Still-water Level Research Articles

Experimental study on the use of artificial meadows that mimic wave-vegetation interactions for coastal protection

A detailed experimental study was conducted on five artificial meadows made of structures that mimic wave-vegetation interactions. The meadows were of different lengths and leaf thicknesses under regular and random waves, such that the leaf thickness changed as the meadow length increased. Different wave heights, periods, and tidal conditions were examined. The results for regular and random waves were consistent. The meadow length had a stronger influence (30%–50%) on wave transmission than leaf thickness (5%–10%). A lower wave transmission was observed at higher wave energies due to enhanced wave-vegetation interaction, higher wave reflection, and effective energy dissipation. Compared with submerged conditions or when the top of the meadow was at still-water level, a lower wave transmission and higher wave reflection and energy dissipation were noted when the leaves emerged in the air. The longest meadow in the emerged condition reduced the wave height by more than 50% at mid meadow. Furthermore, a wave transmission coefficient of 0.3 was achieved by this model, which is desirable for the design of this wave barrier type. The model with the best overall hydrodynamic performance can be used alone or combined with existing natural vegetation for coastal protection.

Experimental study on focused wave breaking on an inclined plate

This study conducts an experimental investigation into the impact of focused wave breaking on an inclined plate, examining characteristics including wave shape, acoustic properties, and impact pressure. The wave's pressure characteristics are primarily dictated by the patterns of wave impact. Variations in the pattern of wave impact are observed with changes in the focal position of the wave group and the inclination of the plate. The position of maximum impact, located near the Still Water Level (SWL), experiences substantial upward or downward shifts corresponding to the plate's inclination. Active acoustic phenomena occur during the interaction between fluid, gas, and solid when waves impact the inclined plate. The sound spectrum indicates an increase in the higher frequency components of sound when compared to wave breaking. The Elementary Loading Processes (ELPs) accurately represent the impact pressure characteristics observed on the inclined plate. The characteristics of impact pressure display high variability across multiple repeated experiments. The differences in impact characteristics under varying plate inclinations can be reflected in the pressure-impulse.

Experimental investigation on the hydrodynamic performance of an inverted trapezoidal breakwater

ABSTRACT The wave transmission, reflection, and dissipation characteristics of conventional (trapezoidal (TBs)) and non-conventional (inverted trapezoidal (ITBs) and rectangular (RB)) breakwaters with the same volume and porosity are evaluated under different submergence ratios, wave heights, and wave periods in regular and random waves. The experimental investigation revealed that the ITB shape is the most efficient cross section for reducing wave transmission coefficient (Kt) when the breakwater is submerged or the still water level (SWL) is at the crest of the breakwater, whereas the conventional TB is the least efficient. Compared to the conventional TB, the ITB reduced Kt by 10%–20% under submerged conditions and by 20%–30% when the SWL is at the breakwater crest. Kt < 0.2 is obtained for a relative water depth d/Lp > 0.2, which is suitable for most wave damping applications in the field when the ITB crest is at the SWL or when the crest emerges.

Multiphase SPH analysis of a breaking wave impact on elevated structures with vertical and inclined walls

Elevated structures are prevalent along shorelines that are susceptible to storm surge flooding to improve coastal resilience. In this work, we explore the influence of front wall inclination on the pressures and forces attracted by an elevated structure in response to extreme wave impact. Multiphase smoothed-particle hydrodynamics was used to examine a typical two-story building 6 m high and 10 m long with three different frontal wall inclinations impinged by a single breaking wave propagating landwards (from left to right). Relative to a vertical surface, both positive (clockwise) and negative (counterclockwise) inclinations of the front wall altered breaking wave pressures depending on the structure's position relative to the still-water level (SWL). When the bottom of the structure is located below the SWL (negative air gap), a positive inclination decreased breaking wave loads by up to 21 %, while a negative inclination may result in 50 % higher pressure maxima. However, for a structure elevated above the SWL (positive air gap), negative and positive inclinations witnessed reductions to the pressure maxima of 35 % and 10 %, respectively, when compared with a vertical surface.

