Session J27: Waves: Surface Waves

Characterizing Energy Dissipation of Shallow-Water Breaking Waves in a Storm Surge

While understanding breaking waves is crucial for the development of parameterizations used in modeling ocean and climate, the complete description of wave breaking is not well understood. We present direct numerical simulations of two-dimensional solitary waves that break on a uniform beach in shallow water, including storm surge represented by an inshore region. The storm surge depth, beach slope, and breaker amplitude are varied to study the breaker property dependence on wave and bathymetric parameters. We classify breaker types and find a separation between plunging and spilling breakers when scaled by wave breaking amplitude and depth. We compare energy dissipation during the breaking process with results from the literature without storm surge. A representation of energy dissipation in this solitary wave breaker data is also compared with prior experiments and simulations of breakers in deep water, and possibilities of a unifying model are explored. We conclude that a previously developed shallow-water inertial dissipation model for wave breaking on a uniform slope can be extended to this storm surge environment with good data collapse.

    

The effect of surfactants on the surface profiles and droplet generation in a plunging breaker

An experimental study is conducted to compare the free surface profile evolution and droplet generation in a deep-water plunging breaker in the presence of three bulk concentrations of soluble surfactant (zero, below the critical micelle concentration (CMC) and above the CMC). The breakers are generated by a programmable wave maker that is set with a single motion profile that produces a dispersively focused wave packet.  The  wave profiles are measured with a cinematic LIF  technique. It is found that a plunging breaker is formed at all surfactant conditions.  In clean water and at the surfactant concentration above the CMC, the plunging jet has very smooth surfaces up to jet impact.  However, at the intermediate surfactant concentration the jet becomes convoluted before impact and the water surface under the jet appears to fall on the forward wave face before  impact.  Droplets are measured with a cinematic inline holography technique.  A preliminary experiment showed that large changes in surface dynamic properties between surfactant conditions have a large effect on the distribution of droplet diameters and velocities. Comprehensive droplet measurements are currently underway.  

    

Relationships between depth-induced breaking of solitary waves and deep-water breakers

Solitary waves offer a convenient way to study depth-limited breaking, but are difficult to relate to general breaking waves. Moreover, the energetic mechanisms of breakers have traditionally been separated into shallow- and deep-water regimes, with corresponding regime-specific parametrizations. In this talk, we will compare direct numerical simulations of depth-induced breaking solitary waves, and their breaking thresholds and energetic dissipations, with a range of experimental and numerical results in both deep and shallow water, over a range of breaker parameters. Core similarities that allow for common comparison will be identified. Particular points of discussion will include the breaking threshold, with respect to geometric, kinematic and dynamic criteria, and fundamental dimensionless parameters governing breaking onset and energetics.   

Effects of Superharmonic Generation on Wave Interactions with a Sea Ice Sheet

In the marginal ice zone (MIZ), ocean wave and sea ice processes are strongly coupled since waves cause ice breakup and the ice attenuates the incident wavefield. Determining the underlying mechanisms of this feedback loop is important in understanding the evolution of the ice pack as well as improving sea ice forecasting. While wave-ice coupling has been studied using linear wave and structural models, few works address nonlinear wave-wave interactions which are important since many key mechanisms are strong functions of wave frequency. We use a modified high-order spectral method, complemented by perturbation analysis, to determine the nonlinear response of a finite ice sheet to waves propagating from open water. We demonstrate that, due to nonlinear energy transfer to shorter waves, (a) the maximum strain in the ice sheet can as much as double the linear prediction under certain conditions and (b) the reflection of wave energy by the ice sheet is a strong function of the nonlinear interaction length scale and can significantly exceed the linear result.   

Breaking wave field statistics with a multilayer numerical framework

Wave breaking in the ocean affects the interaction between the atmosphere and upper ocean in many aspects. Statistical representations of both the waves and wave breaking are necessary at large scale, but the underlying relation between the two still bears uncertainties. Here we present a new numerical framework to simulate a broad-banded wave spectrum and its evolution by solving a semi-discretized form of the Navier-Stokes equation in the physical space. The framework is termed `multilayer model' since there are multiple layers (generalized vertical coordinate), and for each layer the equation is vertically integrated but horizontally discretized. The breaking is modeled by a slope-limiter on the surface height. We use typical wind wave spectra as input and extract the breaking wave front distribution Λ(c) (Phillips 1985). We discuss the dependence of Λ(c) and other statistical quantities (e.g. white cap coverage) on the input wave spectra.   

Dynamic surface drag modeling of wind over ocean waves

The small-scale dynamics near the wavy air-sea interface directly influence the surface wind stress and thus regulate the transfers of momentum and scalars between the atmosphere and ocean, which play an integral role in various geophysical and engineering applications. However, resolving the surface stress above ocean waves remains challenging for both experimental and numerical studies due to the broad range of scales involved. The multiscale height distribution of moving surface waves and the corresponding generation of drag forces at varying small-large scales, in particular, poses unique challenges for large eddy simulations (LESs). Here, to evaluate the surface drag, we developed a wall-layer model for wind stress using a surface-gradient-based drag (SGD) model. Model parameters, including the drag coefficient and roughness parameter, are evaluated using a dynamic methodology based on scale-invariance and self-consistency arguments of the surface drag. The main assumption is that the total drag force is independent of the filter scale and resolution. Results show that the proposed combined SGD and dynamic modeling approach can capture the effects of subgrid-scale waves on wind turbulence without ad hoc prescription of model parameters and resolving the wavy surface.   

