The goal of this paper is to construct a first-order upwind schemefor solving the system of partial differential equations governing theone-dimensional flow of two superposed immiscible layers of shallow waterfluids. This is done by generalizing a numerical scheme presented byBermúdez and Vázquez-Cendón [3, 6, 27] for solving one-layer shallow water equations, consisting in a Q-scheme with a suitable treatment of the source terms.The difficulty in the two layer system comes from the coupling terms involving some derivatives of the unknowns.Due to these terms, a numerical scheme obtained by performing the upwinding of each layer, independently from the other one, can be unconditionally unstable.In order to define a suitable numerical scheme with global upwinding,we first consider an abstract system that generalizes the problem under study.This system is not a system of conservation laws but, nevertheless,Roe's method can be applied to obtain an upwind scheme based on Approximate Riemann State Solvers. Following this, we present some numerical tests to validate the resulting schemes and to highlight the fact that, in general, numerical schemes obtained by applying a Q-scheme to each separate conservation law of the system do not yield good results. First, a simple system of coupled Burgers' equations is considered. Then, the Q-scheme obtained is applied to the two-layer shallow water system.

To ensure integrity of the Loran-C radionavigation system during non-precision approaches, an automatic blinking system notifies the user when the system is not functioning within specifications. To be certain that timely detection of this blinking can be guaranteed, one of the requirements imposed on an airborne Loran-C receiver is that it should flag an alert when the signal to noise ratio drops below –6 . This paper addresses some blinking detection methods, that will ensure safe operation beyond this –6 dB limit. A preliminary version of this article was presented at the Wild Goose Conference in Birmingham, August 1992.

In 1987 a special meeting of IALA held at Trinity House in London expressed a common purpose to enhance and expand existing Loran-C coverage in North-West Europe and the North Atlantic. After two years of negotiation, agreement was finally reached in January of this year to proceed with the project. The countries involved are Canada, France, Germany, Iceland, Ireland, Netherlands, Norway and the United Kingdom, with cooperation from the United States and Denmark. They will re-equip six existing United States Coast Guard stations and use two French stations together with four new transmitters to provide four chains, covering the whole of NW Europe and most of the North Atlantic.

This, and the following five papers, are a selection from those presented at the RIN91 Conference on Small Craft Navigation. The Conference was held at the Warsash Campus, Southampton, over the weekend 6–7 April 1991. Copies of thecomplete proceedings are available from the Director, price £30 to non-members and £20 to members (exc. postage and packing).

This paper is the fourth chapter of a series on Air Navigation Systems during theperiod from the early oceanic flights and the inception of commercial aviation to the introduction of INS in civil aircraft. Comments on the content of the paper would be welcomed by the author and the editor.