Asymptotics of sloshing eigenvalues for a triangular prism

We consider the three-dimensional sloshing problem on a triangular prism whose angles with the sloshing surface are of the form ${\pi}/{2q}$ , where q is an integer. We are interested in finding a two-term asymptotic expansion of the eigenvalue counting function. When both angles are ${\pi}/{4}$ , we compute the exact value of the second term. As for the general case, we conjecture an asymptotic expansion by constructing quasimodes for the problem and computing the counting function of the related quasi-eigenvalues. These quasimodes come from solutions of the sloping beach problem and correspond to two kinds of waves, edge waves and surface waves. We show that the quasi-eigenvalues are exponentially close to real eigenvalues of the sloshing problem. The asymptotic expansion of their counting function is closely related to a lattice counting problem inside a perturbed ellipse where the perturbation is in a sense random. The contribution of the angles can then be detected through that perturbation.

Massed Strandings of Whales and Dolphins – Effects of Wind, Waves and Tides.

We examined125 mass-stranding events of cetaceans (>=10 individuals) on New Zealand shores over the past 40 years. The wind, waves, wave refraction, shore slopes and tides at the dates and locations of these events were considered. The mass-strandings involved 10 different species, but by far the most common involved the Long-finned Pilot Whale, Globicephala melas. Our hypothesis is that mass-stranding is a three-stage process. The first stage is when an animal becomes ill, its body may become bloated and float on the surface, and the wind and waves may drive it ashore. We assume the second stage is that the dying or dead body may be accompanied by pod members as a result of strong social bonds. The third stage involves the tides and the beach slope. If these are of sufficient amplitude, the nearby attendees will quickly become stranded in the intertidal of a gently sloping beach as the water level falls. We have evaluated evidence for the first and third stages. In the overwhelming majority (91%) of the mass-strandings (omitting events inside estuaries), the available data showed that wind and waves would drive floating objects (bodies) toward the stranding site. Examination of the nearshore slopes and the tide ranges showed that the vast majority of the stranding sites were slowly shelving beaches where the tides would retreat rapidly over 10s of metres. These 2 results are even more pronounced if only Pilot Whale mass strandings are considered.

3D Linked Subduction, Dynamic Rupture, Tsunami, and Inundation Modeling: Dynamic Effects of Supershear and Tsunami Earthquakes, Hypocenter Location, and Shallow Fault Slip

Physics-based dynamic rupture models capture the variability of earthquake slip in space and time and can account for the structural complexity inherent to subduction zones. Here we link tsunami generation, propagation, and coastal inundation with 3D earthquake dynamic rupture (DR) models initialized using a 2D seismo-thermo-mechanical geodynamic (SC) model simulating both subduction dynamics and seismic cycles. We analyze a total of 15 subduction-initialized 3D dynamic rupture-tsunami scenarios in which the tsunami source arises from the time-dependent co-seismic seafloor displacements with flat bathymetry and inundation on a linearly sloping beach. We first vary the location of the hypocenter to generate 12 distinct unilateral and bilateral propagating earthquake scenarios. Large-scale fault topography leads to localized up- or downdip propagating supershear rupture depending on hypocentral depth. Albeit dynamic earthquakes differ (rupture speed, peak slip-rate, fault slip, bimaterial effects), the effects of hypocentral depth (25–40 km) on tsunami dynamics are negligible. Lateral hypocenter variations lead to small effects such as delayed wave arrival of up to 100 s and differences in tsunami amplitude of up to 0.4 m at the coast. We next analyse inundation on a coastline with complex topo-bathymetry which increases tsunami wave amplitudes up to ≈1.5 m compared to a linearly sloping beach. Motivated by structural heterogeneity in subduction zones, we analyse a scenario with increased Poisson's ratio of ν = 0.3 which results in close to double the amount of shallow fault slip, ≈1.5 m higher vertical seafloor displacement, and a difference of up to ≈1.5 m in coastal tsunami amplitudes. Lastly, we model a dynamic rupture “tsunami earthquake” with low rupture velocity and low peak slip rates but twice as high tsunami potential energy. We triple fracture energy which again doubles the amount of shallow fault slip, but also causes a 2 m higher vertical seafloor uplift and the highest coastal tsunami amplitude (≈7.5 m) and inundation area compared to all other scenarios. Our mechanically consistent analysis for a generic megathrust setting can provide building blocks toward using physics-based dynamic rupture modeling in Probabilistic Tsunami Hazard Analysis.

