Internal solitary waves with different density distribution approximation schemes in background shear currents

The density distribution scheme determines the characteristics of internal solitary waves (ISWs). Based on three typical density distributions, ISWs are modeled in two-layer, three-layer, and continuous-density systems, while also considering the effect of background shear currents. ISWs are generated using high-level Green–Naghdi (HLGN) and Dubreil-Jacotin-Long (DJL) theories, which serve as initial conditions for the computational fluid dynamics (CFD) flume. In all systems, linear background shear currents can significantly affect the ISW properties, such as wave profiles, induced velocity, propagation speed, and energy distribution. Positive-vorticity background shear currents pycnocline thinning, whereas negative-vorticity currents result in thickening. The ISW shear strength is evaluated by the average rate of change of horizontal velocity at the pycnocline. In the two-layer system, positive-vorticity currents reduce the ISW shear effect, whereas the opposite occurs with negative-vorticity currents. The conclusions for the three-layer and continuous-density systems are in contrast to those of the two-layer system. This indicates that consideration or neglect of the pycnocline thickness may lead to opposite conclusions regarding the effects of background shear currents on the ISW shear effect. Furthermore, the influence of the nonlinear background shear currents is discussed. For most properties, the effects of nonlinear currents are consistent with those of linear currents, although they are generally weak.