Conical Island Research Articles

Boussinesq Modeling of Wave Transformation, Breaking, and Runup. I: 1D

In this paper, we focus on the implementation and verification of an extended Boussinesq model for surf zone hydrodynamics in two horizontal dimensions. The time-domain numerical model is based on the fully nonlinear Boussinesq equations. As described in Part I of this two-part paper, the energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves. Wave runup on the beach is simulated using a permeable-seabed technique. We apply the model to simulate two laboratory experiments in large wave basins. They are wave transformation and breaking over a submerged circular shoal and solitary wave runup on a conical island. Satisfactory agreement is found between the numerical results and the laboratory measurements.

Long wave runup on piecewise linear topographies

We study long-wave evolution and runup on piecewise linear one- and two-dimensional bathymetries analytically and experimentally with the objective of understanding certain coastal effects of tidal waves. We develop a general solution method for determining the amplification factor of different ocean topographies consisting of linearly varying and constant-depth segments to study how spectral distributions evolve over bathymetry, and apply our results to study the evolution of solitary waves. We find asymptotic results which suggest that solitary waves often interact with piecewise linear topographies in a counter-intuitive manner. We compare our analytical predictions with numerical results, with results from a new set of laboratory experiments from a physical model of Revere Beach, and also with the data on wave runup around an idealized conical island. We find good agreement between our theory and the laboratory results for the time histories of free-surface elevations and for the maximum runup heights. Our results suggest that, at least for simple piecewise linear topographies, analytical methods can be used to calculate effectively some important physical parameters in long-wave runup. Also, by underscoring the effects of the topographic slope at the shoreline, this analysis qualitatively suggests why sometimes predictions of field-applicable numerical models differ substantially from observations of tsunami runup.

Numerical Modeling of Tidal Wave Runup

A numerical solution for the 2 + 1 (long-shore and onshore propagation directions and time) nonlinear shallow-water wave equations, without friction factors or artificial viscosity is presented. The models use a splitting method to generate two 1 + 1 propagation problems, one in the onshore and the other in long-shore direction. Both are solved in characteristic form using the method of characteristics. A shoreline algorithm is implemented, which is the generalization of the earlier 1 + 1 algorithm used in the code VTCS-2. The model is validated using large-scale laboratory data from solitary wave experiments attacking a conical island. The method is applied then to model the 1993 Okushiri, Japan, the 1994 Kuril Island, Russia, and the 1996 Chimbote, Peru tsunamis. It is found that the model can reproduce correctly overland flow and even extreme events such as the 30-m runup and the 20-m/s inundation velocities inferred during field surveys. The results suggest that bathymetric and topographic resolution ...

Investigation of computational models of long surface waves in the problem of interaction of a solitary wave with a conic island

Investigation of computational models of long surface waves in the problem of interaction of a solitary wave with a conic island

Shallow-Water Flow around Model Conical Islands of Small Side Slope. I: Surface Piercing

A series of experiments has been conducted to investigate recirculating shallow-water flow in the wakes of conical model islands with gently sloping sides. Four islands have been used with side slopes ranging from 33.1 to 8.0°. For all tests reported here the water depth was less than the island height; the islands are said to be surface piercing. Measurements of flow velocity have been made in the laboratory using a digital particle tracking velocimetry (PTV) system. This produces instantaneous, whole-field velocity vector maps of the wake flows. A “wake stability parameter” \iS, has been used to classify the island wakes into “vortex shedding” or “unsteady bubble” types. The stability parameter is a measure of the stabilizing effect of bed friction relative to the destabilizing influence of transverse shear. For small values of \iS (<0.2) vortex shedding was well organized and vigorous in the island wakes. Vortex shedding was found to cease for larger values of \iS (0.35–0.40). These values are similar to those found by other researchers for the shallow wakes of vertically sided circular cylinders. The influence of the island side slope angle on the wakes is discussed. Depth-averaged and three-dimensional (3D) numerical shallow-water flow models with the usual hydrostatic pressure assumption have been used to simulate the experimental flows. The models are based on a fully coupled semi-implicit Lagrangian numerical method. For cases where vortex shedding occurred, the 3D model was found to predict a more 3D far wake than was observed. The two-dimensional (2D) model produced good overall agreement with experimental results. For very shallow depths with the wake stabilized by bed friction, the 3D model demonstrated closer agreement to the measured results than the 2D model.

Shallow-Water Flow around Model Conical Islands of Small Side Slope. II: Submerged

Experiments have been conducted to study the unsteady wakes of submerged conical islands. The islands used in the tests have side slopes ranging from 8.0 to 33.1°. Experiments in a shallow-water channel with a steady, subcritical free stream showed vortex shedding to occur in the wake when the water depth above the island apex was relatively small. Flow separation from positions near the island apex was found to be important in producing this unsteady wake. As the water depth was increased the shedding was observed to become less vigorous and eventually stop. All islands tested produced similar results with the angle of the island side slope exerting relatively little influence on the process. The results of wind tunnel visualization studies, which used a rigid top plate to produce the effect of fluid depth, support the results from the water channel. Pictures of the surface flow patterns produced on the islands by the wind action are presented. Two-dimensional (2D) and three-dimensional (3D) shallow-wate...

