Modelling of geomagnetic induction in pipelines

International audienceGeomagnetic field variations induce telluric currents in pipelines, which modify the electrochemical conditions at the pipe/soil interface, possibly contributing to corrosion of the pipeline steel. Modelling of geomagnetic induction in pipelines can be accomplished by combining several techniques. Starting with geomagnetic field data, the geoelectric fields in the absence of the pipeline were calculated using the surface impedance derived from a layered-Earth conductivity model. The influence of the pipeline on the electric fields was then examined using an infinitely long cylinder (ILC) model. Pipe-to-soil potentials produced by the electric field induced in the pipeline were calculated using a distributed source transmission line (DSTL) model. The geomagnetic induction process is frequency dependent; therefore, the calculations are best performed in the frequency domain, using a Fourier transform to go from the original time domain magnetic data, and an inverse Fourier transform at the end of the process, to obtain the pipe-to-soil potential variation in the time domain. Examples of the model calculations are presented and compared to observations made on a long pipeline in the auroral zone

Solitary flexural–gravity waves in three dimensions

The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369, 2942–2956 (doi:10.1098/rsta.2011.0104)). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations. This article is part of the theme issue ‘Modelling of sea-ice phenomena’

Stability of periodic traveling flexural‐gravity waves in two dimensions

In this work, we solve the Euler’s equations for periodic waves travelling under a sheet of ice using a reformulation introduced in [1]. These waves are referred to as flexural-gravity waves. We compare and contrast two models for the effect of the ice: a linear model and a nonlinear model. The benefit of this reformulation is that it facilitates the asymptotic analysis. We use it to derive the nonlinear Schrödinger equation that describes the modulational instability of periodic travelling waves. We compare this asymptotic result with the numerical computation of stability using the Fourier-Floquet-Hill method to show they agree qualitatively. We show that different models have different stability regimes for large values of the flexural rigidity parameter. Numerical computations are also used to analyse high frequency instabilities in addition to the modulational instability. In the regions examined, these are shown to be the same regardless of the model representing ice