Extreme Value Analysis of Ocean Still Water Levels along the USA East Coast—Case Study (Key West, Florida)

This paper provides an Extreme Value Analysis (EVA) of the hourly still water level (SWL) record at Key West, Florida dating back to 1913 to understand the statistical likelihood of the combination of high predicted tides and the more dynamic influences (predominantly hurricane induced storm surges) that can drive ocean water levels higher at the coast. The impact of hurricane ‘Wilma’ in 2005 dominates the records, producing a super-elevation of the SWL above Mean Sea Level (MSL) of 1155 mm with an estimated return period of around 147 years. This paper explores the duality of increasing risks of oceanic inundation due to extreme events and increasing mean sea level over time, whilst also providing a range of recommendations for ensuring improved predictive model fitting and robustness of EVA for SWLs measured at tide gauges. When integrated with future IPCC AR6 sea level projections, the return level plots from the EVA provide decision makers with key guidance for design, strategic planning and climate change adaptation purposes at Key West, Florida.

Wave-impact forces and moments due to random waves on a jacket-type platform for different relative submergence of the deck

Force and moment measurements due to wave impacts were conducted on a jacket platform model under six distinct relative deck submergence conditions. The water depth was carefully chosen to facilitate scenarios ranging from sufficient deck air gaps to partial and complete submergence. For the purpose of our analysis, we focused on peak and average peak wave force and moment values. The study uncovers that the peak wave force towards the shore can escalate to 1.5 times the peak wave force towards the sea. Moreover, the ratio of the peak shoreward force to the average peak shoreward force fluctuates between 3 and 4, contingent upon the relative water level at the deck base and the prevailing wave condition. Remarkably, the peak upward wave force on the deck can reach 5 to 7 times the peak inline wave force. A review of existing guidelines suggests a significant need to enhance research regarding the air gap between the deck and the still water level (SWL), as well as its effect on global and local wave forces and moments on the structures. Our finding establishes that the relative water level from the base of the deck is a crucial parameter in the design process of these structures. This study presents a more in-depth understanding of the physical mechanisms at play by utilizing a realistic jacket platform model. It serves as an initial exploration into the influence of air gap and relative water depth on wave-impact forces and moments. The results obtained from this study shed light on optimal design strategies for jacket-type offshore drilling platforms, considering green water effects. This understanding will enhance the life expectancy and survivability of such platforms.

WAVE OVERTOPPING OVER A DIKE FOR VARIABLE WATER LEVEL

The still water level (SWL) during a storm is always dynamic (storm surge). The variability of the water level can be schematized as a time-varying hydrograph of a certain duration. The average wave overtopping discharge q is a function of the ratio between the freeboard Rc (the structure crest elevation above SWL) and the significant wave height Hm0. Since the variation during a storm of the SWL changes the freeboard Rc, the wave overtopping discharge is variable. Typically, in the laboratory the wave overtopping on coastal defense structures is investigated for a constant water level (CWL) and a pre‐determined structural exposure time frame. This exposure time frame is often representative for the storm surge peak or for a statistically representative number of individual waves (e.g. 1000 waves), not considering any variable water level (VWL). For the case of wave overtopping in VWL conditions, no validated prediction formulae exist (Kerpen et al. 2020) and the prediction is rather based on safe assumptions and engineering judgement. This research investigated the influence of a VWL on the prediction of the average wave overtopping discharge q.

DEEP LEARNING OBJECT DETECTION APPLICATION TO SURFING WAVE QUALITY

Quantitative monitoring is imperative to the sustainable management of coastal resources. Surfing resources have been both created and degenerated or destroyed by activities in the coastal zone. Effective surfing wave quality monitoring requires identification and tracking of the breaking part of the wave and the unbroken wave crest. Remote Camera Systems (RCS) have proven their utility in being able to monitor the coastal zone and provide almost continuous, high frequency data collection. RCSs lend themselves very well to the monitoring of surf breaks which are highly dynamic. The images captured from an RCS monitoring a surf break on the west coast of Aotearoa New Zealand are used to train a Convolutional Neural Network (CNN) to detect the break points (BP), associated crest orientation and relative Still Water Level (SWL) of each instance of breaking waves in each image. Model settings and image annotations were modified over a suite of training cases to improve model efficacy, which was evaluated each epoch of training with mean Average-Precision (mAP; max 1). A mAP of 0.794 was achieved for the BP and Crest Point (CP) CNN, and 8.634 for the SWL. The model was used to detect ~1.6 M objects across ~1 million images, with a mean confidence value of all BP-CP detections of 0.63 and more than 70percent of detections being greater than 0.5. This model enables the first automation of meaningful surfing wave quality monitoring.

