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The approximate solution of KdV-type partial differential equations of order seven is presented. The algorithm based on one-dimensional Haar wavelet collocation method is adapted for this purpose. One-dimensional Haar wavelet collocation method is verified on Lax equation, Sawada-Kotera-Ito equation and Kaup-Kuperschmidt equation of order seven. The approximated results are displayed by means of tables (consisting point wise errors and maximum absolute errors) to measure the accuracy and proficiency of the scheme in a few number of grid points. Moreover, the approximate solutions and exact solutions are compared graphically, that represent a close match between the two solutions and confirm the adequate behavior of the proposed method.

This research presents the approximate solution of nonlinear Korteweg-de Vries equation of order nine by a hybrid staggered one-dimensional Haar wavelet collocation method. In literature, the underlying equation is derived by generalizing the bilinear form of the standard nonlinear KdV equation. The highest order derivative is approximated by Haar series, whereas the lower order derivatives are attained by integration formula introduced by Chen and Hsiao in 1997. The findings are shown in the form of tables and a figure, demonstrating the proposed technique’s convergence, robustness, and ease of application in a small number of collocation points.

Herein, we present coastal-wave records under historically extreme conditions caused by a strong typhoon in Japan in 2017. The extreme typhoon generated large infragravity waves, reaching a height of 2 m in shallow water. We took advantage of the extraordinary conditions to analyze the effect of the energetic infragravity waves on the nearshore evolution of relatively short waves. Individual wave analyses clearly demonstrate that the instantaneous water-level rise and drawdown caused by the infragravity waves alternately decelerated and accelerated the breaking of short waves under extreme conditions. This mechanism transmitted the large short-wave energy on the infragravity wave crests to the shore, eventually increasing the height of the nearshore waves. This study provides in situ evidence that the infragravity waves significantly affect nearshore wave characteristics under extreme conditions.

Sloshing occurs when a partially filled tank is subject to external excitation. If the excitation frequency is equal to half of the second-order natural frequency obtained from the linear theory, then second-order resonance may occur. But it gradually modifies to standing waves. Moreover, violent second-order resonant free surface motions may be induced when the sum (or difference) of the excitation frequency and any one of the natural frequencies is equal to another natural frequency. In this study, fully non-linear second-order resonance waves in a three-dimensional shallow water rectangular tank are simulated using a pseudospectral if-transformation model. The model is validated against results from three benchmark tests for which there are published analytical and numerical solutions available. A detailed analysis is presented of sloshing in a shallow water tank, with the main excitation and response frequencies identified from the power spectra. Large amplitude free surface motions are observed whenever second-order resonance occurs. In certain cases, the wave pattern in the tank is different to that predicted from linear analysis of second-order resonance, due to the effect of nonlinearity. Results are presented from a parameter study examining the influences of water depth, base aspect ratio, and excitation amplitude on the wave motions and patterns. It is found that the wave pattern is highly dependent on the water depth in the tank, but relatively insensitive to excitation amplitude. Also, the decay patterns are seen when the second-order resonance excitations are applied vertically. The study demonstrates that second-order resonance can be very pronounced in shallow water. (C) 2012 Elsevier Ltd. All rights reserved.

The objective of this contribution is to analyse the formation of debris waves in natural channels. Numerical simulations are carried out with a 1D code, based on shallow water equations and on the Weighted Averaged Flux method. The numerical code represents the incised channel geometry with a power-law relation between local width and flow depth and accounts for all source terms in the momentum equation. The debris mixture is treated as a homogeneous fluid over a fixed bottom, whose rheological behaviour alternatively follows Herschel-Bulkley, Bingham or Generalised Visco-Plastic models. The code is first validated by applying it to dam-break tests on mudflows down a laboratory chute and verifying its efficiency in the simulation of rapid transients. Then, following the analytical method developed by Trowbridge, the stability of a uniform flow for a Generalised Visco-Plastic fluid is examined, showing that debris flows become unstable for Froude numbers well below 1. Applications of the code to real debris flow events in the Cortina d’Ampezzo area (Dolomites) are presented and compared with available measured hydrographs. A statistical analysis of debris waves shows that a good representation of wave statistics can be obtained with a proper calibration of rheological parameters. Finally, it is shown that a minimum duration of debris event and channel length are required for waves showing-up and an explanation, confirmed both by field data and numerical simulations, is provided.

