3 years ago

Approximate dispersion relations for waves on arbitrary shear flows.

Simen Å. Ellingsen, Yan Li

An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3D generalization of the much used approximation by Skop [1987], developed further by Kirby & Chen [1989], but is shown to be more robust, succeeding in situations where the Kirby & Chen model fails. The two approximations incur the same numerical cost and difficulty.

While the Kirby & Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability.

A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding 2nd order expression proposed by Kirby \& Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our 2nd order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby & Chen.

Publisher URL: http://arxiv.org/abs/1711.02914

DOI: arXiv:1711.02914v1

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.