High-order strongly nonlinear long wave approximation and solitary wave solution. Part 2. Internal waves
Document Type
Article
Publication Date
12-10-2022
Abstract
A strongly nonlinear long-wave approximation is adopted to obtain a high-order model for large-amplitude long internal waves in a two-layer system by assuming the water depth is much smaller than the typical wavelength. When truncated at the first order, the model can be reduced to the regularized strongly nonlinear model of Choi et al. (J. Fluid Mech., vol. 629, 2009, pp. 73–85), which lessens the Kelvin–Helmholtz instability excited by the tangential velocity jump across the interface in the inviscid Miyata–Choi–Camassa (MCC) equations. Using the second-order model, the next-order correction to the internal solitary wave solution of the MCC equations is found and its validity is examined with the Euler solution in terms of the wave profile, the effective wavelength and the velocity profile. It is shown that the correction greatly improves the comparison with the Euler solution for the whole range of wave amplitudes and no further correction is necessary for practical applications. Based on a local stability analysis, the region of stability for the second-order long-wave model is identified in the physical parameter space so that the efficient numerical scheme developed for the first-order model can be used for the second-order model.
Identifier
85143711720 (Scopus)
Publication Title
Journal of Fluid Mechanics
External Full Text Location
https://doi.org/10.1017/jfm.2022.950
e-ISSN
14697645
ISSN
00221120
Volume
952
Grant
DMS-2108524
Fund Ref
National Science Foundation
Recommended Citation
Choi, Wooyoung, "High-order strongly nonlinear long wave approximation and solitary wave solution. Part 2. Internal waves" (2022). Faculty Publications. 2409.
https://digitalcommons.njit.edu/fac_pubs/2409
