A σ‐coordinate non‐hydrostatic model with embedded Boussinesq‐type‐like equations for modeling deep‐water waves

Abstract

SUMMARYA -coordinate non-hydrostatic model, combined with the embedded Boussinesq-type-like equations, a reference velocity, and an adapted top-layer control, is developed to study the evolution of deep-water waves. The advantage of using the Boussinesq-type-like equations with the reference velocity is to provide an analytical-based non-hydrostatic pressure distribution at the top-layer and to optimize wave dispersion property. The -based non-hydrostatic model naturally tackles the so-called overshooting issue in the case of non-linear steep waves. Efficiency and accuracy of this non-hydrostatic model in terms of wave dispersion and nonlinearity are critically examined. Overall results show that the newly developed model using a few layers is capable of resolving the evolution of non-linear deep-water wave groups.

Numerical integration of the contravariant integral form of the Navier–Stokes equations in time-dependent curvilinear coordinate systems for three-dimensional free surface flows

“…Some of the most recent models based on this approach use a coordinate transformation in the vertical direction (named sigma coordinate transformation [7]) by which the Cartesian vertical coordinate is expressed as a function of a moving vertical coordinate, σ , which adjusts to the free surface motions. The use of the above strategy makes it possible to obtain numerical models with excellent dispersive properties even when using a low number (less than ten) of vertical layers [8,9]. A recent development in the three-dimensional models which adopt the σ coordinate consists in the adoption of shock-capturing numerical schemes which can simulate the wave breaking in the surf zone [10][11][12].…”

A Three-Dimensional Numerical Study of Wave Induced Currents in the Cetraro Harbour Coastal Area (Italy)

“…This makes it possible to obtain a computational grid where, at every instant, the top boundary coincides with the free surface and where the zero-pressure condition can be correctly assigned. As demonstrated in several papers [11,[15][16][17][18], this strategy makes it possible to obtain numerical models with good dispersive properties, also by using a small number of grid nodes (less than ten) along the vertical direction. In these models, in order to transform the irregular moving grid into a regular fixed one, the Navier-Stokes equations must be expressed in a time dependent coordinates system.…”

“…In these models, in order to transform the irregular moving grid into a regular fixed one, the Navier-Stokes equations must be expressed in a time dependent coordinates system. In the models proposed by [11,[15][16][17][18] the horizontal coordinates are the Cartesian ones, while the vertical coordinate is a moving coordinate (usually called sigma coordinate). In this paper we adopt a boundary conforming curvilinear grid that makes it possible to reproduce the coastal region with a smaller number of grid nodes in the horizontal directions.…”

Nonlinear waves and nearshore currents over variable bathymetry in curve-shaped coastal areas

“…Some of the most recent three-dimensional non-hydrostatic numerical models make use of coordinate transformation in the vertical direction (σ-coordinate transformation), by which the vertical Cartesian coordinate, z, is expressed as a function of a time-dependent curvilinear coordinate, σ, that follows the free surface movements. The adoption of this strategy allows to obtain numerical models with excellent dispersive properties even using few layers in the vertical direction (Lin and Li 2002;Young and Wu 2010). A recent evolution of the three-dimensional models that adopt a time-varying coordinate makes use of shock-capturing numerical schemes that are able to explicitly simulate wave breaking.…”