Numerical investigation of a three-dimensional compressible multiphase flow model for the suction effect during freak wave impact on a deck

The freak wave impacting a deck with a sharp corner can occur air entrapment. After the freak wave breaks, the trapped air at the bottom of the structure forms a suction effect (i.e. negative pressure) and bubble ruptures near the structure's wall, both of which will lead to the destruction and safety failure of the structure. It is a challenging topic to numerically realize the process of the freak wave slamming on the deck based on three-dimensional compressible multiphase flow. This paper implements the CPU parallel framework through MPI and OpenMP. The CIP(Constrained Interpolation Profile) method is adopted for the convective phase and the THINC/SW(Tangent of Hyperbola for Interface Capturing with Slope Weighting Scheme) method is applied to capture the free surface. The equation of state is added to help the present model realize the unified treatment of compressible region and uncompressed region. The present model is used to study the strong nonlinearity of the freak wave slamming on a box-shape deck with different water depths and wave heights. The importance of a compressible model for the prediction of impact pressure is proved, and the characteristics of wave impact and the mechanism of suction effect are discussed. This is helpful to understand the slamming process of the freak wave.   

Echolocation Through Gravity-Capillary Waves

We present a theoretical model for the radiation and scattering of gravity-capillary waves produced by small insects, represented as an oscillating disk. We derive a solution for the radiated waves along with their added mass and damping relations. The solution for the scattering behavior of these waves off a fixed object on the surface is also described. This model builds upon existing gravity-wave solutions with a modification to the condition on the free surface. These models were compared against results produced in a mechanical wave-maker whose surface topography was measured using the free-surface synthetic Schlieren method. From these models we provide insight into how objects on the free-surface may be sensed remotely.   

Navigation hazards and rogue waves of the Eastern Mediterranean

We present a statistical analysis of the large waves and navigation hazards in the Eastern Mediterranean during the two most intense storms recorded in the last five years¹. A comprehensive analysis of buoy measurements characterize the metocean properties and wave statistics of the observed sea states using state-of-the-art models, such as the Modified-Narrow-Band (MNB) and Generalized Boccotti distributions for crest and wave heights^3,4. A novel space-time wave analysis² is carried out for estimating potential hazards for ship navigation within the area under study. In particular, we consider the scenario of two types of vessels of the Israeli Navy Fleet and a cargo ship similar in size to El Faro² navigating during the most intense sea states of the analyzed storms and provide predictions of the largest encountered waves. The probability that a fixed observer at a point of the ocean encounters a rogue wave of a sea state of significant wave height H_s exceeding the crest height 1.6H_s is approximately 1/10⁵ as predicted by the best performing MNB model. All vessels have higher probabilities (1/100 to 1/30) to encounter a rogue wave exceeding the same threshold when maneuvering through the rough waters of the storms.

    

Transverse instability of concentric solitons

Concentric water waves are among most commonly observed. In the present talk we report a construction of axisymmetric solitary waves on deep and shallow water as well as discuss the properties of the respective governing equations of the nonlinear Schrodinger and Korteweg-de Vries type, which are deduced from the complete fluid dynamics formulation with the help of multiple scales methods. By superimposing azimuthal perturbations to the constructed finite-amplitude solutions we explore their transverse instability using both spectral analysis and Hamiltonian methods, identify the transition curve depending upon the value of surface tension, and contrast with the known stability results for planar solitons on a two-dimensional water surface thereby highlighting the effect of circular geometry of the solitons.   

Microgravity Faraday waves.

The absence of the usual gravitational restoring force produced through our drop tower is known to non-trivially modify the Faraday waves created by a harmonic forcing of an open water container. The water tank is mounted on a frequency-amplitude oscillator which induced the harmonic forcing. The wave characterization is achieved through a set of cameras that image the free-surface to extract the wave amplitudes and frequencies. Experimental results are presented on the Faraday waves produced by several harmonic forcings on a free-surface water system in a microgravity environment and their differences with their g counterparts.   

The interaction between water currents and the dispersion of surface waves

When wind blows over water, the associated water current can be modeled as an inviscid parallel flow, U(z), where z is the vertical coordinate. At the water surface, waves propagate due to two restoring forces: gravity and surface tension. The phase speed, c, of a wave with wavenumber k in quiescent water was found by George Bidell Airy in the 19th century. The water current can change the relation between c and k in a non-trivial manner, because the shear induced vorticity. We regard the waves as neutral perturbations of the flow, and solve the Rayleigh equation using asymptotic techniques along the lines as those used in a similar problem [1]. We obtain new dispersion relations, c=c(k), as perturbation series whose first few terms show good agreement with the numerical solutions. The competition between the shear and gravity/surface tension is expressed by the Froude/Weber number, which have a profound influence on how strongly the current affects the propagation of waves. We find a modification of the Stokes drift which may have consequences on the Langmuir circulation, and more generally on the spread of pollutants on water surfaces.

[1] Bonfils et al. (2022).