Basin Mode Waves in a Rotating, Cylindrical, Water Tank

Abstract

Basin modes, standing waves excited by wind and storms, are possible in every body of water. The frequency and shape of basin mode waves depends on the size, depth, shape, and latitude of the body of water. In small lakes, basin mode waves have short periods of less than an hour. The latitude of the lake has little effect because the scale of the lake is not large enough for the Coriolis force to alter its behavior. In oceans, the period of these waves can exceed a day, and the propagation of waves is dramatically altered by the Coriolis force. For large lakes, such as Lake Superior or Lake Victoria (in Africa), little is known about the nature of the basin mode waves because the scale of these lakes is large enough that the Coriolis Force has an effect, but not so large that they behave as oceans. To understand these waves, I applied analytical and numerical techniques to determine the normal modes in the simplified system of a cylindrical, rotating, water tank. The solution is a Bessel function of tank radius multiplied by a sinusoid of the angle. There are an infinite number of solutions for each mode of Bessel function. After deriving and extending existing solutions, I compared the solutions to normal modes in a numerically modelled lake. I found great similarity between the predictions of linear theory, and the MIT General Circulation Model (MITgcm). The MITgcm replicated a number of the normal modes and approximately matched modal frequencies. The MITgcm also exhibited a Kelvin wave.