A MOMENTUM CONSERVING SCHEME FOR 2-LAYER SHALLOW WATER FLOWS THROUGH CHANNELS WITH IRREGULAR GEOMETRY WITH STUDY CASE MAXIMAL EXCHANGE SOLUTIONS IN THE LOMBOK STRAIT - Veri Swastika, Putu
Internal waves, as opposed to free-surface waves, appear within ocean bodies of varying fluid densities. Lombok Strait is an ideal location for the formation of internal waves due to its complex topography and geometry, stratified fluid, and strong tidal currents. Internal waves in real straits have been reported in the literature, some of which are triggered by tidal waves. These tidal waves will produce exchange flows closely related to internal waves. This exchange flow deforms the interface, which further propagates into internal wave packets. The presence of internal waves is accompanied by surface wave ripples which are detected through SAR images as regular dark and light patterns. Internal wave propagation transports a significant amount of energy and water volume so that it can endanger offshore construction, as well as marine transportation. Until recently, there has been limited research on the current exchange flow in Lombok Strait in the literature. Therefore, it is critical to investigate the steady-state interface caused by the current exchange in the Lombok Strait area first. The main contribution of this research is the development of a numerical model for modelling and simulation of the exchange flow in the Lombok Strait. Here, the Lombok Strait is modelled as a one-dimensional channel with rectangular cross-sections of varying depth and width. The channel under consideration has a sill, a contraction (narrowing), or both. The fluid is assumed to just have two layers of constant density, and free surface deformation is taken into account; the Saint-Venant equations for a 2-layer shallow flow are used here, implying that our approach is hydrostatic. The numerical implementation of the Saint-Venant model is carried out using the MCS (momentum-conserving staggered grid) scheme, which adheres to the momentum balance principle and is applied to a staggered grid. The MCS scheme is validated here by simulating various steady-state solutions, including maximal and submaximal exchange flows, using proper boundary conditions. The simulation results agree well with the analytical solutions, indicating the robustness of the scheme. The scheme is modified to account for external force in the form of a harmonic function with two parameters, namely the amplitude and period of the tidal wave. The barotropic external force is implemented directly via boundary conditions in the two-layer flow model. On a hypothetical channel, various simulations of steady-state conditions under the influence of barotropic forces were performed. Our simulation results are consistent with the quasisteady and time-dependent theories, and a comparison with another rigid-lid numerical model revealed quantitative agreement. The next study will examine the phenomenon of the steady-state interface of the maximal exchange flow in the Lombok Strait. Bathymetry data from the Lombok Strait were used to create a 1-dimensional channel model (a Lombok Strait Model). Following that, a steady interface of maximal exchange flow is simulated, and this steady state is used as the initial condition for simulating the effects of a semi-diurnal tidal wave in the Lombok Strait. Furthermore, as a result of tidal waves flowing over the sill and through the contraction, the process of internal wave formation in the strait area is simulated. Based on this calculation, we can estimate the volume of transport in the Lombok Strait.