Internal solitary waves (ISWs) are high-frequency internal waves characterized by a balance between nonlinearity and dispersion. Mooring observations indicate that the durations experienced by internal solitary waves before and after passing wave crests (or troughs) differ substantially, indicating that both the waveform and frequency of ISWs exhibit asymmetric characteristics. Based on the theoretical solution of the KdV equation for the surface displacement of internal solitary waves, this study introduces an exponential function to accommodate the asymmetric features of wave profiles. An asymmetric bell-shaped function is adopted to fit ten individual solitary waves within the internal solitary wave train captured at the Lufeng mooring station on the morning of September 9, 2020. Using the fitted waveform function, we analyze the influences of the exponential term on the asymmetries of key ISW parameters including amplitude and frequency. Furthermore, by comparing the phase correspondence of sinusoidal waves with wave profiles, the concept of instantaneous frequency is introduced for asymmetric internal solitary waves. The instantaneous frequency of the ISWs as they propagate past the observation site is subsequently calculated. It effectively characterizes frequency variations before and after the wave crest (or trough), consistent with the intrinsic nature of ISWs as non-monochromatic waves. Finally, the study confirms that ISW frequency is constrained by the buoyancy frequency, with the maximum frequency near the pycnocline being approximately 0.1 cycles per minute.
 

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