## 3 Results and Discussions
The time interval for each parabolic shape is approximately 40 when the temperature difference is 2. The time interval for each parabolic shape is approximately 32 when the temperature difference is 3. The fact that the longitudinal velocities at different temperature differences are all positive suggests the presence of a unidirectional flow of fluid from the lower plate to the upper plate. The mean values of longitudinal velocity are 0.00131, 0.00164, and 0.00191, respectively. The amplitudes are \(1.3\times 10^{-5}\), \(1.5\times 10^{-5}\), and \(1.6\times 10^{-5}\), respectively. The amplitude increases as the temperature difference rises. The average speed is 0.00224 when the temperature difference rises to 6. The amplitude increases exponentially, and the oscillation becomes a large amplitude pulsating oscillation. Because the upper monitoring point is in the active zone, the surface reflux intensifies the flow as the temperature difference rises, leading to an increase in the amplitude of longitudinal velocity. The oscillation evolves into a large amplitude pulsating oscillation when the surface flow accelerates to a certain extent. It can be found from Figure 8b that the spectrum of the small temperature difference has two main frequencies. The two corresponding fluctuations in the spectrum are independent of each other. Smaller fluctuations correspond to low-frequency oscillations, while larger fluctuations correspond to high-frequency oscillations. The small-amplitude pulsation oscillation at this time is the double-periodic oscillation. The oscillation energy also has little difference under different temperature differences, with power spectral densities ranging from \(2.6\times 10^{-10}\) to \(2.7\times 10^{-10}\), from \(1.3\times 10^{-9}\) to \(2.2\times 10^{-9}\), and from \(9.7\times 10^{-10}\) to \(2.0\times 10^{-9}\), respectively. Multiple main frequencies appear in the spectrogram under large temperature differences, including \(f_{7}=0.033,f_{8}=0.04,f_{9}=0.19\), and \(f_{10}=0.2\). In the main frequency, the power density of the oscillation is between \(2.1\times 10^{-6}\) and \(3.0\times 10^{-6}\). At present, the oscillation is characterized by the occurrence of multiple periodicities. Compared with the transverse velocity in Figure 7, the oscillations in the longitudinal velocity display a double-periodic oscillation under small temperature differences, which is different from the single-periodic oscillation of the transverse velocity. However, they are all multi-periodic oscillation under large temperature differences. Meanwhile, the power of the longitudinal velocity is smaller than the power of the transverse velocity, indicating that the velocity in the active region of the hot corner changes relatively strongly in the transverse direction. Figure 9a shows the transverse velocity oscillation distribution of the monitoring point \"b\" under various temperature differences. The coordinate of the monitoring point is (\(R\), \(0.5H\)) which is in the middle position of the right interface. Figure 9b is the PSD of transverse velocity. As listed in Figure 9a, under conditions of minimal temperature variation, the average values of velocity are \(-0.000129\), \(-0.000176\), and \(-0.000238\), respectively. The amplitudes are \(2.5\times 10^{-6}\), \(1.2\times 10^{-6}\), and \(1.8\times 10^{-6}\), respectively. The amplitude also magnifies as the temperature difference rises. The oscillation curve gradually transforms to a regular large-amplitude oscillation from a small-amplitude pulsating oscillation as the temperature difference increases. This time interval of regular oscillation is approximately 64. The oscillation enters the large-amplitude pulsation phase when the temperature difference increases to 66. Because the intermediate position of the interface is closer to the vortex core, the transverse velocity oscillation is affected by the micro-scale lateral migration of the vortex core as the temperature difference increases.