Incorporating floating surface objects into a fully dispersive surface wave model

Abstract

The shock-capturing, non-hydrostatic, three-dimensional (3D) finite-volume model NHWAVE was originally developed to simulate wave propagation and landslide-generated tsunamis in finite water depth (Ma et al., 2012). The model is based on the incompressible Navier-Stokes equations, in which the z-axis is transformed to a σ-coordinate that tracks the bed and surface. As part of an ongoing effort to simulate waves in polar marginal ice zones (MIZs), the model has now been adapted to allow objects of arbitrary shape and roughness to float on or near its water surface. The shape of the underside of each floating object is mapped onto an upper σ-level slightly below the surface. In areas without floating objects, this σ-level continues to track the surface and bed as before. Along the sides of each floating object, an immersed boundary method is used to interpolate the effects of the object onto the neighboring fluid volume. Provided with the object's shape, location, and velocity over time, NHWAVE determines the fluid fluxes and pressure variations from the corresponding accelerations at neighboring cell boundaries. The system was validated by comparison with analytical solutions and a VOF model for a 2D floating box and with laboratory measurements of wave generation by a vertically oscillating sphere. A steep wave simulation illustrated the high efficiency of NHWAVE relative to a VOF model. In a more realistic MIZ simulation, the adapted model produced

Wave-induced stress and breaking of sea ice in a coupled hydrodynamic discrete-element wave–ice model

“…Recently, Ma et al (2016) and Orzech et al (2016) implemented in NHWAVE equations for floating objects and other solid "obstacles". Their method is based on immersed boundary techniques (Mittal and Iaccarino, 2005;Ha et al, 2014), suitable for modeling interactions between fully or partially submerged solid bodies (fixed or moving) and the surrounding fluid.…”

“…Their method is based on immersed boundary techniques (Mittal and Iaccarino, 2005;Ha et al, 2014), suitable for modeling interactions between fully or partially submerged solid bodies (fixed or moving) and the surrounding fluid. The algorithms of Orzech et al (2016) are not yet included in the publicly available version of NHWAVE (although the code does contain basic treatment of fixed obstacles); the present model, developed independently, shares many features with their approach but, due to a number of assumptions related to the shape and the characteristics of motion of the floating objects, it is much less general, suitable for the specific configuration analyzed in this work. In contrast, the model of Orzech et al (2016) assumes that floating objects are rigid bodies, making it unsuitable for an analysis of ice deformation and breaking, which is crucial for the present study.…”

“…To close the system of Eqs. (2)- (4) are supplemented by the Poisson equation for pressure (Ma et al, 2012;Orzech et al, 2016). At the bottom, z = −H , the kinematic and free-slip boundary conditions for velocity, and the Neumann boundary condition for pressure are…”

A Coupled System for Investigating the Physics of Wave–Ice Interactions

“…Earlier models (e.g., Hopkins and Shen 2001;Hopkins and Thorndike 2006) represent each complete ice floe as a single element of O(100-1000) m and are applied to larger domains, such as Cook Inlet, Alaska. More recent DEM efforts (e.g., Xu et al 2012;Polojärvi and Tuhkuri 2013;Herman 2013Herman , 2017Orzech et al 2014;Song et al 2014) utilize collections of smaller bonded elements [O(cm-m)] to represent floes or sections of ice. While in general more expensive computationally, this approach allows for investigation of smaller-scale ice floe material properties and behavior in response to wave forcing.…”

“…Waves are simulated with the Non-Hydrostatic WAVE model (NHWAVE;Ma et al 2012Ma et al , 2016Derakhti et al 2015), and ice floes are represented using the DEM package Large-Scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS) Improved for General Granular and Granular Heat Transfer Simulations (LIGGGHTS;Kloss et al 2012). The transfer of energy and momentum between waves and floes is tracked throughout the wave-ice domain by both models (see also Orzech et al 2016b;Bateman et al 2016;Orzech et al 2014). The system is designed to resolve waves at kilometer scales, accurately simulating their evolution and attenuation when passing through a field of ice floes that realistically flex, collide, and fracture.…”