Dominic E. Reeve

A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids

We present a new three-dimensional hybrid level set (LS) and volume of fluid (VOF) method for free surface flow simulations on tetrahedral grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a second-order characteristic based finite volume method. The volume fraction advection is performed using a bounded compressive normalized variable diagram (NVD) based scheme. The interface is reconstructed based on both the level set and the volume fraction information. The novelty of the method lies in that we use an analytic method for finding the intercepts on tetrahedral grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. Furthermore, the advection of volume fraction makes use of the NVD concept and switches between different high resolution differencing schemes to yield a bounded scalar field, and to preserve both smoothness and sharp definition of the interface. The method is coupled to a well validated finite volume based Navier-Stokes incompressible flow solver. The code validation shows that our method can be employed to resolve complex interface changes efficiently and accurately. In addition, the centroid and intercept data available as a by-product of the proposed interface reconstruction scheme can be used directly in near-interface sub-grid models in large eddy simulation.

Bayesian nonparametric quantile regression using splines

A new technique based on Bayesian quantile regression that models the dependence of a quantile of one variable on the values of another using a natural cubic spline is presented. Inference is based on the posterior density of the spline and an associated smoothing parameter and is performed by means of a Markov chain Monte Carlo algorithm. Examples of the application of the new technique to two real environmental data sets and to simulated data for which polynomial modelling is inappropriate are given. An aid for making a good choice of proposal density in the Metropolis-Hastings algorithm is discussed. The new nonparametric methodology provides more flexible modelling than the currently used Bayesian parametric quantile regression approach.

Modeling Floating Object Entry and Exit Using Smoothed Particle Hydrodynamics

This paper investigates fluid and floating object interaction using a novel adaptation of the weakly compressible smoothed particle hydrodynamics (WCSPH) method by incorporating a floating object model. In particular, this paper examines the water impact, hydrodynamic forces, fluid motions, and movement of objects in the conventional case studies of object entry and exit from still water. A two-dimensional wedge drop analysis was examined, and the hydrodynamic forces show acceptable agreement with published experimental and numerical results. The movement of the object is well predicted. The velocity field of the fluid domain is also captured. Simulations for water entry and exit of a buoyant and neutral density cylinder compares well with previous experimental, numerical, and empirical studies in penetration, free surface comparisons, and object movement. These results provide a good foundation to evaluate the accuracy and stability of WCSPH for modeling the interaction between free surface flow and free...

Numerical solution of the elliptic mild-slope equation for irregular wave propagation

In this paper a multigrid method is used to solve the elliptic form of the mild-slope equation for irregular water wave propagation. The effects of shoaling, refraction, diffraction and wave breaking are included. The numerical scheme is very efficient and allows spectral wave calculations to be performed over large study areas at modest computational cost. Model results compare favourably with measurements from wave tank experiments, and demonstrate the large errors in wave amplitude that may occur when using monochromatic models. A sensitivity analysis of the discretisation of the directional spectrum shows that satisfactory results may be obtained with relatively coarse frequency-direction resolution for the cases studied.

A Boolean Approach to Prediction of Long-Term Evolution of Estuary Morphology

Abstract A systems method based on a Boolean approach is used to predict medium- to long-term behaviour of estuary morphology. Boolean networks are formed for various types of generic estuaries by taking into account the feedback involved between various estuary elements and external forcing which drive morphological evolution. A logical framework is then developed, and the Boolean matrix is derived. Various different potential morphological evolutionary pathways are then selected from the Boolean matrix, analysed, and discussed. The Boolean method provides a complementary approach for qualitative modelling of complex estuary systems. The method was applied to the Ribble Estuary in northwest England, and the predictions from the Boolean approach were in very good qualitative agreement with the observed morphological evolution of the Ribble Estuary during the last 150 years.

