Derivations: Linear, Weakly Nonlinear, and Conjugate Flow Theory
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Publisher
Springer International Publishing
Link
https://link.springer.com/content/pdf/10.1007/978-3-030-99210-1_2
Reference5 articles.
1. K. G. Lamb and L. Yan (1996) The evolution of internal wave undular bores: comparisons of a fully nonlinear numerical model with weakly-nonlinear theory, J. Phys. Oceanogr., 26, 2712. This paper presents the version of weakly nonlinear theory (WNL) that I am following (with a minor switch of notation) in the above chapter. The paper also does something that many WNL papers do not; it compares with a simulation. Not surprisingly it finds that WNL is not great as a quantitative tool.
2. J. A. Gear and R. Grimshaw (1983) A second-order theory for solitary waves in shallow fluids, Phys. Fluids, 26, 14. Roger Grimshaw (with various co-workers) has covered every possible take on WNL. I chose an older paper to include here because it shows clearly the difficulty in algebra of extending to higher order.
3. Lamb, K.G., Wan, B. (1998) Conjugate flows and flat solitary waves for a continuously stratified fluid, Phys. Fluids, 10(8), 2061–2079. While the concept of conjugate flow goes back to the work of Benjamin in the 1960s, this paper provides a clear derivation in a manner that exposes the link to internal solitary waves (ISWs). It was also the first to compare flat crested ISWs to conjugate flows.
4. M. Stastna and K. G. Lamb, (2002) Large fully nonlinear internal solitary waves: The effect of background current, Phys. Fluids, 14, 2987. This paper presents the WNL with a background current (many others have done this), but more importantly demonstrates how the presence of a background shear changes exact internal solitary waves. As such I choose to list it since I can point to it for further topics in subsequent Chapters.
5. Barros, R., Choi, W., Milewski, P.A. (2019) Strongly nonlinear effects on internal solitary waves in three-layer flows, J. Fluid Mech., 883, A16-1–16–36. This paper too will find its way into the discussion in a subsequent Chapter. I include it here to illustrate the so–called MCC theory, which extends the KdV theory discussed in this chapter for the case of layered fluids, and as such has strong proponents. I have always found its algebra heavy nature to be a price of entry that is too high for my tastes.
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