The effect of linear shear current on head-on collision of solitons

Head-on collision of two solitary waves in the presence of linear shear currents is studied by the use of the High-Level Green–Naghdi (HLGN) theory. The finite difference method is used to solve the HLGN model in the time-domain simulation. The initial values are obtained by the steady solution of solitary waves in the presence of linear shear currents. Shear currents with different velocities are considered to assess their effect on the solitary-wave collision. Three aspects of the head-on collision process in the presence of shear current are studied, namely, the wave elevation, velocity field, and particle trajectory. Results show that the background linear shear current significantly affects the wave elevation, velocity field, and particle trajectory during the head-on collision. It is observed that in the presence of the current, the wave elevation is narrower near the maximum surface displacement and is wider near the still-water level. It is also shown that near the seafloor, the horizontal velocity is opposite of the current direction, while it is following the current direction near the free surface. The opposite shear current results in the formation of a vortex in the fluid field. At the point of the collision, the vortex appears at a lower vertical position and shifts upstream of the current direction. Following the particle trajectories in the presence of the shear current, it is observed that the particles do not return to their initial positions after the head-on collisions, and the loop motions of the particles become smaller with larger current velocities.

On Solitary Wave Breaking and Impact on a Horizontal Deck

The impact of waves and bores generated by broken solitary waves on horizontal decks of coastal structures was studied by solving the Navier–Stokes equations. Solitary waves of different amplitudes were considered, and submerged ramps were used to bring the waves to the breaking point. The horizontal fixed deck was located downwave of the ramp and placed at various elevations above and below the still-water level. The results include the surface elevation of the wave and the bore-induced horizontal and vertical forces on the deck. The results were compared with laboratory measurements and those due to the bore generated by breaking a reservoir, and a discussion is provided on the relative magnitude of the loads. It is found that breaking solitary waves and dam-break provide reasonable loading conclusions for tsunamis events.

Effect of currents on nonlinear waves in shallow water

Effect of various forms of currents on regular nonlinear waves in shallow water is investigated by use of a computational fluid dynamics approach. A range of wave conditions with different wave heights and wave periods are considered. Effect of three types of currents on these waves is investigated, namely (i) uniform current over the water depth, (ii) shear current from the seafloor to the still-water level, and (iii) a custom current profile that changes over the water depth. The current profiles are considered in both following and opposing directions of the incoming wave, forming in total 18 wave–current configurations. The Navier–Stokes equations for a laminar flow are solved computationally in two dimensions. A numerical wave–current maker is created to generate combined nonlinear waves and currents in shallow water. The effect of the currents on the change of the wave field, including quantitative change of the surface elevation, wave height, wavelength, horizontal particle velocity, and the velocity and pressure fields is presented and discussed. It is found that presence of the current can alter the wave field significantly, and the current profile and direction play a significant role in the change of the wave field. A following current in shallow water increases the peak of surface elevation, horizontal particle velocity and pressure, along with an increase in wavelength and wave height, while an opposing current reduces these. The change of wave height with current direction appears to be opposite to that observed in deep water in the literature. It is also concluded that a linear superposition of the undisturbed wave and current velocities can describe the horizontal particle velocity of the wave–current field for following currents (particularly under the wave trough) reasonably well, but larger differences are observed for opposing currents.

Dynamic Behavior of the Net of a Pile–Net-Gapped Enclosure Aquaculture Facility

A pile–net enclosure aquaculture facility, deployed in inshore waters, is a sustainable and ecological aquaculture pattern for rearing fish and other aquatic animals of economic value in China. It is essential to study the maximum force on and deformation of the net system of a pile–net enclosure facility to prevent its failure, since successful aquaculture is highly dependent on the longevity of the net system. In this study, a pile-net enclosure aquaculture facility with a gapped pile-net configuration was numerically investigated based on the lumped mass model. A Newton’s second-law-based motion equation was solved using Euler’s method. Finally, MATLAB was used to visualize the results. The results highlight that the force of a net system significantly increases with ocean loads, and the load of the entire net is mainly from the top half of the net. Moreover, the maximum force of the vertical rope occurs at the connection of the top channel steel. The maximum force of the horizontal rope and net twine occur in the rope near the still-water level and at the connection of the top channel steel, respectively. Thus, the net at those positions should be reinforced to prevent its failure.

