Edmond Y.M. Lo

Bio: Edmond Y.M. Lo is an academic researcher from Nanyang Technological University. The author has contributed to research in topics: Breaking wave & Flood myth. The author has an hindex of 16, co-authored 60 publications receiving 2065 citations. Previous affiliations of Edmond Y.M. Lo include Massachusetts Institute of Technology.

Incompressible sph method for simulating newtonian and non-newtonian flows with a free surface

Abstract: An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier–Stokes equations. The method uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.

Simulation of near-shore solitary wave mechanics by an incompressible SPH method

Abstract: An incompressible smoothed particle hydrodynamics (SPH) method together with a large eddy simulation (LES) approach is used to simulate the near-shore solitary wave mechanics. The incompressible Navier–Stokes equations in Lagrangian form are solved using a two-step fractional method. This method first integrates the velocity field in time without enforcing incompressibility. The resulting deviation in particle density is projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation. SPH formulations are employed for discretization of relevant gradient and divergence operators. The spatial filtering of the LES approach produces sub-particle scale stresses, which are treated by the Smagorinsky model. The cases of a solitary wave against a vertical wall and running up a plane slope are treated. The wave profiles are in good agreement with reported experimental data or analytical solutions. It is found that the assumption of hydrostatic pressure holds almost everywhere except during the last stages of wave breaking. The dynamic viscosity is also found to be a maximum near the breaking front.

A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation

Abstract: In existing experiments it is known that the slow evolution of nonlinear deep-water waves exhibits certain asymmetric features. For example, an initially symmetric wave packet of sufficiently large wave slope will first lean forward and then split into new groups in an asymmetrical manner, and, in a long wavetrain, unstable sideband disturbances can grow unequally to cause an apparent downshift of carrier-wave frequency. These features lie beyond the realm of applicability of the celebrated cubic Schrodinger equation (CSE), but can be, and to some extent have been, predicted by weakly nonlinear theories that are not limited to slowly modulated waves (i.e. waves with a narrow spectral band). Alternatively, one may employ the fourth-order equations of Dysthe (1979), which are limited to narrow-banded waves but can nevertheless be solved more easily by a pseudospectral numerical method. Here we report the numerical simulation of three cases with a view to comparing with certain recent experiments and to complement the numerical results obtained by others from the more general equations.

1DH Boussinesq modeling of wave transformation over fringing reefs

Abstract: To better understand wave transformation process and the associated hydrodynamic characteristics over fringing coral reefs, we present a numerical study, which is based on one-dimensional (1D) fully nonlinear Boussinesq equations, of the wave-induced setups/setdowns and wave height changes over various fringing reef profiles. An empirical eddy viscosity model is adopted to account for wave breaking and a shock-capturing finite volume (FV)-based solver is employed to ensure the computational accuracy and stability for steep reef faces and shallow reef flats. The numerical results are compared with a series of published laboratory experiments. Our results show that with an appropriate treatment of boundary conditions and a fine-tuned eddy viscosity model, the full nonlinear Boussinesq model can give satisfactory predictions of the wave height as well as the mean water level over various reef profiles with different reef-flat submergences and reef-crest configurations under both monochromatic and spectral waves. The primary 1D wave transformation processes, including nonlinear shoaling, refection, breaking, generation of higher harmonics and infragravity waves, can also be reasonably captured. Finally, the model is applied to study the effects of reef-face slopes and profile shapes on the distribution of the wave height and mean water level over the fringing reefs.

Characteristics of Monochromatic Waves Breaking over Fringing Reefs

Abstract: Yao, Y.; Huang, Z.H.; Monismith, S.G., and Lo, E.Y.M., 2013. Characteristics of monochromatic waves breaking over fringing reefs. A fringing reef is a reef that is directly attached to a shore. Since fringing reefs resemble plane beaches in some aspects, it is important to understand the similarities and discrepancies between the wave breaking over fringing reefs and the wave breaking over plane beaches. With an idealized fringing reef (a plane sloping fore reef and a submerged horizontal reef flat), a series of laboratory experiments were conducted in a wave flume to understand how the reef-flat submergence and the fore-reef slope may affect the characteristics of wave breaking over fringing reefs. The results show that the relative reef-flat submergence (the ratio of the reef-flat submergence to the wave height) is an important factor to characterize most wave-breaking features (the breaker type and location, the surf-zone width, and the incipient breaker depth index). The influence of the fore...

A new view of nonlinear water waves: the Hilbert spectrum

Abstract: We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Abstract: Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Physical Mechanisms of the Rogue Wave Phenomenon

Abstract: A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (Benjamin–Feir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrodinger equation, the Davey–Stewartson system, the Korteweg–de Vries equation, the Kadomtsev–Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.