Ovsyannikov equations describe long-wavelength dynamics of nonlinear waves in two-layer shallow water systems. We suggest their simple generalisations which model qualitatively dispersive properties of such systems. These generalised equations are completely integrable by the known methods of nonlinear physics and we present their periodic and soliton solutions. The theory is illustrated by concrete examples.

We consider the Kakinuma model for the motion of interfacial gravity waves. The Kakinuma model is a system of Euler–Lagrange equations for an approximate Lagrangian, which is obtained by approximating the velocity potentials in the Lagrangian of the full model. Structures of the Kakinuma model and the well-posedness of its initial value problem were analysed in the companion paper [14]. In this present paper, we show that the Kakinuma model is a higher order shallow water approximation to the full model for interfacial gravity waves with an error of order $O(\delta _1^{4N+2}+\delta _2^{4N+2})$ in the sense of consistency, where $\delta _1$ and $\delta _2$ are shallowness parameters, which are the ratios of the mean depths of the upper and the lower layers to the typical horizontal wavelength, respectively, and $N$ is, roughly speaking, the size of the Kakinuma model and can be taken an arbitrarily large number. Moreover, under a hypothesis of the existence of the solution to the full model with a uniform bound, a rigorous justification of the Kakinuma model is proved by giving an error estimate between the solution to the Kakinuma model and that of the full model. An error estimate between the Hamiltonian of the Kakinuma model and that of the full model is also provided.

One new species of Caulleryaspis Sendall & Salazar-Vallejo, 2013 (Annelida: Sternaspidae), C. chicosciencei sp. nov., is described based on material collected in north-eastern Brazil. Specimens were collected in muddy bottoms in the Suape estuary complex in 7–16 m water depth. Caulleryaspis chicosciencei sp. nov. differs from the other known species by the combination of the following characters: small size, abundant cirriform papillae evenly distributed throughout body; chaetigers of introvert with 18–21 falcate hooks per bundle; ventral shield without ribs and undeveloped concentric lines, covered by long cirriform papillae with sediment particles adhered; marginal chaetal fascicles include eight lateral shield chaetae in an oval arrangement, and six posterior shield chaetae in slightly curved pattern. Caulleryaspis chicosciencei sp. nov. is the first species of the genus Caulleryaspis described from Brazil and it increases the number of sternaspids recorded from shallow water in the south-western Atlantic Ocean.

We analyse the vorticity production of lake-scale circulation in wind-induced shallow flows using a linear elliptic partial differential equation. The linear equation is derived from the vorticity form of the shallow-water equation using a linear bed friction formula. The features of the wind-induced steady-state flow are analysed in a circular basin with topography as a concave paraboloid, having a quadratic pile in the middle of the basin. In our study, the size of the pile varies by a size parameter. The vorticity production due to the gradient in the topography (and the distance of the boundary) makes the streamlines parallel to topographical contours, and beyond a critical size parameter, it results in a secondary vortex pair. We compare qualitatively and quantitatively the steady-state circulation patterns and vortex evolution of the flow fields calculated by our linear vorticity model and the full, nonlinear shallow-water equations. From these results, we hypothesize that the steady-state topographical vorticity production in lake-scale wind-induced circulations can be described by the equilibrium of the wind friction field and the bed friction field. Moreover, the latter can also be considered as a linear function of the velocity vector field, and hence the problem can be described by a linear equation.

In this paper we describe a new genus and a new species of Chiridotidae based on specimens collected in shallow water off the South-eastern Brazilian coast. Gymnopipina ikamiaba gen. nov. et sp. nov. is characterized by the complete absence of dermal ossicles in the body, and it differs from the other ossicleless apodids in the number of tentacles and of Polian vesicles, and in the morphology of the calcareous ring. Although not formally tested with a phylogenetic framework, apodids have apparently lost their dermal ossicles multiple times. If these reversions hold true, Gymnopipina gen. nov. represents the fourth independent loss of dermal ossicles in the class Holothuroidea. An identification key to the Brazilian apodid species is also provided.

In this article we study the morphodynamics of the Slufter on the short-term (months) and long-term (years to decades). The Slufter is a small, shallow tidal inlet located on the island of Texel, the Netherlands. A narrow (tens of meters) channel connects the North Sea with a dune valley of 400 ha. This narrow channel is located in between a 400-700 m wide opening in the dunes. Approximately 80% of the basin of the Slufter is located above mean high water level and is flooded only during storms, when a threshold water level is exceeded.

Analysis of historical aerial photographs revealed that the inlet channel migrates about 100 m per year. In the 1970's it migrated to the south, while since 1980 it is migrating to the north. When the channel reached the dunes at the north side of the dune breach the channel was relocated to the south by man. The channel inside the backbarrier basin was less dynamic. It shows a gradual growth and southward migration of a meander on a decadal time scale.

