Ultra Low Frequency Wave Produced by Underwater Oscillating Sphere and Its Measurement

When an underwater target moves in viscous fluid, it may cause the periodic movement of the surrounding fluid and generate ultra-low-frequency (ULF) gravity waves. The initial domain of the gravitational surface wave propagating above the moving target is named circular wave. This article studies the ULF circular wave generated by underwater oscillating sphere, which will provide basis for underwater long-range target detection. Firstly, the circular wave caused by the sphere oscillation in a finite deep fluid is studied based on the theory of linear potential flow. Meanwhile, the multipole expansion theory is established to solve the circular wave field. Secondly, the interface wave generated by the target oscillation in a two-layer fluid are numerically analyzed by comparison with the free surface fluctuation of a single-layer fluid. The results show that the amplitude of the internal interface displacement (AIID) is smaller than that of the free surface (AFSD). When the sphere is in the lower layer, the layering effect of the fluid has significant influences on the AFSD. Finally, the results of the pool experiment verified that the wave generated by the oscillating sphere is the surface gravity wave. Furthermore, the change trend of the test result is consistent with the simulation result.

Hydrodynamic coefficients of a floater near a partially reflecting seawall in the presence of an array of caisson blocks

In the present study, surface gravity wave scattering and radiation by a freely floating rectangular buoy placed near a partially reflecting seawall and in the presence of an array of caisson blocks are analyzed. Various hydrodynamic parameters related to the wave scattering and radiation, such as the added mass and radiation damping coefficients, correspond to sway, heave and roll motions of the floating buoy, horizontal force, vertical force and moment acting on the floating structure, and horizontal wave force acting on the partially reflecting seawall are studied for a variety of wave and structural parameters. The study reveals that the resonating pattern in various hydrodynamic coefficients occurs for moderate values of the wavenumber. Further, when the distance between the floater and the sidewall is an integral time of half wavelength, the resonating behavior in the sway, heave and roll added masses, and associated damping coefficients appears, and the aforementioned hydrodynamic coefficients change rapidly around this zone. These resonance phenomena can be diminished significantly with appropriate positioning of the floater with respect to the sidewall and in the presence of partially reflecting seawall.

Surface gravity wave effects on submesoscale currents in the open ocean

A set of realistic coastal simulations in California allows for the exploration of surface gravity wave effects on currents (WEC) in an active submesoscale current regime. We use a new method that takes into account the full surface gravity wave spectrum and produces larger Stokes drift than the monochromatic peak-wave approximation. We investigate two high wave events lasting several days — one from a remotely generated swell and another associated with local wind-generated waves — and perform a systematic comparison between solutions with and without WEC at two submesoscale-resolving horizontal grid resolutions (dx = 270 m and 100 m). WEC results in the enhancement of open-ocean surface density and velocity gradients when the averaged significant wave height HS is relatively large (> 4.2m). For smaller waves, WEC is a minor effect overall. For the remote swell (strong waves and weak winds), WEC maintains submesoscale structures and accentuates the cyclonic vorticity and horizontal convergence skewness of submesoscale fronts and filaments. The vertical enstrophy ζ2 budget in cyclonic regions (ζ/f > 2) reveals enhanced vertical shear and enstrophy production via vortex tilting and stretching. Wind-forced waves also enhance surface gradients, up to the point where they generate a small-submesoscale roll-cell pattern with high vorticity and divergence that extends vertically through the entire mixed layer. The emergence of these roll-cells results in a buoyancy gradient sink near the surface that causes a modest reduction in the typically large submesoscale density gradients.

Bragg Scattering of Surface Gravity Waves Due to Multiple Bottom Undulations and a Semi-Infinite Floating Flexible Structure

Surface gravity wave interaction with a semi-infinite floating elastic plate in the presence of multiple undulations has been studied under the assumption of linearized water wave theory and small amplitude structural response. The elastic plate is modeled using the Euler-Bernoulli beam equation, whilst the multiple undulations are categorized as an array of submerged trenches or breakwaters. The numerical solution obtained in finite water depth using the boundary element method is validated with the semi-analytic solution obtained under shallow water approximation. Bragg resonance occurs due to the scattering of surface waves by an array of trenches or breakwaters irrespective of the presence of the floating semi-infinite plate. The zero-minima in wave reflection occur when the width of the trench and breakwater is an integer multiple of 0.6 and 0.35 times wavelength, respectively, as the number of trenches or breakwaters increases. In contrast to trenches and breakwaters in isolation, non-zero minima in wave reflection occur in the presence of a semi-infinite plate. Moreover, the number of complete cycles in trenches is less than the number of complete cycles in breakwaters, irrespective of the presence of the floating structure. The frequency of occurrence of zero minimum in wave reflection is reduced in the presence of the semi-infinite plate, and wave reflection increases with an increase in rigidity of the floating plate. Time-dependent simulation of free surface displacement and plate deflection due to multiple undulations of seabed in the presence of the semi-infinite floating plate is demonstrated in different cases.

Performance Assessments of Hurricane Wave Hindcasts

Landfalling tropical cyclones (TC) generate extreme waves, introducing significant property, personal, and financial risks and damage. Accurate simulations of the sea state during these storms are used to support risk and damage assessments and the design of coastal structures. However, the TCs generate a complex surface gravity wave field as a result of the inherently strong temporal and spatial gradients of the wind forcing. This complexity is a significant challenge to model. To advance our understanding of the performance of these models on the eastern seaboard of the United States, we conduct an assessment of four hindcast products, three based on WAVEWATCH-III and the other using the Wave Modeling project, for six major landfall TCs between 2011–2019. Unique to our assessment was a comprehensive analysis of these hindcast products against an array of fixed wave buoys that generate high quality data. The analysis reveals a general tendency for the wave models to underestimate significant wave height (Hs) around the peak of the TC. However, when viewed on an individual TC basis, distinct Hs error patterns are evident. Case studies of hurricanes Sandy and Florence illustrate complex Hs bias patterns, likely resulting from various mechanisms including insufficient resolution, improper wind input and source term parameterization (e.g., drag coefficient), and omission of wave–current interactions. Despite the added challenges of simulating complex wave fields in shallow coastal waters, the higher resolution Wave Information Study and National Centers for Environmental Prediction (ST4 parameterization only) hindcasts perform relatively well. Results from this study illustrate the challenge of simulating the spatial and temporal variability of TC generated wave fields and demonstrate the value of in-situ validation data such as the north Atlantic buoy array.

Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

Internal waves in a stratified fluid with a constant buoyancy frequency were studied, with special attention given to rogue modes, extreme waves, dynamical evolution, and Fermi–Pasta–Ulam–Tsingou type recurrence phenomena. Rogue waves for triads in a general physical setting have recently been derived analytically, but the implications in a fluid mechanics context have not yet been fully assessed. Numerical simulations were conducted for cases of coupled triads where the common member is a daughter wave mode. In sharp contrast with previous studies, rogue modes instead of plane waves were used as the initial condition. Furthermore, spatial dependence was incorporated. Rogue or extreme waves in one set of triads provided a possible mechanism for significant energy transfer among modes of the internal wave spectrum, in addition to the other known theories, e.g., weak turbulence. Remarkably, Fermi–Pasta–Ulam–Tsingou recurrence types of growth and decay cycles arose, similarly to those observed for surface gravity wave groups governed by the cubic nonlinear Schrödinger equation. These mechanisms will enhance our understanding of transport processes in oceans.