• Bush, J.W.M., Stone, H.A., and Bloxham, J., 1992. The Motion of an Inviscid Drop in a Bounded Rotating Fluid, Phys. Fluids A, 4 (6), 1142-1147. 

  •     The motion of a buoyant inviscid drop rising vertically along the rotation axis of a rapidly rotating low viscosity fluid bounded above and below by rigid horizontal boundaries is considered in the case that the drop is circumscribed by a Taylor column which spans the entire fluid depth. Both the shape and steady rise speed of the drop are deduced as a function of its interfacial tension.  The analysis demonstrates that the drop assumes the form of the prolate ellipsoidal figure of revolution which would  obtain in the absence of any relative motion in the surrounding fluid. The hydrodynamic drag on the drop follows simply from the analysis of Moore and Saffman, who considered the equivalent motion of a rigid particle. The rise speed of an inviscid drop is generally half that of an identically shaped rigid particle;  in particular, the rise speed of a spherical inviscid drop is 0.44 that of a rigid sphere. 

  • Woods, A.W. and Bush, J.W.M., 1999. The dimensions and dynamics of megaplumes, J. Geophys. Res., 104, 20495-20507. 

  •     We investigate the generation of megaplumes by the release of buoyant hydrothermal fluid from the seafloor. We show that   megaplumes   may be generated from  various modes of venting, including both the instantaneous and continuous release of hydrothermal effluent from either a point or  line source. The hydrothermal effluent forms a buoyant plume which rises through the water column to its neutral buoyancy height and then intrudes laterally to form a neutral cloud. Owing to the influence of the Earth's rotation, whose magnitude is omega = f / 2 , the neutral cloud eventually becomes unstable, giving rise to geostrophic  vortices that propagate away from the source. By combining the scaling laws governing turbulent plumes and geostrophic vortices, we establish new relationships between the megaplume geometry  and  the source  conditions. 
        We find that megaplumes whose radius greatly exceeds their height of rise are formed from sources which persist for at least several days, since, in the deep ocean, the radii of eddies produced by short lived releases of buoyant fluid are comparable to their rise height. Our model  predicts the total buoyancy, B,  of the hydrothermal effluent  released in forming such megaplume structures. For a maintained source, B ~ N2R2hH , where H is the height of the plume in the water column, R and h are the megaplume radius and half-depth and N is the Brunt-Vaisala frequency characterising the  oceanic stratification. Laboratory experiments suggest that the constant of proportionality depends on the geometry of the source and has a value of 0.8 for a linear source and 0.5 for a localised source. We also find that for a long-lived source of fluid, there is a maximum megaplume size, R = HN / f , and that the buoyancy contained within this maximal megaplume scales as B ~ H4N4 / f 2
        Finally, we calculate the total megaplume heat content  in terms of the total buoyancy release and the thermal anomaly of the megaplume, by considering the effects of the ambient stratification in both temperature and salinity on plume properties. Applying the model to data from three historic megaplume events at the Juan de Fuca ridge, we estimate that the EP86 and EP93a,b megaplumes were produced by sources of effluent which persisted for times in excess of 106, 105 and 105 s, and that  the total heat released was approximately 4*1016, 2*1015 and 1*1015 J, respectively. 

    0, owing to the long retention time of fluid within the bodies.  For highly permeable two-dimensional bodies, Dxx = alpha (Cyy + 1) U L, where Cyy is the added-mass coefficient characterising the flow around an impermeable body moving parallel to the y-axis.  Consequently, dispersion by highly permeable bodies is enhanced when the bodies are slender, in contrast to the low permeability limit. 
        The influence of finite tracer diffusivity on longitudinal dispersion is also considered and demonstrated to make a negligible contribution when kappa > 0 provided Pe >> max(1, 1 / kappa)$ and for impermeable bodies provided Pe >> 1 .  The coefficient of longitudinal dispersion for Pe << 1 is calculated using Maxwell's (1873) method. When the body is impermeable, the longitudinal dispersivity is Dxx = (1 - (Cxx+1) alpha ) D2 , where D2 is the molecular diffusivity outside the body. Here the influence of body bluffness is to reduce longitudinal dispersion, which is opposite to the high Pe regime. 

  • Bush, J.W.M. and Hasha, A.E., 2004. On the collision of laminar jets: fluid chains and fishbones, J. Fluid Mech., 511, 285-310.

       We present the results of a combined experimental and theoretical investigation of the family of free surface flows generated by obliquely colliding laminar jets. We present a parameter study of the flow, and describe the rich variety of forms observed. When the jet Reynolds number is sufficiently high, the jet collision generates a thin fluid sheet that evolves under the combined influence of surface tension and fluid inertia. The resulting flow may take the form of a fluid chain: a succession of mutually orthogonal links, each composed of a thin oval film bound by relatively thick fluid rims. The dependence of the form of the fluid chains on the governing parameters is examined experimentally. An accompanying theoretical model describing the form of a fluid sheet bound by stable rims is found to yield good agreement with the observed chain shapes. In another parameter regime, the fluid chain structure becomes unstable, giving rise to a striking new flow structure ressembling fluid fishbones. The fishbones are demonstrated to be the result of a Rayleigh-Plateau instability of the sheet's bounding rims amplified by the centripetal force associated with the flow along the curved rims.  

  • Peacock, T., Blanchette, F. and Bush, J.W.M., 2005. The stratified Boycott effect. J. Fluid Mech., 529, 33-49.

       We present the results of an experimental investigation of the flows generated by monodisperse particles settling in a stratified ambient with an inclined sidewall. In this configuration, upwelling beneath the inclined wall associated with the Boycott effect is opposed by the ambient density stratification. For sufficiently weak stratification, the Boycott layer transports dense fluid from the bottom to the top of the system. Subsequently, the upper clear layer is mixed by the convective motions resulting from the combined influence of the newly emplaced dense saline fluid and the buoyant fluid released by the particle settling at the top of the suspension. For sufficiently strong stratification, layering occurs. Within each layer, convection erodes the initially linear density gradient, generating a step-like density profile throughout the system. Particles are transported across the discrete density jumps between layers by millimetric plumes of particle-laden fluid. Mixing models are developed to describe the evolution of particle concentration and salinity in both the low and high stratification limits, and geophysical applications are discussed.  

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