@article{Hooi_Tiong_Tay_Chiew_Sze_2018, title={Numerical Simulation of Shoaling Internal Solitary Waves in Two-layer Fluid Flow}, volume={34}, url={https://matematika.utm.my/index.php/matematika/article/view/1000}, DOI={10.11113/matematika.v34.n2.1000}, abstractNote={<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p>In this paper, we look at the propagation of internal solitary waves over<br />three different types of slowly varying region, i.e. a slowly increasing slope, a smooth<br />bump and a parabolic mound in a two-layer fluid flow. The appropriate mathematical<br />model for this problem is the variable-coefficient extended Korteweg-de Vries equation.<br />The governing equation is then solved numerically using the method of lines. Our<br />numerical simulations show that the internal solitary waves deforms adiabatically on<br />the slowly increasing slope. At the same time, a trailing shelf is generated as the<br />internal solitary wave propagates over the slope, which would then decompose into<br />secondary solitary waves or a wavetrain. On the other hand, when internal solitary<br />waves propagate over a smooth bump or a parabolic mound, a trailing shelf of negative<br />polarity would be generated as the results of the interaction of the internal solitary<br />wave with the decreasing slope of the bump or the parabolic mound. The secondary<br />solitary waves is observed to be climbing the negative trailing shelf.</p></div></div></div>}, number={2}, journal={MATEMATIKA}, author={Hooi, Mun Hoe and Tiong, Wei King and Tay, Kim Gaik and Chiew, Kang Leng and Sze, San Nah}, year={2018}, month={Dec.}, pages={333–350} }