Correlated internal waves in the nonlocal Ostrovsky equation

We derive a nonlocal Ostrovsky equation to describe two internal waves generated at distinct locations and times, together with their correlations and interactions. When the initial conditions are PT symmetry invariant, the internal waves can either exhibit cnoidal wave structures that are largely insensitive to rotational effect, or, in the case of solitary waves, evolve into nonlinear wave packets under rotation. In this scenario, the two waves possess antiphase amplitudes, resulting in a nodal surface of zero displacement at the middepth layer. In contrast, under the PT symmetry breaking initial conditions, the two internal waves develop snoidal waveforms, with rotation producing a pronounced asymmetry with two nonequivalent crest heights within each wave period. In this case, the two waves exhibit amplitude anticorrelation and phase lag, causing partial destructive interference. Furthermore, the results demonstrate that stronger rotation cannot only accelerate the attenuation of internal solitary waves, but also enhance the peak asymmetry of the snoidal waveforms, whereas introducing shear flow can partially mitigate rotational effect.