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The aim of the present work is to develop a model able to represent the propagation and transformation of waves in nearshore areas. The focus is on the phenomena of wave breaking, shoaling and run-up. These different phenomena are represented through a hybrid approach obtained by the coupling of non-linear Shallow Water equations with the extended Boussinesq equations of Madsen and Sorensen. The novelty is the switch tool between the two modelling equations: a critical free surface Froude criterion. This is based on a physically meaningful new approach to detect wave breaking, which corresponds to the steepening of the wave's crest which turns into a roller. To allow for an appropriate discretization of both types of equations, we consider a finite element Upwind Petrov Galerkin method with a novel limiting strategy, that guarantees the preservation of smooth waves as well as the monotonicity of the results in presence of discontinuities. We provide a detailed discussion of the implementation of the newly proposed detection method, as well as of two other well known criteria which are used for comparison. An extensive benchmarking on several problems involving different wave phenomena and breaking conditions allows to show the robustness of the numerical method proposed, as well as to assess the advantages and limitations of the different detection methods.

The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which allows the elevation reconstruction of water waves in intermediate and shallow waters. From comparisons with numerical Euler solutions and wave-tank experiments we show that our nonlinear method provides much better results of the surface elevation reconstruction compared to the linear transfer function approach commonly used in coastal applications. More specifically, our methodaccurately reproduces the peaked and skewed shape of nonlinear wave fields. Therefore, it is particularly relevant for applications on extreme waves and wave-induced sediment transport., Comment: To appear in J. Fluid Mech

The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up.

To describe the strongly nonlinear dynamics of waves propagating in the final stages of shoaling and in the surf and swash zones, fully nonlinear models are required. The ability of the Serre or Green Naghdi (S-GN) equations to reproduce this nonlinear processes is reviewed. Two high-order methods for solving S-GN equations, based on Finite Volume approaches, are presented. The first one is based on a quasi-conservative form of the S-GN equations, and the second on a hybrid Finite Volume/Finite Difference method. We show the ability of these two approaches to accurately simulate nonlinear shoaling, breaking and runup processes.

The Tribolium genome contains 21 nuclear receptors, representing all of the six known subfamilies. When compared to other species, this first complete set for a Coleoptera reveals a strong conservation of the number and identity of nuclear receptors in holometabolous insects. Two novelties are observed: the atypical NR0 gene knirps is present only in brachyceran flies, while the NR2E6 gene is found only in Tribolium and in Apis. Using a quantitative analysis of the evolutionary rate, we discovered that nuclear receptors could be divided into two groups. In one group of 13 proteins, the rates follow the trend of the Mecopterida genome-wide acceleration. In a second group of five nuclear receptors, all acting together at the top of the ecdysone cascade, we observed an overacceleration of the evolutionary rate during the early divergence of Mecopterida. We thus extended our analysis to the twelve classic ecdysone transcriptional regulators and found that six of them (ECR, USP, HR3, E75, HR4 and Kr-h1) underwent an overacceleration at the base of the Mecopterida lineage. By contrast, E74, E93, BR, HR39, FTZ-F1 and E78 do not show this divergence. We suggest that coevolution occurred within a network of regulators that control the ecdysone cascade. The advent of Tribolium as a powerful model should allow a better understanding of this evolution.

Ecdysteroid hormones are major regulators in reproduction and development of insects, including larval molts and metamorphosis. The functional ecdysone receptor is a heterodimer of ECR (NR1H1) and USP-RXR (NR2B4), which is the orthologue of vertebrate retinoid X receptors (RXR alpha, beta, gamma). Both proteins belong to the superfamily of nuclear hormone receptors, ligand-dependent transcription factors that share two conserved domains: the DNA-binding domain (DBD) and the ligand-binding domain (LBD). In order to gain further insight into the evolution of metamorphosis and gene regulation by ecdysone in arthropods, we performed a phylogenetic analysis of both partners of the heterodimer ECR/USP-RXR. Overall, 38 USP-RXR and 19 ECR protein sequences, from 33 species, have been used for this analysis. Interestingly, sequence alignments and structural comparisons reveal high divergence rates, for both ECR and USP-RXR, specifically among Diptera and Lepidoptera. The most impressive differences affect the ligand-binding domain of USP-RXR. In addition, ECR sequences show variability in other domains, namely the DNA-binding and the carboxy-terminal F domains. Our data provide the first evidence that ECR and USP-RXR may have coevolved during holometabolous insect diversification, leading to a functional divergence of the ecdysone receptor. These results have general implications on fundamental aspects of insect development, evolution of nuclear receptors, and the design of specific insecticides.

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \cite{matsuno3} and Choi \cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equations with the fully nonlinear shallow water Green-Naghdi equations represents a relevant model for describing ocean wave propagation from deep to shallow waters.