Tide level in time and frequency domains at Dili port: Characteristic feature of a Lorentz oscillator

Abstract

Tide level during one year in time-domain measured at Dili port (East Timor) is analyzed by the frequency spectrum with the Fast Fourier Transform (FFT), together with the autocorrelation function (AF). The frequency spectrum shows a characteristic feature of the Lorentz-type resonance (Lorentz oscillator) with the special peaks which are attributed to the major tide constituents related to the gravitational motions of the sun and the moon. The Lorentz-type resonance occurs in water fluid systems under the periodic change in gravitational potential, which is similar to the electronic polarization under an electric potential change. The 1/f characteristics found at high frequencies in the power spectrum (the so-called 1/f characteristics in frequency domain) can be originated only from the gravitational effect, while its origin is usually discussed in terms of meteorology such as atmospheric pressure.

Statistical and spectral analysis of wind power: Fractional oscillation dynamics

“…We hence ignore the 2nd peak in the present analysis. Interestingly, the feature of 1/f α (α ~ 2) at high frequencies has been found in the tidal-height spectrum at Dili port (Belo et al 2021).…”

“…The a-value and its functional origin will be discussed later. At lower frequencies, the spectrum shows a constant, which is often called a low pass filter (Belo et al 2021). At around 10 -5 Hz, a peak is observed, which corresponds to 1-day period.…”

“…Note in the tide dynamics that the power spectrum of tide in Dili port follows just 1/f at high frequencies, which is completely different from the present wind case. The tide dynamics is dominated only by the gravitational effect without involving the meteorological one (Belo et al 2021).…”

“…It is discussed that the physical origin of the parameter a lies in the fractional dynamics of wind power, which leads to the Cole-Davidson type relaxation (Nigmatullin, Ryabov 1997). This is different from the dynamics of tide (Belo et al 2021), in which a Lorentz-type relaxation is found in the frequency domain.…”

“…In the present paper, as a series report of the tide dynamics (Belo et al 2021), by using a small-size wind generator, we elucidate the nature of wind power at the Hera campus, Universidade Nacional Timor Lorosa'e, East Timor (8.55° S, 125.56° E). The wind speed variations throughout three months (June to September 2019) will be characterised in terms of a histogram, a probability distribution, and a power spectrum through the Fast Fourier Transform (FFT).…”