Maximum Run-Up and Alongshore Mass Transport Due to Edge Waves

The edge wave on a uniform-sloped seabed was described by the velocity-potential function by Mok and Yeh in 1999. Edge waves cannot be extended above a certain level from the still-water level, and the upper limit of the run-up of the edge waves for given conditions is found here. In this study, quantitative mass transport by the edge waves of the beach is introduced. The maximum run-up height is decided from the wave’s amplitude at shoreline, and the maximum run-up distance from the shoreline is proportional to the wavelength of the edge waves. The fluid alongshore-mass-transport profile shows that the strongest mass transport rate corresponds to the position offshoreward multiplied by 0.0362 times the wavelength, and its magnitude is 1.23 times the mass-transport rate at the shoreline. The maximum cross-sectional total mass-transport rate is 0.214 times the mass transport at the shoreline, multiplied by the wavelength for the maximum run-up condition. This study suggests that edge waves cannot be increased infinitely and that there is a maximum run-up on the coast.

Bore Impact on Decks of Coastal Structures

Bore impact on horizontal fixed decks of coastal structures is studied by use of the Level I Green–Naghdi (GN) equations and the Navier–Stokes (NS) equations. The bore is generated by the breaking of a water reservoir, and may represent the propagation of a tsunami on land or broken storm waves. The bore-induced horizontal and vertical forces are determined and their variation with the bore and deck conditions is studied in this work. Various conditions of deck location with respect to the water level are considered, including cases with the deck under or above the still-water level. Two types of bore are considered, namely (i) a bore generated by a dam break, where the reservoir water depth is substantially larger than the downstream depth, and (ii) a bore generated by an initial mound of water, where the reservoir water depth is comparable to the downstream depth. It is shown that these mechanisms result in the formation of significantly different bore shapes. It is also shown that the relative height of the reservoir and the downstream water depth play a significant role in the bore generation and its impact on coastal structures. It is also found that the bore-induced forces vary almost linearly with the change in amplitude of the reservoir, while a change in the length of the reservoir has little effect on the loads. The horizontal force on submerged decks is shown to be independent of the submergence depth of the deck; this is due to the uniform velocity distribution over the water column of the bore. Results of the GN and NS models are compared with each other for submerged cases and the limitations, accuracy, and efficiency of these models in studying this problem are discussed. Results of the GN equations are in close agreement with the NS equations, making them a computationally efficient alternative for the study of this problem.

Deriving the 100-Year Total Water Level around the Coast of Corsica by Combining Trivariate Extreme Value Analysis and Coastal Hydrodynamic Models

As low-lying coastal areas can be impacted by flooding caused by dynamic components that are dependent on each other (wind, waves, water levels—tide, atmospheric surge, currents), the analysis of the return period of a single component is not representative of the return period of the total water level at the coast. It is important to assess a joint return period of all the components. Based on a semiparametric multivariate extreme value analysis, we determined the joint probabilities that significant wave heights (Hs), wind intensity at 10 m above the ground (U), and still water level (SWL) exceeded jointly imposed thresholds all along the Corsica Island coasts (Mediterranean Sea). We also considered the covariate peak direction (Dp), the peak period (Tp), and the wind direction (Du). Here, we focus on providing extreme scenarios to populate coastal hydrodynamic models, SWAN and SWASH-2DH, in order to compute the 100-year total water level (100y-TWL) all along the coasts. We show how the proposed multivariate extreme value analysis can help to more accurately define low-lying zones potentially exposed to coastal flooding, especially in Corsica where a unique value of 2 m was taken into account in previous studies. The computed 100y-TWL values are between 1 m along the eastern coasts and a maximum of 1.8 m on the western coast. The calculated values are also below the 2.4 m threshold recommended when considering the sea level rise (SLR). This highlights the added value of performing a full integration of extreme offshore conditions, together with their dependence on hydrodynamic simulations for screening out the coastal areas potentially exposed to flooding.

Wave diffraction by floating bodies in water of finite depth using an exact DtN boundary condition

For the exact Non-Reflecting Boundary Conditions (NRBCs) or so-called Dirichlet-to-Neumann (DtN) boundary conditions, the artificial boundary is usually chosen as a spherical or ellipsoidal surface by which the computational domain is enclosed fully with finite volume. For the wave diffraction problem in finite-depth water unbounded horizontally, the free water boundary condition and wall boundary condition should be satisfied on still water level (SWL) and seabed, respectively. In this paper, the artificial boundary for DtN condition is chosen as only a lateral cylindrical surface by which it is impossible to envelope the objects and fluid domain fully, but possible by adding still water surface and seabed. A novel DtN condition on the artificial boundary is suggested and then Boundary Element Method (BEM) implementation is described to solve the three-dimensional wave diffraction problems by arbitrary-shaped floating bodies in water of finite depth. Upon successful verification for the case of a bottom-truncated cylinder, the scheme is applied to a single chamfer box and an array of chamfer boxes.

