Spontaneous and artificial void wave propagation beneath a flat-bottom model ship

Although the practical use of bubbly drag reduction for marine vessels has begun to spread, it is unclear how bubbles migrate along spatially developing turbulent boundary layers. We measured the spatiotemporal distribution of the local void fraction beneath a 4-m-long fully transparent flat-bottom model ship towed in a 100-m-long water tank with a ship speed of up to 3.00 m/s. Bubbles were injected with both constant and periodically fluctuated air flow rates into the turbulent boundary layers. With constant flow rates, 2-5-mm bubbles caused spontaneous void waves, i.e., quasiperiodic fluctuation of the local void fraction, standing at 4-8 Hz. When repetitive bubble injection, which formed artificial void waves downstream, was applied, void waves propagated at 47%-53% of the ship speed. During the propagation, we found the apparent diffusion coefficient of the void wave taking values down to 10(-4) m(2)/s and even negative values when the repetition frequency was set lower than the spontaneous frequency of void waves. This indicates that the void waves persist for several tens of meter in application to ship hulls.