Stagnant peaked free surface released at a sloping beach

A stagnant free-surface flow is an instantaneous flow field of pure acceleration with zero velocity and a deformed surface. There exists a potential-flow acceleration field. With zero velocity and the acceleration field given, there is a limiting free-surface position which possesses one peak at its point of highest elevation. By complex analysis, it can be shown that the surface peak has a right angle. We elaborate on an elementary model of two-dimensional stagnant free-surface flow with a peak. Our model may serve to describe a situation of maximal single-wave run-up with a given energy at a uniformly sloping beach. The highest possible run-up of an incoming solitary wave corresponds to zero kinetic energy. It encompasses an idealized situation where the kinetic wave energy is converted into potential energy in a water mass piling up along the slope to become stagnant at one single moment. Multipoles with singularities outside the fluid domain may give rise to a smooth and gradual deceleration needed for a non-breaking run-up process. A pair of dipoles with an orientation perpendicular to a given slope represents the stagnant acceleration fields with the highest surface peak spatially concentrated along the slope. Thereby, a one-parameter family of surface shapes is constituted, only dependent on the slope angle. The initial flow field, the initial free surface, the initial isobars and the geometric parameters are all calculated for different slope angles.

TSUNAMI RUNUP AMPLIFICATION OF BREAKING AND NON-BREAKING ERROR-FUNCTION WAVES OVER A SLOPING BEACH IN SHADOW ZONE BY A SMALL ISLAND

The time series of free surface elevation measured in and outside the shadow zone were compared and analyzed in the time-frequency domain by employing the continuous wavelet transform. Regardless of the conditions of the ERF wave in the shadow zone, an increase in magnitude of energy is noticeable not only in the peak frequency within a range of approximately 0.8 to 1 Hz but also in the low-frequency range of around 0.1 Hz corresponding to second up to third crest of the leading wave. To determine the effective frequency of ERF waves and evaluate their runup characteristics, we applied a new method of describing the ERF wave, which consists of linear superposition of two solitary waves. As a result, the ERF waves show the same trend in runup characteristics as for solitary waves.

Wave-Induced Distribution of Microplastic in the Surf Zone

In this study, the wave-induced distribution of 13 microplastic (MP) samples of different size, shape, and density was investigated in a wave flume with a sandy mobile beach bed profile. The particle parameter were chosen based on an occurrence probability investigated from the field. MP abundances were analyzed in cross-shore and vertical direction of the test area after over 40,000 regular waves. It was found, that MP particles accumulated in more shallow waters with increasing size and density. Particles with high density (ρs>1.25 g/cm3) have been partly confined into deeper layers of the sloping beach during the formation of the bed profile. Particles with a density lower than that of water used in the experiments floated constantly in the surf zone or deposited on the beach caused by wave run-up. A correlation was found between the settling velocity of the MP particles and the flow velocity at the accumulation point and a power function equation developed. The obtained results were critically discussed with findings from the field and further laboratory studies.

Habitat Preference and Abundance of Mole Crab Based on Sea Tides in Coastal Area of Kebumen Regency

Mole crab is an important resource in the food chain cycle and an initial level consumers in sandy areas. Mole crab lives in the swash zone that is affected by sea tides. Comparison of habitat and abundance of each station based on tides in terms of the type of utilization of the study location. The purpose of this study was to determine the abundance at high tide and low tide, species, and habitat preferences of mole crab, also to determine the relationship between their habitat preferences and their abundance. The method used in this study was descriptive exploratory and uses purposive random sampling technique. Abundance data collection was done by using a 10 x 10meter transect quadrant at two spring tides and two neap tides in the swash zone area. The results showed that the abundance of mole crab at high tide was 214 - 239 ind/100m2 and at low tide was 378 - 509 ind/100m2. There are three types of mole crab that has been found, Emerita emeritus, Hippa adactyla and Albunea symmysta. Favored habitat of mole crab in coast area of Kebumen Regency has a flat to sloping beach, wide swash zone at high tide 14.5 - 24.5m, and at low tide is 20 - 32.5m, medium sized beach sand (0.25-0.5mm), and has low organic material values. The results of the PCA (Principal Component Analysis) analysis that the sediment grain size and the width of the swash zone have a positive correlation with the abundance of mole crab.