On the Oval Shapes of Beach Stones

This article introduces a new stochastic non-isotropic frictional abrasion model, in the form of a single short partial integro-differential equation, to show how frictional abrasion alone of a stone on a planar beach might lead to the oval shapes observed empirically. The underlying idea in this theory is the intuitive observation that the rate of ablation at a point on the surface of the stone is proportional to the product of the curvature of the stone at that point and the likelihood the stone is in contact with the beach at that point. Specifically, key roles in this new model are played by both the random wave process and the global (non-local) shape of the stone, i.e., its shape away from the point of contact with the beach. The underlying physical mechanism for this process is the conversion of energy from the wave process into the potential energy of the stone. No closed-form or even asymptotic solution is known for the basic equation, which is both non-linear and non-local. On the other hand, preliminary numerical experiments are presented in both the deterministic continuous-time setting using standard curve-shortening algorithms and a stochastic discrete-time polyhedral-slicing setting using Monte Carlo simulation.

Method of the Laboratory Wave Generation for Two Dimensional Hydraulic Model Experiment in the Coastal Engineering Fields: Case of Random Waves

The experiments in coastal engineering are very complex and a lot of components should be concerned. The experience has an important role in the successful execution. Hydraulic model experiments have been improved with the development of the wave generator and the advanced measuring apparatus. The hydraulic experiments have the advantage, that is, the stability of coastal structures and the hydraulic characteristics could be observed more intuitively rather than the numerical modelings. However, different experimental results can be drawn depending on the model scale, facilities, apparatus, and experimenters. In this study, two-dimensional hydraulic experiments were performed to suggest the guide of the test wave(random wave) generation, which is the most basic and important factor for the model test. The techniques for generating the random waves with frequency energy spectrum and the range for the incident wave height [(HS)M/(HS)T = 1~1.05] were suggested. The proposed guide for the test wave generation will contribute to enhancing the reliability of the experimental results in coastal engineering.

Assessment of random wave energy dissipation due to submerged aquatic plants in shallow water using deep water wave conditions

This article addresses the random wave energy dissipation due to submerged aquatic plants in shallow water based on deep water wave conditions including estimation of wave damping. The motivation is to provide a simple engineering tool suitable to use when assessing random wave damping due to small patches of plants in shallow water. Examples of application for typical field conditions are provided. The present method versus common practice is discussed. A possible application of the outcome of this study is that it can be used as a parameterization of wave energy dissipation due to vegetation patches of limited size in operational estuarine and coastal circulation models.

Sound Field Reconstruction in Rooms with Deep Generative Models

The characterization of Room Impulse Responses (RIR) over an extended region in a room by means of measurements requires dense spatial with many microphones. This can often become intractable and time consuming in practice. Well established reconstruction methods such as plane wave regression show that the sound field in a room can be reconstructed from sparsely distributed measurements. However, these reconstructions usually rely on assuming physical sparsity (i.e. few waves compose the sound field) or trait in the measured sound field, making the models less generalizable and problem specific. In this paper we introduce a method to reconstruct a sound field in an enclosure with the use of a Generative Adversarial Network (GAN), which s new variants of the data distributions that it is trained upon. The goal of the proposed GAN model is to estimate the underlying distribution of plane waves in any source free region, and map these distributions from a stochastic, latent representation. A GAN is trained on a large number of synthesized sound fields represented by a random wave field and then tested on both simulated and real data sets, of lightly damped and reverberant rooms.

On the Effects of Non-Gaussian Wave-Slope Distribution on the Failure Probability of an Armour block of Rubble Mound Breakwater

This study examined the effect of non-Gaussian wave slope distribution on the failure probability of an armoring rock of rubble mound breakwater using numerical simulation. Numerical simulation was carried out using the Van der Meer equation and Level III reliability design method based on the Monte Carlo simulation. In doing so, modified Glukhovskiy wave height distribution and situ wave height data collected at Ulleungdo from January 1, 1979-December 31, 2019 were used. Tri-modal Gaissuian wave slope distribution was also used, which showed good agreements with situ wave data collected at Mangbang from April 26, 2017, to April 20, 2018. The probability coefficients of tri-modal Gaussian distribution were estimated using Matlab-based statistics and machine learning toolbox, MLE [Maximum Likelihood Estimates]. In the numerical simulation, the intrinsic limitations of Gaussian distribution were revealed, such as imposing a non-negligible probability mass even in the negative wave slope, under-shooting in longer and shorter waves, and over-shooting in mid-scale waves. In the case of failure probability of an armoring rock, Gaussian distribution was shown to give underestimated failure probability. The extent of underestimation was more considerable at Mangbang, where a tidal terrace of lower depth and gently varying slope was developed than at Ulleungdo. These differences were triggered by the presence of probability plateau formed in wave slope distribution whenever infra-gravity waves appear in random wave packet due to the resonant wave-wave interaction. Therefore, it can be easily conceivable that probability plateau has a significant effect on the armoring rock failure probability. Therefore, PIANC's recommendation that wave slope follows Gaussian distribution needs to be amended. Moreover, the reliability-based design of breakwater should be implemented based on tri-modal Gaussian wave slope distribution, which can accurately reproduce probability plateau.