Kinematics of the First Wave Faraday Mode on the Side Wall of a Rectangular Vessel

Мұқаба

Дәйексөз келтіру

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Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Рұқсат ақылы немесе тек жазылушылар үшін

Аннотация

New results of experiments on studying the first Faraday wave mode on the surface of a shallow liquid in a rectangular vessel are given. For regular waves, resonance dependences were measured and the wave profiles were analyzed. It is shown that the presence of a moving local surface elevation in the form of a hump is associated with the nonlinearity of wave oscillations of liquid. A comparison is made with a theoretical model of nonlinear gravity waves. The mechanism of breaking the first Faraday wave mode consisting in the formation of a plane jet ejection on the side wall of the vessel as a result of focusing fluid flows in the growing crest and surface hump has been studied.

Толық мәтін

Рұқсат жабық

Авторлар туралы

V. Kalinichenko

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Хат алмасуға жауапты Автор.
Email: kalin@ipmnet.ru
Ресей, Moscow

Әдебиет тізімі

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2. Fig. 1. Profiles of regular waves with a time step of a quarter period: a-c - n = 1, (h = 5, 7.5, 10 cm, T = 1.356, 1.224, 1.110 s, H = 4.0, 5.8, 7.9 cm); d - n = 2, T = 0.814 s, H = 4.4 cm. The time interval for the three profiles on a-d corresponds to a quarter of the wave period.

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3. Fig. 2. a) Resonance dependences of H (Ω) for the first 1-4 and second 5 modes of regular waves at the water surface of different depth h: 1-4 - n = 1, h = 5, 7.5, 10, 20 cm; 5 - n = 2, h = 5 cm; solid curves - calculated dependence of H (Ω) for Faraday gravity waves [15, 17]; b) dependence of the wave steepness of the limiting height on the dimensionless depth of the liquid (n = 1).

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4. Fig. 3. Regular wave on the free surface of water (h = 10 cm; T = 1.058 s; Ω = 11.87 s-1; H = 10.8 cm; ω = 5.938 s-1; s = 0.7 cm): a) sequence of snapshots of the free surface during the half-period of the wave (video recording at a frame rate of 1000 fps); b) profiles and velocities of the free surface particles calculated by (2.1).

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5. Fig. 4. Regular wave profiles and trajectories of tracer particles (h = 10 cm; T = 1.058 s; H = 10.8 cm; ω = 5.938 s-1; s = 0.7 cm): 1-6 - t = 0, 40, 80, 120, 160, 240 ms; right half of the vessel. Frames 1 and 4 show the velocity field of tracer particles.

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6. Fig. 5. Sequence of frames (from left to right) showing the process of the second wave mode collapse: a) - collapse of a cavern in the centre of the vessel and formation of a jet burst at the stage of crest formation; b) - two caverns and formation of two flat jets (arrows) on the side walls of the vessel at the stage of wave trough formation; n = 2; h = 5 cm; s = 1. 9 cm; Ω = 15.70 s-1; time step 0.04 s; video recording, 120 k/s; H1 - height of the surge.

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7. Fig. 6. Decaying first wave mode at the free water surface (h = 10 cm; T = 1.026 s; Ω = 12.24 s-1; ω = 6.12 s-1; s = 0.7 cm).

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8. Fig. 7. Detail of the process of flat jet formation on the side wall: 1-6 - t = 0, 40, 80, 120, 160, 200 ms; overlay of 20 video frames (20 ms). The experimental parameters are the same as in the caption to Fig. 6.

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9. Fig. 8. Breakdown of the first mode on the sidewall during video angles: 1-6 - t = 0, 40, 80, 120, 160, 200 ms. The experimental parameters are the same as in the caption of Fig. 6.

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10. Fig. 9. a) Time dependence of the jet burst height on the side wall for the first wave mode: 1, 2 - T = 1.058, 1.026 s (wave period); 3 - calculation according to (2.1); h = 10 cm; s = 0.7 cm; ω = 5.938 s-1 (based on the results of video recording at a speed of 1000 k/s); b) Time dependence of the jet burst height in the dimensionless form H1* (t*): 1-4 - (h, s, Ω / 2, Hlim) = (5, 1.9, 4.88, 4), (7.5, 1.9, 5.51, 5.5), (10, 1.9, 5.72, 7), (10, 0.7, 6.12, 7).

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