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

Enhancing student learning and engagement of scientific concepts through case studies in integrated science

Context-based learning activities, such as case studies, that bring to light the relevance of science increase student engagement, improve student performance, and attract students to study science at the university level. Meanwhile, integrated science education is based on an approach that emphasizes the interconnectedness of scientific fields, such as astronomy, chemistry, physics, biology, Earth sciences, and computer science. By incorporating case studies in integrated science courses, students are provided with real-world scenarios that enable them to explore the interdisciplinary nature of science while acquiring a deeper understanding of foundational scientific concepts and their application to real-world situations. These case studies foster active and collaborative learning, helping students develop their problem-solving and critical thinking skills by analyzing and interpreting data from multiple scientific perspectives. Furthermore, this approach can stimulate students to formulate innovative solutions to problems, enhancing their creativity and scientific curiosity. Overall, an integrated science approach that centers on case studies creates a more engaging and effective learning environment that can lead to improved outcomes in science education. This presentation discusses the implementation of this approach at the university level and provides practical ideas on its implementation

Stability of periodic travelling wave solutions to Korteweg-de Vries and related equations

In this talk, we explore the simplest equation that exhibits high frequency instabilities, the fifth-order Korteweg-de Vries equation. We show how to derive the necessary condition for an instability of a perturbation of a small amplitude, periodic travelling wave solutions. We proceed by examining how these unstable perturbations change and grow in time as the underlying solution changes. We conclude by commenting on what happens with a different nonlinearity in the underlying equation.Non UBCUnreviewedAuthor affiliation: University of WashingtonPostdoctora