Reproducibility Limits of the Frequency Equation for Estimating Long-Linear Internal Wave Periods in Lake Biwa - Hibiki Yoneda; Chunmeng Jiao; Keisuke Nakayama; Hiroki Matsumoto; Kazuhide Hayakawa (Hydrology, 2025)
In a large deep lake, the generation of internal Kelvin waves and internal Poincaré waves due to wind stress on the lake surface is a significant phenomenon. These internal waves play a crucial role in material transport within the lake and have profound effects on its ecosystem and environment. Our study, which investigated the modes of internal waves in Lake Biwa using the vertical temperature distribution from field observations, has yielded important findings. We have demonstrated the applicability of the frequency equation solutions, considering the Coriolis force. The period of the internal Poincaré waves, as observed in the field, was found to match the solutions of the frequency equation. For example, observational data collected in late October revealed excellent agreement with the theoretical solutions derived from the frequency equation, showing periods of 14.7 h, 11.8 h, 8.2 h, and 6.3 h compared to the theoretical values of 14.4 h, 11.7 h, 8.5 h, and 6.1 h, respectively. However, the periods of the internal Kelvin waves in the field observation results were longer than those of the theoretical solutions. The Modified Mathew function uses a series expansion around <semantics>qi=0</semantics>, making it difficult to estimate the periods of internal Kelvin waves under conditions where <semantics><mfenced close="|" open="|">qi</mfenced>>1.0</semantics>. Furthermore, in lakes with an elliptical shape, such as Lake Biwa, the elliptical cylinder showed better reproducibility than the circular cylinder. These findings have significant implications for the rapid estimation of internal wave periods using the frequency equation.