Special modes with narrow amplification diagrams in harbor oscillations: definition and parametric study

Natural modes characterized by amplification diagrams with extremely narrow peaks are frequently observed in harbor oscillations, referred to as extreme modes. This study presents a detailed numerical investigation into extreme modes. A new definition of extreme modes is established based on the modal structure instead of solely relying on the frequency–response diagram. Extreme modes arise when they primarily oscillate between the harbor walls, and one or more nodal lines intersect the harbor entrance. Subsequently, the variations exhibited by the extreme mode in response to varying geometry and wave parameters are explored, with specific consideration given to the influences of wave direction, partial reflection, and topography. The creation of an extra entrance in the oscillatory direction of the extreme mode may cause it to disappear. Moreover, the extreme mode can be significantly mitigated by slightly reducing the wave reflection between harbor walls. Changing the entrance position can adjust the modal structure and prevent nodal lines from crossing the entrance, thereby averting excessively high amplification factors. Under symmetrical conditions, extreme modes may not be activated, but slight asymmetries in wave direction, topography, or harbor layout can trigger them. The extreme modes exhibit heightened sensitivity to variations in entrance width and length compared to ordinary modes. A reduction in entrance width or an extension of the entrance length can notably intensify the extreme mode.