We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant/ shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On contrary, the proposed scheme is "well-balanced": it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism., Comment: 36 pages

In this study, a pseudospectral sigma-transformation model is developed to simulate fully nonlinear sloshing waves in a three-dimensional shallow water rectangular tank. The sigma-transformation maps the physical domain including the water free surface onto a fixed rectangular computational domain. Chebyshev collocation formulae are used to discretize the governing equation and boundary conditions in the computational domain. The numerical model is validated for three well known analytical and numerical sloshing problems. An extensive study is then made of sloshing in a shallow water tank, and the effects of excitation frequency, base aspect ratio, and amplitude of excitation on the wave motions and patterns are considered. Wave regimes and patterns are considerably influenced by the base aspect ratio. In a shallow water tank with a non-square base, different wave regimes are observed during small-amplitude resonant excitation. Also, bores develop during large amplitude resonance excitation. The present study demonstrates that a pseudospectral sigma-transformation can accurately model nonlinear sloshing waves in a rectangular tank. Also, results show that contrary to the situation in deeper water tanks, sloshing in shallow water strongly depends on the base aspect ratio. (C) 2012 Elsevier Ltd. All rights reserved.

Adaptation to climate impacts on groundwater resources in developed and developing countries has not received adequate attention. This reflects the often poorly understood impacts of climate change, the hidden nature of groundwater and the general neglect of groundwater management. Many developing countries are highly reliant on groundwater. Given expectations of reduced supply in many regions and growing demand, pressure on groundwater resources is set to escalate. This is a crucial problem and demands urgent action. This report addresses the impacts of climate change on groundwater and adaptation options. The Earth's climate is projected to become warmer and more variable. Increased global temperatures are projected to affect the hydrologic cycle, leading to changes in precipitation patterns and increases in the intensity and frequency of extreme events; reduced snow cover and widespread melting of ice; rising sea levels; and changes in soil moisture, runoff and groundwater recharge. Increased evaporation and the risk of flooding and drought could adversely affect security of water supply, particularly surface water. Due to these pressures, as well as global population growth, demand for groundwater is likely to increase.

Modern design formula for coastal structures (like rock stability formula and overtopping formula use wave parameters (H2% and Tm-1,0) which are not readily available from standard boundary condition wave data. For transforming values like Hs and Tp to the parameters used in the new formulas, often-fixed conversion factors are used. However, this may lead to significant errors. Therefore, it is better to calculate these new parameters with an appropriate wave transformation model. The one-dimensional Graphical User Interface for SWAN (SwanOne) is presented as a simple tool to perform the required transformation.

Seiche waves in a small glass tank partly filled with water were filmed with a digital video camera. The video clips were analyzed with Logger Pro to determine the period of the oscillations at different water depths. The calculated velocity of surface gravity waves in the region of transition between the deep and shallow water approximations was found to agree with theoretical predictions.

Modern design formula for coastal structures (like rock stability formula and overtopping formula use wave parameters (H2% and Tm-1,0) which are not readily available from standard boundary condition wave data. For transforming values like Hs and Tp to the parameters used in the new formulas, often-fixed conversion factors are used. However, this may lead to significant errors. Therefore, it is better to calculate these new parameters with an appropriate wave transformation model. The one-dimensional Graphical User Interface for SWAN (SwanOne) is presented as a simple tool to perform the required transformation.

SUMMARY The two-dimensional linearized shallow water equations are considered in unbounded domains with density stratication. Wave dispersion and advection eects are also taken into account. The innite domain is truncated via a rectangular articial boundary B, and a high-order open boundary condition (OBC) is imposed on B. Then the problem is solved numerically in thenite domain bounded by B. A recently developed boundary scheme is employed, which is based on a reformulation of the sequence of OBCs originally proposed by Higdon. The OBCs can easily be used up to any desired order. They are incorporated here in anite dierence scheme. Numerical examples are used to demonstrate the performance and advantages of the computational method, with an emphasis is on the eect of stratication. Published in 2004 by John Wiley & Sons, Ltd.

As an alternative to a more or less standard derivation procedure for design wave heights in relatively shallow water, two improvements of the procedure are suggested which lead to less conservative results. These improvements are based on observations of shallow water effects on both the decay of total wave energy density and on the extreme waves in the wave height distribution. Existing semi-empirical formulations to account for these effects are adopted and somewhat further evaluated here. The implications of introducing the improved procedures for the resulting design wave loading on a slender cylinder are indicated.

As an alternative to a more or less standard derivation procedure for design wave heights in relatively shallow water, two improvements of the procedure are suggested which lead to less conservative results. These improvements are based on observations of shallow water effects on both the decay of total wave energy density and on the extreme waves in the wave height distribution. Existing semi-empirical formulations to account for these effects are adopted and somewhat further evaluated here. The implications of introducing the improved procedures for the resulting design wave loading on a slender cylinder are indicated.