## 3 Results and Discussions
The interface deformation is convex from z = 0 to 0.5 and concave at z = 0.5 to 1. The degree of convexity and concaveness increases as the temperature difference increases. Because the near-hot end temperature of the system exceeds the near-cold end temperature, as well as the gas side pressure at the upper end surpassing the lower end's gas side pressure, the overall surface deformation is concave and convex from top to bottom, respectively. Moreover, the conversion process between surface flow and volume reflow of the system will accelerate with an increase in the temperature differential. The internal disturbance of the liquid bridge will intensify, resulting in a rise in the convexity and concavity of the interface with the augmentation of the temperature differential. Figure 7a exhibits the oscillation distribution of the transverse velocity at the upper monitoring point \"a\" for various temperature differences. The location of the monitoring point is listed in Figure 1, and the coordinate is (\(R\), 0.9\(H\)). Figure 7b shows the power spectral density (PSD) of transverse velocity. As shown in Figure 7a, the transverse velocity oscillation at the upper monitoring point is approximately a small amplitude sinusoidal oscillation when the temperature differential is small in the yellow portion. The mean values of transverse velocity are \(-\)0.0025, \(-\)0.00276, and \(-\)0.00294, respectively. The amplitudes are 2.5 \(\times\) 10\({}^{-5}\), 3.4 \(\times\) 10\({}^{-5}\), and 4.0 \(\times\) 10\({}^{-5}\), respectively. The amplitude magnifies as the temperature increases. Furthermore, the magnitude of the velocity oscillation escalates from 10\({}^{-5}\) to 10\({}^{-3}\) when the temperature difference rises to 6. The oscillation is converted into a large amplitude pulsation oscillation. The oscillation amplitude is large and irregular. As listed in Figure 7b, the oscillation power density (in the yellow portion) at small temperature differences slowly increases as the temperature difference rises, ranging from 7.5 \(\times\) 10\({}^{-9}\) to  
Figure 5: (**a**) Variation of transverse velocity on right free surface; (**b**) variation of longitudinal velocity on right free surface (\(R\) = 5 mm, \(Ar\) = 1.0, \(Pr\) = 5.54, \(Le\) = 25.8, \(Ca_{C}\) = \(-\)0.021, \(\rho_{l}/\rho_{g}\) = 597.9). \(3.9\times 10^{-8}\). For sinusoidal oscillations under small temperature difference conditions, there is only one fundamental frequency in the corresponding PSD diagram. The frequencies are \(f_{1}=0.16,f_{2}=0.17\), and \(f_{3}=0.13\), respectively. Therefore, the oscillation under small temperature difference is a single-periodic oscillation. As for oscillations under a large temperature difference, there are multiple dominant frequencies, including \(f_{4}=0.014\), \(f_{5}=0.035,f_{6}=0.1,f_{7}=0.11\), and \(f_{8}=0.21\). In the main frequency, the power density of the oscillation is between \(1.2\times 10^{-5}\) and \(2.0\times 10^{-5}\). These five frequencies are independent to each other, so the pulsating oscillation under large temperature differences is a multi-periodic oscillation. Figure 6: Deformation trend of right free surface (\(R=5\) mm, \(Ar=1.0\), \(Pr=5.54\), \(Le=25.8\), \(Ca_{C}=-0.021\), \(\rho_{l}/\rho_{g}=597.9\)). Figure 7: (a) Oscillation of transverse velocity at monitoring point “a” under different temperature difference conditions; (b) power spectrum density of transverse velocity (\(R=5\) mm, \(Ar=1.0\), \(Pr=5.54\), \(Le=25.8\), \(Ca_{C}=-0.021\), \(\rho_{l}/\rho_{g}=597.9\)). Figure 8a exhibits the oscillation distribution of the longitudinal velocity of the upper monitoring point \"a\" under different temperature difference conditions, and Figure 8b is the PSD of longitudinal velocity. Figure 8a shows that the longitudinal velocity exhibits a small amplitude pulsation oscillation characteristic under the small temperature difference condition, and the oscillation exhibits a regular parabolic shape.