Annual down-glacier drainage of lakes and water-filled crevasses at Helheim Glacier, southeast Greenland

Supraglacial lake drainage events are common on the Greenland Ice Sheet. Observations on the west coast typically show an up-glacier progression of drainage as the annual melt extent spreads inland. We use a suite of remote sensing and modelling techniques in order to study a series of lakes and water-filled crevasses within 20km of the terminus of Helheim Glacier, south east Greenland. Automatic classification of surface water areas shows a down-glacier progression of drainage, which occurs in the majority of years between 2007 and 2014. We demonstrate that a linear elastic fracture mechanics model can reliably predict the drainage of the uppermost supraglacial lake in the system, but cannot explain the pattern of filling and draining observed in areas of surface water downstream. We propose that the water levels in crevasses downstream of the supraglacial lake can be explained by a transient high-pressure wave passing through the subglacial system following the lake drainage. We support this hypothesis with analysis of the subglacial hydrological conditions, which can explain both the position and interannual variation in filling order of these crevasses. Similar behaviour has been observed in association with jokulhaups, surging glaciers, and Antarctic subglacial lakes, but has not previously been observed on major outlets of the Greenland Ice Sheet. Our results suggest that the behaviour of near-terminus surface water may differ considerably from that of inland supraglacial lakes, with the potential for basal water pressures to influence the presence of surface water in crevasses close to the terminus of tidewater glaciers.

Extreme water levels of the Vistula River and Gdansk Harbour

Using Canonical Correlation Analysis (CCA), Rozynski et al. (2006) have demonstrated that there is a weak correlation between the water levels of Vistula River and Gdansk Harbour. Herein the CCA analysis serves as a first step for a univariate bootstrap resampling technique, applied to investigate coincident extreme water levels of Vistula River and Gdansk Harbour. The CCA-derived assumption of statistical independence is argued as being a suitable working approximation for (outline) engineering design. This allows the goodness-of-fit of different statistical models to be assessed in a quantitative manner with a bootstrap method. This also provides a convenient means of defining extreme levels together with their confidence intervals. The analysis with two statistical methods provides insight into the character of joint coastal extremes in an estuary of a large north European river. The rationale and methodology are at least partly applicable to similar estuaries of northern Europe.

Numerical Study for Small Negative Freeboard Wave Overtopping and Overflow of Sloping Sea Wall

In this paper, an extended version of the model of Lin and Liu (1998) is applied in order to study the cases of small negative freeboard wave overtopping and overflow of seawalls. The model computes a finite difference solution of the incompressible Reynolds equations for the mean flow field and the k - e equations for the turbulent field are obtained on a non-uniform mesh. The free surface locations are presented by the volume of fluid (VOF) data on the mesh. The extended model includes the capability of simulating flows in porous media, which use the resultant spatially averaged equations in order to describe the mean motion of flow, and also uses an internal source function to generate waves. The model performance is being compared against laboratory models and other numerical models. The model reproduces the results of the well-known weir equation very well and is then used to investigate combined discharge because of the overflow and wave overtopping of impermeable seawalls for increasing wave activity for a range of negative level freeboard values. Results for irregular wave attach are presented together with suggested extensions of design formulae.

Modelling beach-structure interaction using a Heaviside technique: application and validation

ABSTRACT Valsamidis, A., Cai, Y., Reeve, D.E., 2013. Modelling beach-structure interaction using a Heaviside technique: application and validation In this study, an analytical solution, based on a Heaviside technique, is developed to model the shoreline evolution in the vicinity of a groyne due to a random sequence of waves. The beach at Borth, Wales, UK was used as a case-study. A wave time-series covering a time period of about 12 years, was used to test the performance of a recently constructed coastal defence scheme. Transformations of the wave time-series from offshore to nearshore were performed using a semi-empirical procedure. Three different wave breaking formulae were independently applied to the wave model, and their effects to the consequent shoreline evolution were investigated. In addition, three different longshore transport formulae were compared. These were the CERC, the Kamphuis and the Bayram formulae. Results showed that the CERC formula predicted a significantly greater amount of sediment transport and hence erosion on the downdrift side of the groyne while the models based on Kamphuis and the Bayram formulae gave comparable results. All the results exhibited a strong sensitivity to the temporal resolution of the forcing. Finally, some sensitivity to the treatment of wave breaking was found.

Analysis of Climate Change Effects on Seawall Reliability

Crown heights of seawalls should be designed to suppress overtopping discharge to a permissible level. The permissible level is determined from viewpoints of the structure types of coastal seawalls and hinterland use. It is usually difficult to design the crown heights of seawalls, especially in the present time where climate change due to global warming is expected. This study analyzes climate change effects such as sea level rise (SLR) and increase of waves and surges on the failure probability of seawalls under various conditions of crown height, toe depth and slope by using a Level III reliability analysis. It was found that the difference of SLR trends (fast, medium or low) has less impact on overtopping rates than the differences in wave height change for a seawall at a target location.