# Numerical Simulation of the Force Acting on the Riser by Two Internal Solitary Waves
###### Abstract
The internal wave observation method in the nearshore area has been constantly innovated [11]. Some scholars have confirmed that the pressure gradient in the nearshore basin is very important to the internal wave propagation through the influence of the single point model and the idealized cross-section model on the generation of internal waves and the front on the edge of the continental shelf [12; 13]. After that, some scholars studied the changes in wave velocity and energy conversion on the edge of the continental shelf through acoustic and microscopic data and infrared heat conduction maps. Through the combination of field observation and numerical simulation, some scholars have studied the dynamic characteristics of internal waves in tropical reservoirs with two basin structures in different flood seasons [14]. The results show that the internal waves in the basin are generated by the natural oscillation of wind, and the amplitude of internal waves in the two basins is different due to the different oscillation frequencies. The study of internal waves on the resuspension of sediment at the bottom of the boundary, sediment transport, and boundary layer mixing is also a research focus [15]. A 2014 environmental assessment report in the waters of Gibraltar noted that the vertical mixing of ocean currents depends on the interaction of internal tides and short-period internal waves [16]. Internal wave motion and the collision process have also been described in detail; [PERSON] and [PERSON] pointed out that the mixing of background media appears at the stratification and bottom boundary of the watershed driven by turbulence and proposed that with the enhancement of the nonlinearity of an internal solitary wave, the requirements for accuracy in its simulation also increase greatly [17; 18]. Steady stratified flow through hills with a Gaussian shape is also a focus in the field of environmental hydrodynamics. Some scholars use the high-resolution finite-difference numerical method to study Lee waves passing through smooth axisymmetric hills and discuss the effects of the Reynolds number and Froude number on the results [19]. Many theories and experiments have studied the causes of internal waves in the actual marine environment for a long time. Many experts and scholars have also conducted much tracking research on the occurrence of internal waves in different regions [20]. At present, many researchers have conducted extensive studies on the generation of solitary waves and their interaction with ocean structures [21]. A modified Morison equation that includes a convection term has shown that the force of a cylindrical structure could be better predicted by reducing the inertia coefficient and the resistance coefficient [22]. The large eddy simulation (LES) model can be used to study the force of internal solitary waves on a pair of cylinders arranged in series [23], which can then be used to understand internal solitary waves' effect on different cylinder diameters, their evolution process, and influence [24]. [PERSON]'s empirical formula and modal separation method estimate the force and torque exerted by internal solitons on cylindrical piles [25; 26]. The horizontal velocity and acceleration on the vertical wave profile can then be estimated to simulate the force and torque on the riser. The waveform of internally isolated waves will change to different degrees after passing through a sloping topography with a certain angle. [PERSON] et al. first applied the Reynolds number of internally isolated waves (\(\text{Re}_{\text{ISW}}\)) to collapsing and plunging breakers and demonstrated that the density ratio of flow field stratification has less effect on waveform breaking [27]. Another study characterizes the evolution of internal isolated waves over slope terrain with different parameters such as slope and initial wave amplitude, and the results show that the wave amplitude increases and then decreases during the propagation process, and the maximum wave amplitude is at the shoulder of the slope [28].