Measurement of Capillary Oscillations of the Sea Surface

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Capillary waves on the sea surface have a significant effect on the scattering of both optical and microwave radiation. Although the amplitude of capillary waves is fractions of a millimeter, the slopes formed on capillary waves often exceed 30°, which leads to a strong change in the effective reflection, absorption, and backscattering cross sections. Capillary waves are studied in detail in pools; however, in natural marine conditions, they could only be measured indirectly, usually by reflections or glare. In this paper, a remote method for measuring slopes, amplitudes, and direction of the wave vector of the capillary wave structure in natural conditions is proposed and applied. In the proposed method, distortions of laser beams falling from top to bottom on the sea surface are recorded on a video camera. The authors managed to solve the inverse problem of calculating all the parameters of a capillary wave based on the shape of a capillary comb in video frames. The sensitivity of the method for measuring the wave amplitude is 30 µm at a distance to the surface of over 4 m.

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作者简介

V. Sterlyadkin

MIREA – Russian Technological University

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Email: sterlyadkin@mail.ru
俄罗斯联邦, Moscow

K. Kulikovsky

MIREA – Russian Technological University

Email: sterlyadkin@mail.ru
俄罗斯联邦, Moscow

A. Zadernovsky

MIREA – Russian Technological University

Email: sterlyadkin@mail.ru
俄罗斯联邦, Moscow

参考

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2. Fig. 1. Scheme of measurements by laser wavegraph (a): 1 - the scanner illuminates separate points of the sea surface and unfolds the laser beam on orthogonal sections in the centre; 2 - the video camera registers the scattered image; b - a separate video frame. The upper edge of the image corresponds to the water-air interface.

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3. Fig. 2. Distortion of laser beams by capillary waves: a - night measurements. The sections have a scale of 50 mm. Almost vertical axis X defines the undistorted line of the laser beam, capillary wave forms short-period deviations from the smooth line ab, which is caused by the gravity wave; b - daytime measurements of capillary waves.

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4. Fig. 3. The image of a straight white thread travelled through a capillary wave on a surface depends on the angle between the wave vector k and the video camera axis X: a - θ = 20°; b - θ = 40°; c - θ = 55°. The image of the bright lower edge of the aquarium can be seen at the bottom.

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5. Fig. 4. Path of rays through the agitated sea surface: a - lateral view, ray projections on the xz plane; b - top view, xy section. Vector n1, is perpendicular to the plane of incidence passing through three points A, B, C; unit vector n2 is the normal to the sea surface at point A.

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6. Fig. 5. Dependence of slopes ξy on the deviation y of the beam from the unperturbed line at the x-coordinate specified in the legend. The angle θ between the wave vector k and the X axis is 45°.

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7. Fig. 6. Schematic of maximum gradients measurement by beam deflection at the bottom of the aquarium (a); video frame of measurements, a ruler and a black cloth are located at the bottom (b).

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8. Fig. 7. Digitised video frame (X, Y coordinate axes in pixels, px) shown in Fig. 2a, where image calibration is taken into account. The wave vector k of the capillary wave is rotated with respect to the X axis by the angle θ = -140°.

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9. Fig. 8. Dependence of the slope ξy of the normal to the surface on the beam displacement along the y-axis at the coordinate x = 170 mm and different orientation of the wave vector relative to the X-axis. The dotted line shows that the same in magnitude but opposite in sign surface slopes lead to different displacement along the y-axis, i.e. to asymmetry of the capillary lattice.

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10. Fig. 9. Dependence of the maximum capillary wave slope ξmax on the total capillary comb amplitude at the coordinate x = 170 mm. The angle θ of wave vector deviation from the x-axis is presented in the legend. The dotted line corresponds to the considered example.

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