. V. Guzanov, A. Z. Kvon,
UDC 532.59
S. M. Kharlamov, and D. M. Markovich
Abstract: The decay of a two-dimensional solitary wave into three-dimensional waves in film flow along a vertical plate has been studied using a high-speed laser-induced fluorescence technique that allows high spatial and temporal resolution measurements of the thickness of wave liquid films. It has been shown that the three-dimensional wave packet resulting from the decay of a two-dimensional solitary wave has a strong perturbing effect on the falling film and leads to the formation of rivulets on its surface. Keywords: liquid film, solitary wave, transverse instability, three-dimensional wave, laser-induced fluorescence. DOI: 10.1134/S0021894420030013 INTRODUCTION Viscous liquid film flows under gravity are ubiquitous both in nature and industrial applications. In many cases of practical interest, film flow is unstable, with two-dimensional and three-dimensional waves propagating on its free surface and affecting flow characteristics. A large number of reduced-dimension models have been proposed to describe the evolution of waves on flowing liquid films, in particular, models based on the boundarylayer approximation, which provide an explanation for many observed features of wave flow, especially in the case of two-dimensional waves, for which there is a large body of experimental data. Although three-dimensional wave regimes of film flow are considered regimes of the final stage of wave evolution in a wide range of liquid flow rates, they have been investigated less extensively than two-dimensional regimes, in particular, due to the fact that a comparison of simulation and experiment results requires sophisticated methods for measuring the characteristics of three-dimensional waves with high accuracy. Experimental data obtained using such methods are generally well consistent with the results of calculations performed using boundarylayer models. For example, the results of modeling [1, 2] of three-dimensional solitary waves and transverse instability of two-dimensional using the Shkadov model [3] are in agreement with experimental data [4, 5]. The results of modeling the formation of three-dimensional waves due to instability in the transverse direction (hereinafter, transverse instability) of regular two-dimensional waves using a more complex boundary-layer model [6] are in qualitative agreement with the results of experiments [7, 8], in which the development of transverse instability
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090, Russia; ∗ [email protected]; [email protected]; [email protected]; [email protected]; [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 3, pp. 5–10, May–June, 2020. Original article submitted March 18, 2020; revision submitted March 18, 2020; accepted for publication March 30
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