On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements
On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements
复制标题
关于陡峭重力波产生的寄生毛细波：空间和时间测量的实验研究
DOI：
10.1017/s0022112093002605
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发表时间：
1993
影响因子：
3.7
通讯作者：
C. Ting
中科院分区：
文献类型：
--
作者：
M. Perlin;Huanjay Lin;C. Ting
据报道，对陡峭的高频重力波（∼ 4 至 5 Hz）及其产生的寄生毛细波进行了实验研究。使用新技术进行空间和时间非侵入式表面测量。该技术采用柱面透镜放大垂直尺寸，并结合增强型高速成像系统，以 10 μm 量级的垂直表面高程分辨率促进不同尺度的测量。因此，高频寄生毛细波和底层重力波在空间和时间上同时准确地测量。提出了空间表面高程测量的时间序列。结果表明，毛细波的位置在随底层重力波的相速度移动的坐标系中是准静止的。毛细管的振幅和波数在空间中被调制；然而，它们不会相对重力波传播。由于毛细管振幅明显减小，然后在类似复发的现象中再次增加，因此推测存在共振机制。将测量的表面轮廓与 Longuet-Higgins (1963) 和 Crapper (1970) 的理论以及 Schwartz & Vanden-Broeck (1979) 的精确二维数值公式进行比较。实验波列和理论波列在振幅和波数方面都存在显着差异。当在 Longuet-Higgins 模型中使用重力波的实测相速度、幅度和波长时，毛细波幅度的理论预测远小于实测幅度。此外，与实验相比，该理论预测毛细管的波数更大。 Crapper 模型预测了重力波前向面上正确的数量级毛细波振幅，但与实验相比，预测了背风面上更大的振幅。此外，它预测的毛细管波数比实验确定的要大。将测量的轮廓与使用 Schwartz & Vanden-Broeck 数值公式确定的稳态、对称、周期解的多个解进行比较，显示出类似的差异。特别是，数值模型中假设的关于波峰和波谷的波形对称性排除了与实验的积极比较，实验中的底层波在前表面上比在背风表面上表现出明显更大的毛细管。此外，对于相同的无量纲表面张力和陡度参数，先验未知的多重数值解使比较变得复杂。最后，利用波场的时间周期性，构建几个连续波长的合成图像，根据该图像计算势能和表面能作为下游距离的函数。
An experimental investigation of steep, high-frequency gravity waves (∼ 4 to 5 Hz) and the parasitic capillary waves they generate is reported. Spatial, as well as temporal, non-intrusive surface measurements are made using a new technique. This technique employs cylindrical lenses to magnify the vertical dimension in conjunction with an intensified, high-speed imaging system, facilitating the measurement of the disparate scales with a vertical surface-elevation resolution on the order of 10 μm. Thus, high-frequency parasitic capillary waves and the underlying gravity wave are measured simultaneously and accurately in space and time. Time series of spatial surface-elevation measurements are presented. It is shown that the location of the capillary waves is quasi-stationary in a coordinate system moving with the phase speed of the underlying gravity wave. Amplitudes and wavenumbers of the capillaries are modulated in space; however, they do not propagate with respect to the gravity wave. As capillary amplitudes are seen to decrease significantly and then increase again in a recurrence-like phenomenon, it is conjectured that resonance mechanisms are present. Measured surface profiles are compared to the theories of Longuet-Higgins (1963) and Crapper (1970) and the exact, two-dimensional numerical formulation of Schwartz & Vanden-Broeck (1979). Significant discrepancies are found between experimental and theoretical wavetrains in both amplitude and wavenumber. The theoretical predictions of the capillary wave amplitudes are much smaller than the measured amplitudes when the measured phase speed, amplitude, and wavelength of the gravity wave are used in the Longuet-Higgins model. In addition, this theory predicts larger wavenumbers of the capillaries as compared to experiments. The Crapper model predicts the correct order-of-magnitude capillary wave amplitude on the forward face of the gravity wave, but predicts larger amplitudes on the leeward face in comparison to the experiments. Also, it predicts larger capillary wavenumbers than are experimentally determined. Comparison of the measured profiles to multiple solutions of the stationary, symmetric, periodic solutions determined using the Schwartz & Vanden-Broeck numerical formulation show similar discrepancies. In particular, the assumed symmetry of the waveform about crest and trough in the numerical model precludes a positive comparison with the experiments, whose underlying waves exhibit significantly larger capillaries on their forward face than on their leeward face. Also, the a priori unknown multiplicity of numerical solutions for the same dimensionless surface tension and steepness parameters complicates comparison. Finally, using the temporal periodicity of the wave field, composite images of several successive wavelengths are constructed from which potential energy and surface energy are calculated as a function of distance downstream.