Conditional Phase-lock Averaged Mode of Burst in Turbulent Boundary Layer over Superhydrophobic Surface

Multi-scale wavelet analysis along the longitudinal direction was conducted on the large-sample-size time series of instantaneous velocity fields of the turbulent boundary layer over a smooth hydrophilic surface, an isotropic and an anisotropic superhydrophobic surface respectively measured by Time-Resolved Particle Image Velocimetry(TRPIV), and the distribution of turbulent fluctuating kinetic energy with different longitudinal spatial scales and different normal coordinates was obtained. It was found that the isotropic and anisotropic superhydrophobic surface significantly suppressed the kinetic energy of turbulent fluctuation at all scales. The two types of burst events of the coherent structure were detected respectively by using the positive maxima and negative minima of the wavelet coefficients at each scale. The conditional phase-locked averaged modes of the streamwise fluctuating velocity, normal-wall fluctuating velocity and spanwise fluctuating vorticity of the two burst events were obtained by the conditional phase-locking averaging method at the same scale. It was found that the phase averaged modes of the streamwise and wall-normal fluctuating velocities of the two bursts conformed to the shear layer characteristics of the eject-sweep and swept-eject modes. The phase-locked averaged mode of the fluctuating vorticity corresponded to the structural feature of a quadrupole vortex packet with alternating positive and negative distributions in the streamwise and wall-normal directions, and its streamlines were manifested as a dynamic system of saddle point-focus. Isotropic and anisotropic superhydrophobic surfaces can significantly suppress the burst intensity of coherent structures at various scales.