Structure of bubble plumes in linearly stratified environments

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Abstract
Bubble plumes in a linearly stratified ambient fluid are studied. Four well-defined flow regions were observed: an upward-moving bubble core, an inner plume consisting of a mixture of bubbles and relatively dense fluid, an annular downdraught and beyond that a horizontal intrusion flow. Depending on the gas flow rate with respect to the stratification, three types of intrusions were documented. At large gas flow rates a single intrusion was observed. As the gas flow rate was decreased, the buoyancy flux was insufficient to carry the lower fluid to the surface and a stack of intrusions were formed. At very low gas flow rates the intrusions became unsteady. The transition between these three regimes was observed to occur at critical values of the parameters N3H4/(QBg), QBg/ (4πα2u3sH), and H/HT, where N is the buoyancy frequency, H is the water depth, HT is equal to H + HA, HA being the atmospheric pressure head, QB is the gas flow rate at the bottom, g the acceleration due to gravity, α the entrainment coefficient and us the differential between the bubble and the average water velocity commonly called the slip velocity. The height between intrusions was found to scale with the Ozmidov length (QBg/N3)¼, the plunge point entrainment with the inner plume volume flux ( and the radial distance to the plunge point with (Q0g/N3)¾, where Q0 is the gas flow rate at the free surface.These results were used to construct a double annular plume model which was used to investigate the efficiency of conversion of the input bubble energy to potential energy of the stratification; the efficiency was found to first increase, reach a maximum, then decrease with decreasing gas flow rate. This agreed well with the results from the laboratory experiments.

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