Concave Wave Research Articles

Impact dynamics of debris flow against rigid obstacle in laboratory experiments

Debris-flow impact against rigid obstacle involves instant redirection of flow velocity and elevation of flow depth, and could serve as a stringent approach for verification of the two-phase flow models. In this study, kinetic and dynamic behavior of debris-flow impact with varying flow regime has been analyzed on the basis of laboratory tests with distributed measurement. Debris flows interact with obstacle in the modes of vertical jet (deflected vertically) and momentum jump (reflected upstream). The experimental results are further adopted to verify the predictability of vertical jet model and momentum jump model. Our findings highlight that, due to the elevated confining stress in the impact area, the liquefaction ratio increases, resulting in a more “fluid-like” state of debris flow. The two analytical models could distinguish the runup height around the threshold Froude number 3–4. However, the impact loads under both modes could be very close, because the effective impact in the vertical jet mode only concentrates in the lower portion of runup height. The potential threat of flip-through impact (shock impact by a steep or concave wave front) should also be considered, as its impulse load could be much higher than the predicted load by vertical jet and momentum jump models.

Change of Surface and Electrical Characteristics of Silicon Wafer by Wet Etching(1) - Surface Morphology Changes as a Function of HF Concentration -

The electrical properties and surface morphology changes of a silicon wafer as a function of the HF concentration as the wafer is etched were studied. The HF concentrations were 28, 30, 32, 34, and 36 wt%. The surface morphology changes of the silicon wafer were measured by an SEM (<TEX>$80^{\circ}$</TEX> tilted at <TEX>${\times}200$</TEX>) and the resistivity was measured by assessing the surface resistance using a four-point probe method. The etching rate increased as the HF concentration increased. The maximum etching rate 27.31 <TEX>${\mu}m/min$</TEX> was achieved at an HF concentration of 36 wt%. A concave wave formed on the wafer after the wet etching process. The size of the wave was largest and the resistivity reached 7.54 <TEX>$ohm{\cdot}cm$</TEX> at an 30 wt% of HF concentration. At an HF concentration of 30 wt%, therefore, a silicon wafer should have good joining strength with a metal backing as well as good electrical properties.

Numerical investigation of large amplitude second mode internal solitary waves over a slope-shelf topography

A numerical study of the propagation and transformation of large amplitude second mode concave internal solitary waves (ISWs) over a slope-shelf topography is presented. A fully nonlinear and non-hydrostatic numerical model is employed and solved. The fluid stratification, amplitude of the incident wave, and inclination of the bottom topography are taken close to those in the northern South China Sea (SCS), where the continental slope and shelf span quite a large area. It is found that the incoming wave adjusts permanently to the changing depth in deep water without essential changes of the wave profile until it gets close to the shelf break, where the frontal face becomes flatter and the rear face steeper. A very steep wave structure is formed at the leading edge just after the wave passes by the shelf break. This steep structure does not progress into a new soliton of concave type, but slopes more and more gently. The trailing edge of the initial concave wave becomes steeper and steeper and gradually develops into a packet of convex ISWs. Finally the rear convex wave packet catches up with the frontal concave wave. The two wave systems then “merge” and travel forward steadily with almost permanent profile. No events of wave breaking occur with the model configuration close to the realistic slope-shelf of the northern SCS. Finally, amplitudes of the incident wave and inclination of the slope are varied, and different scenarios take place before and after the wave reaches the shelf break.

Convex and concave types of second baroclinic mode internal solitary waves

Abstract. Two types of second baroclinic mode (mode-2) internal solitary waves (ISWs) were found on the continental slope of the northern South China Sea. The convex waveform displaced the thermal structure upward in the upper layer and downward in the lower layer, causing a bulge in the thermocline. The concave waveform did the opposite, causing a constriction. A few concave waves were observed in the South China Sea, marking the first documentation of such waves. On the basis of the Korteweg-de Vries (K-dV) equation, an analytical three-layer ocean model was used to study the characteristics of the two mode-2 ISW types. The analytical solution was primarily a function of the thickness of each layer and the density difference between the layers. Middle-layer thickness plays a key role in the resulting mode-2 ISW. A convex wave was generated when the middle-layer thickness was relatively thinner than the upper and lower layers, whereas only a concave wave could be produced when the middle-layer thickness was greater than half the water depth. In accordance with the K-dV equation, a positive and negative quadratic nonlinearity coefficient, α2, which is primarily dominated by the middle-layer thickness, resulted in convex and concave waves, respectively. The analytical solution showed that the wave propagation of a convex (concave) wave has the same direction as the current velocity in the middle (upper or lower) layer. Analysis of the three-layer ocean model properly reproduced the characteristics of the observed mode-2 ISWs in the South China Sea and provided a criterion for the existence of convex or concave waves. Concave waves were seldom seen because of the rarity of a stratified ocean with a thick middle layer. This analytical result agreed well with the observations.

Three‐dimensional shoaling of large‐amplitude internal waves

The three‐dimensional (3‐D) shoaling of large‐amplitude internal waves (LAIW) is studied in the framework of a fully nonlinear nonhydrostatic numerical model. The vertical fluid stratification, parameters of the propagating waves and bottom topography were taken close to those observed in the northern part of the Andaman Sea. It was found that three‐dimensional evolution of LAIWs propagating from the deep part of a basin onto the shelf differs from two‐dimensional shoaling in many ways largely because of the process of wave refraction developing in the areas of local bottom elevations or depressions. In the 3‐D case the wave refraction produces concave and convex fragments of the wave fronts which may lead to the transverse redistribution of energy along the wave. Results demonstrate that concave wave fragments work as optical lenses focusing the wave energy to the centers of curvature. This process is especially important for LAIWs in shallow water zones where wave amplitudes are close to the saturation level. In general, the wave refraction leads to more fast wave breaking than that in the 2‐D case. As a results, it should be expected to find localized regions of higher levels of water mixing and turbulence in the vicinity of local banks and headlands where LAIWs produce concave patterns. The areas of local bottom depressions, on the contrary, should be considered as potential places with lower level of background mixing.

Beyond the Kuramoto-Zel’dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon

In numerical experiments with the Fitzhugh-Nagumo set of reaction-diffusion equations describing two-dimensional excitable media, unusual solutions are found that correspond to a concave spiral wave steadily rotating round a circular obstacle in a finite-size medium. Such a wave arises in the region of parameters corresponding to the solitonlike regime (see text); it appears due to the interaction between the peripheral areas of a “seed” spiral wave with a convex front and the echo waves incoming from the outer boundaries of a medium. The solutions obtained are in contradiction with intuition and represent a numerical counterexample to the known theories that forbid steadily moving excitation waves with concave fronts. Nevertheless, a concave spiral wave is a stable object; being transformed to the usual spiral wave with a convex front by suppressing echo at the outer boundaries of the medium, it is again recovered upon restoring the echo conditions. In addition to the single-arm spiral concave wave, solutions are obtained that describe multiarm waves of this type; for this reason, the concave fronts of these waves are a coarse property.

The behavior of weak shock waves near focal points and caustics

The paper is concerned with the theoretical description of focusing weak, N-shaped shock waves. The shock rise times of the incoming shock fronts are assumed to be very small, but finite. Furthermore, focusing is assumed to be caused by only slightly concave wave fronts. The functional correspondence of refraction effects included already in a linear wave theory and steepening effects described by nonlinear wave theories are discussed in details by singular perturbation methods. Preliminary numerical evaluations of the resulting implicit solution agree well with known experimental data.