| 摘要: | 突波(瘋狗浪、rogue wave)為突然出現、消失的時空局部罕見極端事件。其難以預測，卻廣泛存在於許多受強外界驅動的非線性系統中。水波系統裡，多數實驗皆透過機械控制槳葉，在局部區域產生紊波或大振幅瘋狗浪，探討其統計行為。然而，自然中常見的水波——風驅動之風浪(wind-wave)，其多尺度紊波的時空間波形演化和瘋狗浪的形成，卻鮮少探討。
本研究中，我們建立水平風驅動之風浪系統，並藉由光擴散成像技術，重建三維空間上波高分布。隨著風速提升，我們觀察到系統進入穩定紊波狀態，伴隨出現具有不規則波包的間歇性行進高頻大振幅水波、以及局部隨機出現的瘋狗浪。此外，經由隨機共振，在強風驅動下，水面亦於紊波中篩選出系統的尺度的盪動模態(sloshing mode)。對於上述間歇性大振幅行進波之生成，我們發現，其乃肇因於盪動波在槽畔小向風距離(fetch)處之週期性水面升降，而致之水面風速調變(modulation)。在此風速調變中，高水面具有高風速下，強大的風浪交互作用產生大振幅行進波。隨著此行進波向下游傳播，由於進一步的紊流風和水波相互作用，使振幅包絡形狀變差，導致非高斯水面高度分布具有高度拉伸的尾巴，以及瘋狗浪在大向風距離處的生成。
為了探討多尺度風浪紊波模態間之交互作用、及瘋狗浪之後續生成機制，利用希爾伯特-黃轉換，將多尺度紊波振動拆解成不同模態。我們發現，在高波峰區域，不同模態之間具有很強的相位-振幅調製，大尺度模態波峰上易產生高振幅的小尺度模態。經由此現象，可以擴展先前提出的風浪交互作用觀點：在風場吹拂下，波峰相對於波谷，由於具有較強的風浪交互作用，水面振動之大尺度模態波峰能夠激發小尺度模態之產生。這種機制可能是水面上多尺度風浪紊波形成的通用途徑之一。另一方面同時也發現，行進波峰成新月形狀、並具有2+1維時空間調製，而瘋狗浪多數好發於兩交錯新月波之尾部。基於惠更斯原理(Huygens principle)，可以了解，各個同步之小尺度模態形成的聚焦結構，是瘋狗浪在2+1維風浪紊波中形成的重要因素之一。;
Rogue wave events (RWEs), the unpredictable, spatiotemporal localized, and suddenly appeared rare extreme events, extensively appear in several nonlinear wave systems. Although RWEs are firstly observed on wind-driven ocean surfaces, in water surface wave systems, the previous laboratory studies are mainly focused on mechanically generated waves.
In this work, using diffusive light photography, we experimentally investigate the spatiotemporal dynamics of RWEs formation on the system of water surface wave solitary driven by wind. After the transition to steady wave turbulent state by increasing averaged wind speed, it is found that RWEs uncertainly emerge in the traveling burst with intermittent large irregular envelopes and high-frequency fluctuations. The bursts are associated with the stochastic resonant slow periodic wave, called sloshing wave or seiche, selected by the finite tank length under noisy driving. We propose that the emergence of the sequential large-amplitude bursts is caused by the modulated surface wind speed through the slow oscillated surface level of the sloshing wave in the small fetch region. As the bursts propagate downstream, their envelope shapes deteriorate through further turbulent wind and water wave interactions, which cause the non-Gaussian water surface height histogram with a highly stretched tail, and the generation of the uncertain RWEs in the middle fetch region.
To study the interactions between different modes in turbulence and the following formation process of the RWEs, Hilbert-Huang transformation is used to decompose wave turbulence with multiscale. It is found that the propagating crests are 2+1D spatiotemporally modulated, and the rogue waves mostly appear on the crossing tail of two crescent wind-generated wave crests. By decomposing the continuous power spectrum into empirical mode functions with specific scales, the strong phase-amplitude couplings among the different modes are identified on the high crests. That manifests the slow modes crests excite the fast modes, because of robust wind-wave interactions according to the wind profile. This mechanism may be one of the generic routes to excite the multiscale wave turbulent on the wind-driven water surface. Together with Huygens principle, the synchronized focusing structure with concave crest fronts of different modes is the key to RWE generation. |