Drivers of extreme water levels in a large, urban, high-energy coastal estuary – A case study of the San Francisco Bay

Reliable and long-term hindcast data of water levels are essential in quantifying return period and values of extreme water levels. In order to inform design decisions on a local flood control district level, process-based numerical modeling has proven an essential tool to provide the needed temporal and spatial coverage for different extreme value analysis methods. To determine the importance of different physical processes to the extreme water levels we developed a process-based numerical model (Delft3D Flexible Mesh) and applied it to simulate a large, urban, high-energy coastal estuary (the San Francisco Bay). The unstructured grid with 1D/2DH model elements, allows for efficient model simulations and therefore it was possible to simulate over 70 years between 1950 and 2019. Results show significant skill in reproducing observations for the entire modeled time period with an average root-mean-square error of 8.0 cm. A process-based modeling approach allows for the explicit in- and exclusion of different physical processes to quantify their importance to the extremes. For the 100-year still water level (SWL), tide (70%) and non-tidal residual (NTR) (25%) explain the majority of the simulated high water levels in the Bay relative to Mean Higher High Water (MHHW). However, closer to the Delta, local fluvial inflow increases in importance. For longer return periods, the importance of tide decreases and the importance of remote NTRs and fluvial inflow increases.

Experimental study of breaking wave loads on elevated pile cap with rectangular cross-section

Elevated pile caps are always located close to the still-water level, where breaking waves can induce great impact loads and threaten the structural stability of bridges. This paper focuses on the interaction between breaking waves and an elevated pile cap with a rectangular cross-section. An elevated cap specimen under three breaking wave conditions was employed in the experimental program. The breaking wave loads, including the resulting horizontal and vertical loads, overturning moments, and water pressures exerted on the specimen, were measured simultaneously. The effects of clearance, breaker location, and structural orientation on the breaking wave loads were investigated, and a probabilistic description of breaking wave load was presented. The results show that with increasing clearance, the horizontal breaking wave load and overturning moment increased, while the vertical load decreased when the specimen was above the still-water level. The maximum horizontal wave load was observed when the specimen was located at the breaker tongue of the wave crest. The magnitude of the maximum horizontal and vertical load varied with structural orientations of the elevated pile cap. GEV distribution is effective in modeling the stochastic maximum horizontal and vertical breaking wave load.

Probabilistic structure of events controlling the after-storm recovery of coastal dunes

Coastal dunes protect beach communities and ecosystems from rising seas and storm flooding and influence the stability of barrier islands by preventing overwashes and limiting barrier migration. Therefore, the degree of dune recovery after a large storm provides a simple measure of the short-term resiliency (and potential long-term vulnerability) of barrier islands to external stresses. Dune recovery is modulated by low-intensity/high-frequency high-water events (HWEs), which remain poorly understood compared to the low-frequency extreme events eroding mature dunes and dominating the short-term socio-economic impacts on coastal communities. Here, we define HWEs and analyze their probabilistic structure using time series of still-water level and deep-water wave data from multiple locations around the world. We find that HWEs overtopping the beach can be modeled as a marked Poisson process with exponentially distributed sizes or marks and have a mean size that varies surprisingly little with location. This homogeneity of global HWEs is related to the distribution of the extreme values of a wave-runup parameter, [Formula: see text], defined in terms of deep-water significant wave height [Formula: see text] and peak wavelength [Formula: see text] Furthermore, the characteristic beach elevation at any given location seems to be tied to a constant HWE frequency of about one event per month, which suggests a stochastic dynamics behind beach stabilization. Our results open the door to the development of stochastic models of beach, dune, and barrier dynamics, as well as a better understanding of wave-driven nuisance flooding.

Experimental Study of Wave Run-Up on Tripod Offshore Wind-Turbine Foundations

Abstract For the design of offshore wind turbines, the airgap height of a service platform above still water level (SWL) is dependent on the maximum level of wave run-up in seas. A number of labora...