Hassan Smaoui

Modelling and numerical simulation of turbulence, waves and suspended sediments for pre-operational use in coastal seas

Abstract The role of small-scale processes in models of coastal seas is reviewed, and the respective uses of vertically integrated and vertically resolving models are described. Although applied with heavily tuned empirical parameters to the Holderness coast a vertically integrated model shows the importance of surface waves for predicting suspended particulate matter (SPM) and their distributions. In formulating a generic vertically resolving module, as kernel, the k–e turbulence closure has been selected. On a uniform vertical grid this model gave reasonably accurate results for a neutrally stratified channel flow forced by an M2 tidal wave (Elbe estuary) as well as on a nonuniform grid highly refined in the high-dissipation near-bed region for short-period (8 s) surface waves in a laboratory flume. The model was completed with modules accounting for the effect of waves on the turbulent kinetic energy (TKE) influx at the surface and on the apparent roughness at the bottom. It was finally coupled with different versions of vertically high resolving SPM models. In test applications to the English Channel and to the Sylt–Romo Bight (Germany/Denmark) the generic model versions performed with sufficient accuracy. However, in both cases: (i) fine tuning of erosion and deposition terms was necessary thus underlining the need for further experimental research towards an improved data base on erodible sediments and SPM; (ii) the parameters of the submodel for the TKE injection by surface waves could not be determined consistently and indicate the existence of a further still hidden parameter; (iii) the technical basis for in situ observations of small-scale processes in the coastal zone needs further improvements and consolidation.

Flux-limiter schemes for oceanic tracers: application to the English Channel tidal model

A 2-D numerical model has been used to simulate the dynamics of the Eastern part of the English Channel. This area is characterized by a strong tidal turbulent regime and a frontal zone identified near the French coast by a low-salinity band. The model uses the characteristics method with a bi-cubic interpolation to approximate the advective terms. Results show that the model overestimates the band width of the frontal zone. This anomaly is caused certainly by the numerical diffusion introduced by the interpolation procedure used with the characteristics scheme. In order to reduce this non-physical diffusion, we investigate, in this study, the flux-limiter schemes as an alternative of the characteristics method. To illustrate the improvements provided by this type of schemes, comparisons in 2-D model cases are made between the upwind and centred scheme with more recent higher order schemes combined with limiters namely Minmod, Superbee, Van Leer and Monotonized Centred (MC) (also called MUSCL scheme). Numerical simulations show that when the CFL condition is satisfied, the flux limiter schemes reduce the numerical diffusion and suppress the oscillations caused by the non-limited higher order schemes. For the model and realistic cases, the Superbee limiter was found to be a good compromise between shape preservation and computational cost.

Reynolds number variation in oscillatory boundary layers. Part I. Purely oscillatory motion

A numerical model based upon a low Reynolds number turbulence closure is proposed to study Reynolds number variation in reciprocating oscillatory boundary layers. The model is used to compute the boundary layer for flow regimes ranging from smooth laminar to rough turbulent. Criteria for fully developed turbulence are derived for walls of the smooth and rough types. In particular, a new criterion to identify the rough turbulent regime is determined based on the time-averaged turbulence intensity. The reliability of the present model is assessed through comparisons with detailed experimental data collected by other investigators. The model globally improves upon standard high Reynolds number closures. Variation through the wave cycle of the main flow variables (ensemble-averaged velocity, shear stress, turbulent kinetic energy) is remarkably well-predicted for smooth walls. Predictions are satisfactory for rough walls as well. Yet, the turbulence level in the rough turbulent regime is overpredicted in the vicinity of the bed.

3-D NUMERICAL SIMULATION OF CONVOY-GENERATED WAVES IN A RESTRICTED WATERWAY

We consider waves generated by the passing of convoys in a restricted waterway. The magnitude of these waves depends mainly on the geometrical and kinematical parameters of the convoy, such as the speed and the hull geometry. The objective of this study is to predict the relationship between these geometrical and kinematical parameters and the amplitude of ship-generated waves as well as the water plane drawdown. Numerical simulations are conducted by solving the 3-D Navier-Stokes equations along with the standard k-ε model for turbulent processes. The results are compared first with the empirical model and second with experimental measurements performed by the French company Compagnie National du Rhône (CNR).

Meshless method for shallow water equations with free surface flow

Solving problems with free surface often encounters numerical difficulties related to excessive mesh distortion as is the case of dambreak or breaking waves. In this paper the Natural element method (NEM) is used to simulate a 2D shallow water flows in the presence of theses strong gradients. This particle-based method used a fully Lagrangian formulation based on the notion of natural neighbors. In the present study we consider the full non-linear set of Shallow Water Equations, with a transient flow under the Coriolis effect. For the numerical treatment of the nonlinear terms we used a Lagrangian technique based on the method of characteristics. This will allow avoiding divergence of Newton-Raphson scheme, when dealing with the convective terms. We also define a thin area close to the boundaries and a computational domain dedicated for nodal enrichment at each time step. Two numerical test cases were performed to verify the well-founded hopes for the future of this method in real applications.

Numerical study of coastal sandbar migration, by hydro-morphodynamical coupling

We present a numerical model based on the hydro-morphodynamical coupling to study coastal sandbar migration. In order to improve both nonlinear and dispersive wave processes in relatively shallow water, we developed a finite element model based on the Legendre polynomials and on the Extended Boussinesq model. This model reproduces the propagation of wave trains with a high degree of accuracy on a greater range of depths than the standard Boussinesq models. We also implemented the Total Variation Diminishing schemes to improve the quality of the computed hydrodynamic fields, especially in areas where sharp flow gradients occurred. The coupled morpho-hydrodynamical model is then used to simulate the migration of real sandbars observed at Rousty beach (Mediterranean French coast). For verification the model results are compared with field measurements obtained from a small-scale field campaign carried out over two years at Rousty beach, and the results of this comparison are thoroughly discussed and analyzed.

Extension of the skin shear stress Li’s relationship to the flat bed

A proper estimation of the skin shear stress τs is necessary for a proper evaluation of sediment flux at the sediment–fluid interface. Several empirical formulas of the skin shear stress have been proposed in the literature for rippled bed as function of the factor form η/λ (η and λ are respectively the height and wavelength of the bedform). These formulas express that in the presence of bedform, τs is a partition of the total shear stress τb. In contrast, when the bottom is flat, τs is exactly equal to τb. Based on in situ measurements, Li (J Geophys Res 99:791–799, 1994) has proposed a new formula of τs depending on u*/η (u* is the friction velocity,

3D Numerical Modeling of Sediment Resuspension Induced by the Compounding Effects of Ship-Generated Waves and the Ship Propeller

{u_{*}=\sqrt{\tau_{b}/\rho}}