The reactors of Taylor-Couette type are relatively recent application in the engineering processes field. The stability and the flow structure in this device are examined under the effect combined of the free surface and the fluid's height in annular space. The exploitation of the flow regimes is carried out according to the number of Taylor for various values of aspect ration Gamma. By means of ultrasonic velocimetry (UPV) we determine axial average velocity profile and the axial wavelength. We also carry out the spectral analysis by Fourier's fast transform of the fluctuations associated with the average velocity values in order to analyze the flow structure. We particularly aim for checking the presence or the absence of the azimuth wave according to the filling height and the rotational velocity imposed. We highlight the effects of free surface and aspect ratio on the conditions of appearance of the second instability ( wavy mode). The analysis of the fluctuation shows that the appearance of the azimuth wave regime (Wavy mode) is delayed when the aspect ration decreases. Below a critical value noted Gamma c = 10, the azimuth wave regime is not observed any more.