Turbulence Dissipation by the Oscillation of Microbubbles

With the objective of interfering with the Reynolds stress transfer of momentum to the sublayer, the loss factor is derived for turbulence dissipation by the resistive oscillation of microbubbles in the buffer layer region of a turbulent boundary layer in water. The rectilinear motion of a single bubble is examined under the influence of pressure gradients in its vicinity. It is presumed that both turbulence pressures and velocities can be represented by wavenumber-frequency spectra. Stokes drag is assumed for the bubble. The loss factor is found to be independent of the magnitudes of the fluctuating pressures and velocities. In addition to the spatial density of bubbles, the loss factor is found to depend only on a Reynolds number-like parameter involving the product of the frequency with the square of the bubble radius. The Reynolds parameter dependence has a form similar to that of a simple resonant response, although it is clear that no actual resonance is involved. With three diameters bubble spacing, the peak value of the loss factor is found to be approximately 2% at a parameter value of nine. The apparent bandwidth of the loss factor response is about one decade, suggesting that the phenomena is not “finely tuned”. For turbulence with typically large wavenumbers, very large spatial decay rates are suggested.