The short-term dynamics of the Slufter were studied during a field campaign in 2008. The campaign aimed at identifying the dominant hydrodynamic processes and morphological change during fair weather conditions and during storm events. During fair weather flow velocities in the main inlet channel were 0.5-0.8 m/s at water depths of 0-1.5 m, slightly ebb-dominant and associated morphological change was small. When water levels were above critical levels during a storm period the hydrodynamics in the main channel drastically changed. The flow in the main channel was highly ebb dominant. Long ebb periods with typical flow velocities of 2 m/s were alternated by much shorter flood periods with typical velocities of 0.5-1 m/s. This resulted in a net outflow of water via the main channel, while we measured a net inflow of water at the beach plain. During the storm period in 2008 we measured a 10 m migration of the channel to the north.

We conclude that the Slufter is a storm-dominated tidal inlet system.

A new set of boundary conditions has been derived by rigorous methods for the shallow water equations in a limited domain. The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions. The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain. The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.

In this paper, a bilayer model is derived to simulate the evolution of a thin film flow over water. This model is derived from the incompressible Navier–Stokes equations together with suitable boundary conditions including friction and capillary effects. The derivation is based on the different properties of the fluids; thus, we perform a multiscale analysis in space and time, and a different asymptotic analysis to derive a system coupling two different models: the Reynolds lubrication equation for the upper layer and the shallow water model for the lower one. We prove that the model verifies a dissipative entropy inequality up to a second-order term. Moreover, we propose a correction of the model – by taking into account the second-order extension for the pressure – that admits an exact dissipative entropy inequality. Two numerical tests are presented. In the first test, we compare the numerical results with the viscous bilayer shallow water model proposed in Narbona-Reina et al. (Comput. Model. Eng. Sci., 2009, Vol. 43, pp. 27–71). In the second test, the objective is to show some of the characteristic situations that can be studied with the proposed model. We simulate a problem of pollutant dispersion near the coast. For this test, the influence of the friction coefficient on the coastal area affected by the pollutant is studied.

In this paper, we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough topography. The major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface tracking. An analytical integration method is presented for the friction force term to remove the stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by introducing an empirical parameter, the water depth tolerance, as extensively adopted in literatures. We propose a problem independent formulation for this parameter, which provides a stable scheme and preserves the overall truncation error of . The method is applied to solve problems with complex rough topography, coupled with h-adaptive mesh techniques to demonstrate its robustness and efficiency.

We consider the propagation of a non-Boussinesq gravity current in an axisymmetric configuration (full cylinder or wedge). The current of density ρc is released from rest from a lock of radius r0 and height h0 into an ambient fluid of density ρa in a container of height H. When the Reynolds number is large, the resulting flow is governed by the parameters ρc/ρa and H* = H/h0. We show that the one-layer shallow-water model, carefully combined with a Benjamin-type front condition, provides a versatile formulation for the thickness and speed of the current, without any adjustable constants. The results cover in a continuous manner the range of light ρc/ρa ≪ 1, Boussinesq ρc/ρa ≈ 1, and heavy ρc/ρa ≫ 1 currents in a fairly wide range of depth ratio, H*. We obtain finite-difference solutions for the propagation and show that a self-similar behaviour develops for large times. This reveals the main features, in particular: (a) The heavy current propagates faster and its front is thinner than that for the light counterpart; (b) For large time, t, both the heavy and light currents spread like t1/2, but the thickness profiles display significant differences; (c) The energy-constrained propagation with the thickness of half-ambient-depth (when H* is close to 1) is a very limited occurrence, in contrast to the rectangular geometry counterpart in which this effect plays a major role. The predictions of the simple model are supported by some axisymmetric Navier–Stokes finite-difference simulations.

Population changes and reproduction of the alien polychaete, Streblospio gynobranchiata, living in 5, 15 and 30 m depths of the south Caspian Sea (Noor coast) was studied seasonally during 2005. Density and biomass of S. gynobranchiata increased with increasing depth, total organic matter and decreased with sand percentage of the substrate. Maximum density was 10311.11 ± 1596.4 ind m−2 and biomass 2320 ± 359.19 mg m−2 were observed in 30 m depth in winter. The maximum and minimum densities and biomass were obtained in winter and summer, respectively. Mature females were observed in all seasons, but reproduction peaks were observed in summer and autumn.

In this work we introduce an accurate solver for theShallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.

We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with $\gamma=\displaystyle{{c_{p}}/{c_{v}}}=2$ . These equations also modelizethe shallow water problem in height-flow rate formulation used tosolve the flow in lakes and perfectly well-mixed sea. We establisha convergence result for the time-discretized problem when themomentum equation and the continuity equation are solved with theGalerkin method, without adding a penalization term in thecontinuity equation as it is made in Lions (1998). The secondpart is devoted to the numerical analysis and mainly deals withproblems of geophysical fluids. We compare the simulationsobtained with this compressible isentropic Navier–Stokes model andthose obtained with a shallow water model (Di Martino et al., 1999). At first,the computations are executed on a simplified domain in order tovalidate the method by comparison with existing numerical resultsand then on a real domain: the dam of Calacuccia (France). At last, we numerically implement an analyticalexample presented by Weigant (1995) which shows thateven if the data are rather smooth, we cannot have bounds onρ in Lp for p large if $\gamma<2$ when N=2.