The nonlinear evolution equation on the shallow water wave

Based on the variation principle, the nonlinear evolution model for the shallow water waves is established. The research shows the Duffing equation can be introduced to the evolution model of water wave with time.

A SINGULAR EXACT SOLUTION FOR NONLINEAR SHALLOW-WATER ON A ROTATING EARTH

In this paper, we present an exact solution for nonlinear shallow water on a rotating planet. It is a kind of solitary waves with always negative wave height and a celerity smaller than linear shallow water propagation speed square-root gh. In fact, it propagates with a speed equal to (1 + a/h) square-root gh(1 + a/h) where a is the negative wave height. The lowest point of the water surface is a singular point where the first order derivative has a discontinuity of the first kind. The horizontal scale of the wave has actually no connection with the water depth.

Intra-habitat heterogeneity of microbial food web structure under the regime of eutrophication and sediment resuspension in the large subtropical shallow Lake Taihu, China

Planktonic microbial community structure and classical food web were investigated in the large shallow eutrophic Lake Taihu (2338 km(2), mean depth 1.9 m) located in subtropical Southeast China. The water column of the lake was sampled biweekly at two sites located 22 km apart over a period of twelve month. Site 1 is under the regime of heavy eutrophication while Site 2 is governed by wind-driven sediment resuspension. Within-lake comparison indicates that phosphorus enrichment resulted in increased abundance of microbial components. However, the coupling between total phosphorus and abundance of microbial components was different between the two sites. Much stronger coupling was observed at Site 1 than at Site 2. The weak coupling at Site 2 was mainly caused by strong sediment resuspension, which limited growth of phytoplankton and, consequently, growth of bacterioplankton and other microbial components. High percentages of attached bacteria, which were strongly correlated with the biomass of phytoplankton, especially Microcystis spp., were found at Site 1 during summer and early autumn, but no such correlation was observed at Site 2. This potentially leads to differences in carbon flow through microbial food web at different locations. Overall, significant heterogeneity of microbial food web structure between the two sites was observed. Site-specific differences in nutrient enrichment (i.e. nitrogen and phosphorus) and sediment resuspension were identified as driving forces of the observed intra-habitat differences in food web structure.