Characteristics of Long Waves Trapped by Conical Island

Characteristics of Long Waves Trapped by Conical Island

Laboratory experiments of tsunami runup on a circular island

Laboratory experiments of a 7.2-m-diameter conical island were conducted to study three-dimensional tsunami runup. The 62.5-cm tall island had 1 on 4 side slopes and was positioned in the center of a 30-m-wide by 25-m-long flat-bottom basin. Solitary waves with height-to-depth ratios ranging from 0.05 to 0.20 and “source” lengths ranging from 0.30 to 7.14 island diameters were tested in water depths of 32 and 42 cm. Twenty-seven capacitance wave gages were used to measure surface wave elevations at incident and four radial transects on the island slope. Maximum vertical runup measurements were made at 20 locations around the perimeter of the island using rod and transit. A new runup gage was located on the back or lee side of the island to record runup time series.

Unsteady surface-velocity field measurement using particle tracking velocimetry

A method has been developed for obtaining surface-velocity fields in unsteady flows which is useful for hydraulic model studies. The method is based on the established technique of Particle Tracking Velocimetry (PTV) but unlike other whole-field systems is suitable for use over relatively wide areas. Results are presented from its application to flows around conical model islands with uniform sloping sides from which strong vortex shedding occurs. To allow an assessment of accuracy, simultaneous LDA measurements were taken in the wake of an island and comparisons of velocity prediction are presented.

Evolution of atomic-scale roughening on Si(001)-(2×1) surfaces resulting from high temperature oxidation

Scanning tunneling microscopy was used to study surface morphology on Si(001)-(2×1) samples following elevated temperature O2 exposure as a function of pressure (1×10−8&amp;lt;Pox&amp;lt;5×10−6 Torr), temperature (500&amp;lt;Ts&amp;lt;700 °C), and dose [10–800 langmuir (L)]. At low O2 doses (Dox&amp;lt;50 L; Ts≥600 °C and Pox&amp;lt;1×10−7 Torr) preferred B-type step retraction is observed, but single A-domain formation is prevented due to step pinning by nucleated oxide clusters. These pinning centers roughen the surface via step ‘‘fingering’’ at low doses, while at higher doses result in the formation of three-dimensional conical islands, similar to oxidation-induced ‘‘growth features’’ reported previously by Smith and Ghidini [J. Electrochem. Soc. 129, 1300 (1982)] at higher temperatures. Surface etching rates were determined by measuring the island heights as a function of exposure, and a sticking coefficient s of 0.04 (±0.02) was estimated for O2 reaction on Si(001) at 600 °C. For moderate O2 doses (&amp;lt;1000 L) surface etching was found to dominate SiO2 growth up to pressures several orders of magnitude above the commonly accepted oxidation ‘‘critical line,’’ causing significant atomic-scale roughening under these oxidation conditions.

New solutions for the propagation of long water waves over variable depth

Based on the linearized long-wave equation, two new analytical solutions are obtained respectively for the propagation of long surface gravity waves around a conical island and over a paraboloidal shoal. Having been intensively studied during the last two decades, these two problems have practical significance and are physically revealing for wave propagation over variable water depth. The newly derived analytical solutions are compared with several previously obtained numerical solutions and the accuracy of those numerical solutions is discussed. The analytical method has the potential to be used to find solutions for wave propagation over more natural bottom topographies.

Storm surges due to a symmetrical wind stress near a circular island

Abstract The initial-value problem of generation of storm surges by any symmetrically distributed and time-periodic surface wind near a circular island with variable topography is solved. The general steady-state motion at any distance is determined, and some of its characteristics are described. Graphical illustrations are provided for a physically plausible wind stress distribution near a conical island.

87:6274 Formation of a tombolo between the upheaving two conical islands: Hashima, Masahiro, 1986. Mer, Tokyo, 24(4):193–197. (In Japanese, English abstract.)

87:6274 Formation of a tombolo between the upheaving two conical islands: Hashima, Masahiro, 1986. Mer, Tokyo, 24(4):193–197. (In Japanese, English abstract.)

Wave-Island Interactions About Circular Artificial Islands

The behavior of waves interacting with islands has gained renewed interest with the construction of exploratory drilling islands in the Arctic. This paper focuses upon the behavior of waves incident upon axisymmetric islands characterized by circular contours which vary with water depth. The island profiles of Arthur and Pocinki, which have closed form solutions, and a single tier conical island are examined. A new dimensionless formulation of Arthur’s ray theory and an extremely accurate numerical procedure to evaluate the ray integrals are presented. It is shown that each island profile leads to a distinct wave pattern about the island. These wave patterns are presented in figures which portray the wave capture and wave breaking about circular islands. It is intended that the methodology presented be used to initially assess trends and to evaluate the need for more refined analyses.

Scale effects in a wave-refraction experiment

The experimental results of Provis (1975, 1976) for wave amplification at a conical island bear little resemblance to the theoretical predictions of Smith & Sprinks (1975). Here Provis's suggestion is confirmed: that his experiments were dominated by viscous damping and by standing waves between the island and the wavemaker. Estimates are given as to how large an experiment needs to be to avoid these important scale effects.

Longshore circulation around a conical island

This paper is concerned with the averaged circulation caused by waves breaking along the beach of a constant slope around a circular island in a sea of constant depth. It is reasoned that the refraction pattern determines the extent of longshore circulation. In particular, for an island so large that there is a lee shore which is not affected by the refracting waves, two current cells are found on two sides of the island with respect to the wave direction, without significant penetration in the lee shore region. This enhances the creation of two sand spits which may grow to form a looped bar, or two tombolos to connect with the neighboring mainland. For an island so small that the extent of the lee shore vanishes, the two current cells collide at the center of the island lee and form a single rip current. This is used to explain the presence of a single tombolo.

Scattering of surface waves by a conical island

A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.