Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Virtual Special Issue: “The impact of temperature on human health: new insights”

Ambient temperature is one of the basic parameters characterising human comfort: are we too hot, too cold, or just right? The impact of temperature goes beyond comfort: inadequate temperature and temperature variations have consequences on human health, as the increasing numbers of studies have demonstrated. The topic is of particular significance at the times when climate change shifts the traditional – as we know them- temperature zones, and brings much wider temperature variations. For these reasons the impact of temperature on health has been one of the most popular topics among the articles submitted and published in Science of the Total Environment over the last few years. This Virtual Special Issue compiles 18 articles published in our journal on this topic since 2012. It is worth briefly summarizing the rich scientific insights brought by these articles, as well as broader considerations, particularly those extending to management, discussed by the authors of the articles.

Coastal environmental gradients – Key to reproduction habitat mapping of freshwater fish in the Baltic Sea

Habitat requirements of fish are most strict during the early life stages, and the quality and quantity of reproduction habitats lays the basis for fish production. A considerable number of fish species in the northern Baltic Sea reproduce in the shallow coastal areas, which are also the most heavily exploited parts of the brackish marine area. However, the coastal fish reproduction habitats in the northern Baltic Sea are poorly known. The studies presented in this thesis focused on the influence of environmental conditions on the distribution of coastal reproduction habitats of freshwater fish. They were conducted in vegetated littoral zone along an exposure and salinity gradient extending from the innermost bays to the outer archipelago on the south-western and southern coasts of Finland, in the northern Baltic Sea. Special emphasis was placed on reed-covered Phragmites australis shores, which form a dominant vegetation type in several coastal archipelago areas. The main aims of this research were to (1) develop and test new survey and mapping methods, (2) investigate the environmental requirements that govern the reproduction of freshwater fish in the coastal area and (3) survey, map and model the distribution of the reproduction habitats of pike (Esox lucius) and roach (Rutilus rutilus). The white plate and scoop method with a standardized sampling time and effort was demonstrated to be a functional method for sampling the early life stages of fish in dense vegetation and shallow water. Reed-covered shores were shown to form especially important reproduction habitats for several freshwater fish species, such as pike, roach, other cyprinids and burbot, in the northern Baltic Sea. The reproduction habitats of pike were limited to sheltered reed- and moss-covered shores of the inner and middle archipelago, where suitable zooplankton prey were available and the influence of the open sea was low. The reproduction habitats of roach were even more limited and roach reproduction was successful only in the very sheltered reed-covered shores of the innermost bay areas, where salinity remained low (< 4‰) during the spawning season due to freshwater inflow. After identifying the critical factors restricting the reproduction of pike and roach, the spatial distribution of their reproduction habitats was successfully mapped and modelled along the environmental gradients using only a few environmental predictor variables. Reproduction habitat maps are a valuable tool promoting the sustainable use and management of exploited coastal areas and helping to maintain the sustainability of fish populations. However, the large environmental gradients and the extensiveness of the archipelago zone in the northern Baltic Sea demand an especially high spatial resolution of the coastal predictor variables. Therefore, the current lack of accurate large-scale, high-resolution spatial data gathered at exactly the right time is a considerable limitation for predictive modelling of shallow coastal waters.