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Internal waves in a shear background current: Transition from solitary-wave regime to dispersive-wave regime
Phys. Rev. Fluids 4, 094801 – Published 11 September, 2019
DOI: https://doi.org/10.1103/PhysRevFluids.4.094801
Abstract
Nonlinear internal waves propagating in a quasi-two-layer stratification with a shear background current are investigated by means of high-resolution direct numerical simulations. The simulations are performed in a two-dimensional rectangular domain, representing a laboratory-scale tank of finite length. The internal waves are generated using the lock-release mechanism, while the background shear currents are induced by basin-scale internal seiches created using a tilted tank suddenly returned to the untilted configuration. Both mechanisms are readily realizable in a laboratory environment. Depending on the configuration of the initial density profile, both internal solitary-like waves (ISWs) and finite-amplitude dispersive wave trains (DWTs) may be observed in the simulations. The ISWs are observed when the pycnocline is located relatively far away from the middepth and/or the background shear is oriented against the wave-induced velocity shear. Comparison of the waveforms observed in the simulations to those described by the fully nonlinear Dubreil-Jacotin–Long (DJL) theory suggests that these waves are indeed solitary-like, implying that laboratory experiments of ISWs propagating in a shear background current can be realized in a relatively straightforward manner. As the pycnocline approaches the middepth and/or the background shear reverses its polarity and increases its magnitude, the waves tend to have a smaller amplitude and a larger half-width. When a wave's amplitude is less than approximately 3% of its half-width, the dispersive effect becomes dominant and the wave loses its solitary-like form. In this case, a finite-amplitude DWT is formed instead, in which the leading wave has a reduced propagation speed from the ISW propagation speed. Analysis based on the DJL theory suggests that exact solitary waves of similar amplitude in such a background environment have an extremely large half-width that is on the same order of magnitude as the finite length of the simulation domain, implying that their formation cannot be supported in a laboratory environment.
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