Non-uniform Bathymetry Research Articles

Observations of two-dimensional turbulence in the surfzone

Low-frequency, many-minute-period horizontal surfzone eddies are an important mechanism for the dispersion of material, transporting larvae, pollutants, sediment, and swimmers both across and along the nearshore. Previous numerical, laboratory, and field observations on alongshore uniform bathymetry with no or roughly uniform mean background flows suggest that the low-frequency eddies may be the result of a two-dimensional inverse energy cascade that transfers energy from relatively small spatial-scale vorticity injected by depth limited breaking waves to larger and larger spatial scales. Here, using remotely sensed high-spatial resolution estimates of currents, those results are extended to surfzones with strong complex mean circulation patterns [flows O(1 m/s)] owing to nonuniform bathymetry. Similar to previous results, wavenumber spectra and second-order structure functions calculated from the observations are consistent with a two-dimensional inverse energy cascade. The size of the largest eddies is shown to depend on the surfzone width and the spatial scales of the mean currents. Third-order structure functions also are consistent with an inverse cascade for spatial scales greater than ∼50 m. At smaller scales, the third-order structure functions suggest a mixture of inverse and forward cascades.

An experimental study on nonlinear wave dynamics for freak waves over an uneven bottom

The effect of the non-uniform bathymetry on the nonlinear wave dynamics for the freak wave is investigated experimentally, with emphasis on the interrelations between different nonlinear behaviors resulting from various geometric parameters and spectral analysis. Both the frequency modulation and the nonlinear phase coupling can be provoked by the decreasing water depth and weakened after the top peak of the bar, the nonlinear exhibition for transferring energy to high-frequency contents over shoal supports that frequency modulation can reflect nonlinear phase coupling well. The consistent change of the Hilbert energy spectrum and the bicoherence shows that the main nonlinear interaction in the process of wave propagation in shallowing water is quadratic nonlinearity. In addition, the geometric study is conducted to investigate the effect of the water depth on the parametric variations, the research results show that the mean asymmetry and kurtosis change abruptly when the wave approaches the top peak of the bar. As the wave propagates along the water flume, freak waves can be generated at various locations, however, they appear more frequently as waves propagate close to the shallowest water depth, and the maximum probability of occurrence for a freak wave can be up to about 1%.

Extreme wave runup at the Seisho Coast during Typhoons Faxai and Hagibis in 2019

Two successive extreme typhoons, Faxai and Hagibis, hit Eastern Japan and left devastating damage along its long coastline due to high waves. During the two typhoons, the characteristics of extreme waves at Seisho Coast, the most affected coast, were investigated. The investigations were based on wave observation data, post-event surveys, and numerical simulations. The observation data confirmed that extreme wave fields were generated on the coast during both typhoons and that Hagibis produced higher waves than Faxai. The maximum spectral significant wave height of incident short waves exceeded 8 m at the depth of 13 m and that of infragravity waves reached 2 m in shallower water during Hagibis. The post-event surveys revealed that the typhoons produced different variations of runup heights over nonuniform bathymetry along the coast. Wave hindcast results suggested that the overall variability of runup heights was primarily attributed to alongshore variations of the beach slope rather than offshore wave conditions. Further numerical investigations of nearshore waves using SWASH were conducted to reveal the mechanisms of local extreme runup, which could not be explained solely by cross-shore wave processes. The model results suggested the significant involvement of two-dimensional wave processes in the observed variations. Further detailed analyses revealed that local high runup was caused by concentrations of incident short waves during Faxai. Conversely, infragravity waves trapped on the coastal bathymetry contributed to extreme runup during Hagibis. This study highlights the importance of considering nonlinear wave processes over a broad coastal area for predicting local wave impacts under extreme wave conditions.

Statistical properties of wave kinematics in long-crested irregular waves propagating over non-uniform bathymetry

Experimental and numerical evidence have shown that nonuniform bathymetry may alter significantly the statistical properties of surface elevation in irregular wave fields. The probability of “rogue” waves is increased near the edge of the upslope as long-crested irregular waves propagate into shallower water. The present paper studies the statistics of wave kinematics in long-crested irregular waves propagating over a shoal with a Monte Carlo approach. High order spectral method is employed as wave propagation model, and variational Boussinesq model is employed to calculate wave kinematics. The statistics of horizontal fluid velocity can be different from statistics in surface elevation as the waves propagate over uneven bathymetry. We notice strongly non-Gaussian statistics when the depth changes abruptly in sufficiently shallow water. We find an increase in kurtosis in the horizontal velocity around the downslope area. Furthermore, the effects of the bottom slope with different incoming waves are discussed in terms of kurtosis and skewness. Finally, we investigate the evolution of kurtosis and skewness of the horizontal velocity over a sloping bottom in a deeper regime. The vertical variation of these statistical quantities is also presented.

Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry

We present experimental evidence of formation and persistence of localized waves, breathers, and solitons, occurring in a random sea state and uniformly traveling over non-uniform bathymetry. Recent studies suggest connections between breather dynamics and irregular sea states and between extreme wave formation and breathers, random sea states, or non-uniform bathymetry individually. In this paper, we investigate the joint connection between these phenomena, and we found that breathers and deep-water solitons can persist in more complex environments. Three different sets of significant heights have been generated within a Joint North Sea Wave Observation Project wave spectrum, and the wave heights were recorded with gauges in a wave tank. Statistical analysis was applied to the experimental data, including the space and time distribution of kurtosis, skewness, Benjamin–Feir index, moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random wave field and traveling over shoals, valleys, and slopes were compared with exact solutions of the nonlinear Schrödinger equation with a good match, demonstrating that these localized waves have the same structure as deep-water breathers. We identify the formation of rogue waves at moments and over regions where the kurtosis and skewness have local maxima. These results provide insights for understanding of the robustness of Peregrine and higher-order Akhmediev breathers, Kuznetsov–Ma solitons, and rogue waves, and their occurrence in realistic oceanic conditions, and may motivate analogous studies in other fields of physics to identify limitations of exact weakly nonlinear models in non-homogeneous media.

MRT-Lattice Boltzmann Model for Multilayer Shallow Water Flow

The objectives of this study are to introduce a multiple-relaxation-time (MRT) lattice Boltzmann model (LBM) to simulate multilayer shallow water flows and to introduce graphics processing unit (GPU) computing to accelerate the lattice Boltzmann model. Using multiple relaxation times in the lattice Boltzmann model has an advantage of handling very low kinematic viscosity without causing a stability problem in the shallow water equations. This study develops a multilayer MRT-LBM to solve the multilayer Saint-Venant equations to obtain horizontal flow velocities in various depths. In the multilayer MRT-LBM, vertical kinematic viscosity forcing is the key term to couple adjacent layers. We implemented the multilayer MRT-LBM to a GPU-based high-performance computing (HPC) architecture. The multilayer MRT-LBM was verified by analytical solutions for cases of wind-driven, density-driven, and combined circulations with non-uniform bathymetry. The results show good speedup and scalability for large problems. Numerical solutions compared well to the analytical solutions. The multilayer MRT-LBM is promising for simulating lateral and vertical distributions of the horizontal velocities in shallow water flow.

Rip currents and alongshore flows in single channels dredged in the surf zone

AbstractTo investigate the dynamics of flows near nonuniform bathymetry, single channels (on average 30 m wide and 1.5 m deep) were dredged across the surf zone at five different times, and the subsequent evolution of currents and morphology was observed for a range of wave and tidal conditions. In addition, circulation was simulated with the numerical modeling system COAWST, initialized with the observed incident waves and channel bathymetry, and with an extended set of wave conditions and channel geometries. The simulated flows are consistent with alongshore flows and rip‐current circulation patterns observed in the surf zone. Near the offshore‐directed flows that develop in the channel, the dominant terms in modeled momentum balances are wave‐breaking accelerations, pressure gradients, advection, and the vortex force. The balances vary spatially, and are sensitive to wave conditions and the channel geometry. The observed and modeled maximum offshore‐directed flow speeds are correlated with a parameter based on the alongshore gradient in breaking‐wave‐driven‐setup across the nonuniform bathymetry (a function of wave height and angle, water depths in the channel and on the sandbar, and a breaking threshold) and the breaking‐wave‐driven alongshore flow speed. The offshore‐directed flow speed increases with dissipation on the bar and reaches a maximum (when the surf zone is saturated) set by the vertical scale of the bathymetric variability.

Solitary Wave Breaking on Irregular 3D Bathymetry Using a Coupled Potential + Viscous Flow Model

A three-dimensional (3D) coupled potential + viscous flow model based on a domain decomposition method is developed and applied to study shoaling and breaking of a solitary wave on a nonuniform bathymetry. The flow domain is decomposed into two subdomains separated by an interface: a wave generation and propagation subdomain modeled by a potential-flow (PF) solver and a shoaling and surf zone subdomain modeled by a Navier-Stokes equation (NSE) solver. The PF solver, based on a boundary-element method, is capable of modeling the motion of a piston wavemaker and the propagation of the resulting wave downstream. After the wave passes through the interface, it continues to propagate in the viscous-flow (NSE) subdomain, which is solved by a FEM. A free-surface capturing feature of the NSE solver allows simulation of wave breaking and the postbreaking behavior. Numerical results show good agreement with those of a large-scale wave-basin experiment of a solitary wave run-up on a 3D wedge. The simulation shows that breaking criteria and categorization for plane slopes do not apply to this particular bathymetry. The velocity and vorticity patterns during wave breaking are also examined to demonstrate the capabilities of the viscous-flow solver.

Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water

Using a Boussinesq model with improved linear dispersion, we show numerical evidence that bottom non-uniformity can provoke significantly increased probability of freak waves as a wave field propagates into shallower water, in agreement with recent experimental results [K. Trulsen, H. Zeng, and O. Gramstad, “Laboratory evidence of freak waves provoked by non-uniform bathymetry,” Phys. Fluids 24, 097101 (2012)]. Increased values of skewness, kurtosis, and probability of freak waves can be found on the shallower side of a bottom slope, with a maximum close to the end of the slope. The increased probability of freak waves is typically seen to endure some distance into the shallower domain, before it decreases and reaches a stable value depending on the depth. The maxima of the statistical parameters are observed both in the case where there is a region of constant depth after the slope, and in the case where the uphill slope is immediately followed by a downhill slope. In the case that waves propagate over a slope from shallower to deeper water, however, we do not find any increase in freak wave occurrence.

Applying microprocessor analysis methods to river network modelling

This paper describes the Simulation Program for River Networks (SPRINT) that is proposed as a tool for studying Continental River Dynamics (CRD), the solution of physics-based equations for large-scale river networks. Existing coupled hydrologic/hydraulic models have been unable to solve the full Saint-Venant equations for river networks larger than O(103) elements, but continental scales require 106–107 elements. The new model solves the full nonlinear Saint-Venant equations for one-dimensional (1D) unsteady flow and stage height in river channel networks with non-uniform bathymetry, and is demonstrated to compute networks of O(105) elements more than 330 times faster than real time on a desktop computer. The model incorporates ideas that were originally developed to address Very Large System Integration (VLSI) problems in microprocessor design, where solving large nonlinear computational problems is a common challenge. Computational speed is increased by applying Jacobian bypass techniques in a Newton–Raphson solution and smoothing the geometric depth-area and friction-area relationships where discontinuities otherwise slow convergence. Pre-processing of junction relationships is used to remove temporal nonlinearities where river tributaries meet. Model input/output are simplified and made readily accessible to other software through use of Application Programming Interface (API) standards and a “netlist” idea that was previously used to describe electric circuit topology. The model is tested on both simple and complex geometry through comparisons with the HEC-RAS model. A example simulation is conducted for 1.5 × 104 river km of the Guadalupe and San Antonio river network during a 14 day rain event.

Laboratory evidence of freak waves provoked by non-uniform bathymetry

We show experimental evidence that as relatively long unidirectional waves propagate over a sloping bottom, from a deeper to a shallower domain, there can be a local maximum of kurtosis and skewness close to the shallower side of the slope. We also show evidence that the probability of large wave envelope has a local maximum near the shallower side of the slope. We therefore anticipate that the probability of freak waves can have a local maximum near the shallower side of a slope for relatively long unidirectional waves.

Multilayer shallow water flow using lattice Boltzmann method with high performance computing

A multilayer lattice Boltzmann (LB) model is introduced to solve three-dimensional wind-driven shallow water flow problems. The multilayer LB model avoids the expensive Navier–Stokes equations and obtains stratified horizontal flow velocities as vertical velocities are relatively small and the flow is still within the shallow water regime. A single relaxation time BGK method is used to solve each layer coupled by the vertical viscosity forcing term. To increase solution stability, an implicit step is suggested to obtain flow velocities. The main advantage of using the LBM is that after selecting appropriate equilibrium distribution functions, the LB algorithm is only slightly modified for each layer and retains all the simplicities of the LBM within the high performance computing (HPC) environment. The performance of the parallel LB model for the multilayer shallow water equations is investigated on CPU-based HPC environments using OpenMP. We found that the explicit loop control with cache optimization in LBM gives better performance on execution time, speedup and efficiency than the implicit loop control as the number of processors increases. Numerical examples are presented to verify the multilayer LB model against analytical solutions. We demonstrate the model’s capability of calculating lateral and vertical distributions of velocities for wind-driven circulation over non-uniform bathymetry.

A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying

A Riemann flux that uses primitive variables rather than conserved variables is developed for the shallow water equations with nonuniform bathymetry. This primitive-variable flux is both conservative and well behaved at zero depth. The unstructured finite-volume discretization used is suitable for highly nonuniform grids that provide resolution of complex geometries and localized flow structures. A source-term discretization is derived for nonuniform bottom that balances the discrete flux integral both for still water and in dry regions. This primitive-variable formulation is uniformly valid in wet and dry regions with embedded wetting and drying fronts. A fully nonlinear implicit scheme and both nonlinear and time-linearized explicit schemes are developed for the time integration. The implicit scheme is solved by a parallel Newton-iterative algorithm with numerically computed flux Jacobians. A concise treatment of characteristic-variable boundary conditions with source terms is also given. Computed results obtained for the one-dimensional dam break on wet and dry beds and for normal-mode oscillations in a circular parabolic basin are in very close agreement with the analytical solutions. Other results for a forced breaking wave with friction interacting with a sloped bottom demonstrate a complex wave motion with wetting, drying and multiple interacting wave fronts. Finally, a highly nonuniform, coastline-conforming unstructured grid is used to demonstrate an unsteady simulation that models an artificial coastal flooding due to a forced wave entering the Gulf of Mexico.