Resonant triad interactions of gravity waves in cylindrical basins

التفاصيل البيبلوغرافية
العنوان: Resonant triad interactions of gravity waves in cylindrical basins
المؤلفون: Durey, Matthew, Milewski, Paul A.
سنة النشر: 2023
المجموعة: Mathematics
Physics (Other)
مصطلحات موضوعية: Physics - Fluid Dynamics, Mathematics - Dynamical Systems
الوصف: We present the results of a theoretical investigation into the existence, evolution and excitation of resonant triads of nonlinear free-surface gravity waves confined to a cylinder of finite depth. It is well known that resonant triads are impossible for gravity waves in laterally unbounded domains; we demonstrate, however, that horizontal confinement of the fluid may induce resonant triads for particular fluid depths. For any three correlated wave modes arising in a cylinder of arbitrary cross-section, we prove necessary and sufficient conditions for the existence of a depth at which nonlinear resonance may arise, and show that the resultant critical depth is unique. We enumerate the low-frequency triads for circular cylinders, including a new class of resonances between standing and counter-propagating waves, and also briefly discuss annular and rectangular cylinders. Upon deriving the triad amplitude equations for a finite-depth cylinder of arbitrary cross-section, we deduce that the triad evolution is always periodic, and determine parameters controlling the efficiency of energy exchange. In order to excite a particular triad, we explore the influence of external forcing; in this case, the triad evolution may be periodic, quasi-periodic, or chaotic. Finally, our results have potential implications on resonant water waves in man-made and natural basins, such as industrial-scale fluid tanks, harbours and bays.
Comment: 31 pages, 6 figures
نوع الوثيقة: Working Paper
DOI: 10.1017/jfm.2023.441
URL الوصول: http://arxiv.org/abs/2301.02163
رقم الأكسشن: edsarx.2301.02163
قاعدة البيانات: arXiv