Abstract. A simple explicit numerical scheme is proposed for the solution of the GardnerOstrovsky equation ut + cux + αuux + α1u 2 ux + βuxxx x = γu which is also known as the extended rotation-modified Korteweg-de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth' rotation. Particular versions of this equation with zero some of coefficients, α, α1, β, or γ are also known in numerous applications. The proposed numerical scheme is a further development of the well-known finite-difference scheme earlier used for the solution of the KdV equation. The scheme is of the second order accuracy both on temporal and spatial variables. The stability analysis of the scheme is presented for infinitesimal perturbations. The conditions for the calculations with the appropriate accuracy have been found. Examples of calculations with the periodic boundary conditions are presented to illustrate the robustness of the proposed scheme.
The adiabatic decay of different types of internal wave solitons caused by the Earth's rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions: (u + c u + α u u + α u u + β u) = γ u. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth's rotation described by the parameter γ. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity α (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity α determines only a polarity of solitary wave when α < 0 or the asymmetry of solitary waves of opposite polarity when α > 0. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when α is negative, are structurally unstable. Under the influence of Earth's rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.
Monitoring of water sources is a major concern worldwide. Wireless sensor networks (WSN) may be used for this monitoring. However, current systems employ mainly physical sensors for variables such as temperature, pressure, humidity and light. Wireless chemical sensors networks (WCSNs) for environmental monitoring are scarce due to the lack of autonomy of conventional sensors. This paper presents results of a WCSN for monitoring pH based on ion selective field effect transistors (ISFETs). Sensing nodes employ a human interface required for in situ calibration of chemical sensors. Unlike most studies, our work evaluates the network employing chemical measurements and wireless network metrics. Results show zero packet losses by using a time division multiple access (TDMA) protocol. The network allows wireless communication within 300 m including attenuation from buildings and trees. Therefore, the system presented in this paper is suitable for long range applications with unobstructed line of sight. pH measurements present a standard deviation below 1%, showing high repeatability. When compared to a commercial pH meter, difference in measurements is below 5%. As a consequence, accuracy is adequate for the application. Measurements also presented high stability during 3 h of continuous measurement.
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