Pendekatan matematis pada pembangkitan gelombang internal di Selat Makassar

Abstract

In Makassar strait, which is located between the islands of Kalimantan and Sulawesi, the fascinating phenomena of internal waves can be observed. Internal waves are gravity waves that oscillate within, rather than on the surface of, a fluid medium. Internal waves occur in the interior of water in seas, which exist due to a difference in density of the lower and upper layer of the fluid. Typical characteristics of internal waves are their large wavelength and amplitude. This research aims to derive a dispersion relation based on the basic equations of two-layers fluid, to determine the internal waves in the Makassar Strait, and to create a simulation of generation of the internal waves using the software Mathematica. The results show that the generation mechanism of these internal waves can be formulated based on the Kelvin-Helmholtz dispersion relation for a two-layers fluid. This dispersion relation can also be used as classification criteria of instability of internal waves. Emphasis is given to the types of instability, i.e. temporal and spatial instability. Temporal stability occurs if current velocity in the upper part of fluid is less than its critical velocity. For the spatial instability, internal waves in Makassar strait can be approximated for both layers as deep water waves. The spatially stable region is reached when the frequency of the lower part of fluid is smaller than the critical frequency, or when the frequency of the upper part of fluid is larger than the critical frequency.