Convection from near-point sources of buoyancy occurs at the deep-sea floor where hot hydrothermal fluids are steadily vented. All along ridge crest spreading centers, buoyant plumes rich in chemicals and particles ascend several hundred meters into the water column while being bent over and advected away by ambient currents [Baker et al., 1995]. In those benthic environments, cross-flow strength, fluid turbulence, planetary rotation, background stratification, and source buoyancy flux all combine to determine dispersion patterns of heat and other constituents emanating from hydrothermal vents. In this paper, a model of buoyant plumes in rotating, stratified cross flows appropriate to conditions of ridge crest hydrothermal plumes is described. The focus of results is on rotation, intensity of turbulent mixing, and cross-flow strength as factors that determine downstream plume attributes.
Hydrothermal plumes are one of many examples in the natural environment where a localized source of buoyancy causes materials to rise into an overlying fluid and forced circulation to develop. In all cases, turbulence and, in many cases, rotation and cross flow are important to the dynamics of ensuing plumes. Plumes from industrial stacks, terrestrial volcanoes, forest fires, and oceanic thermal and waste water discharges provide instances of buoyant plumes or buoyant jets occurring in a cross flow. A related problem in the industrial realm involves injection of one fluid as a jet into another as occurs, for example, with fuel injection into jet engines [e.g., Claus and Vanka, 1992]. Numerical model results for jets entering unstratified, nonrotating cross flows [Sykes et al., 1986] provide useful points of comparison for results here. Jets and buoyant jets are different from buoyant plumes in that jets have momentum at source points independent of forces of buoyancy caused by density anomalies. Buoyant plumes, which lack initial upward momentum, are reasonable idealizations for many hydrothermal discharges; initial upward momentum found at a typical hydrothermal vent orifice must give way to buoyancy forces within vertical distances very much smaller than plume rise height.
Model approaches to plumes of this kind are generally classified as integral or numerical. The seminal paper for the integral method is that of Morton et al. [1956], who closed one-dimensional vertical mass, momentum, and heat conservation equations by making fluid entrainment into the rising plume stem at each level proportional to plume upward velocity. The resulting set of ordinary differential equations can be readily solved to address maximum rise height and dilutions within the plume stem. On the other hand, integral models provide no information on distributions in the plume cap region or in regions exterior to the plume where recirculations develop. The integral approach has since been extended and heavily used to describe a variety of jets and plumes, including those rising into cross flows [e.g., Slawson and Csanady, 1967; Middleton and Thomson, 1986; Davidson, 1989]. The literature on jets, buoyant jets, and plumes in cross flows is extensive; reviews by List [1982], Hanna et al. [1982], and Weil [1988] are good sources of information on fundamentals of integral models.
Unlike integral models, more computationally taxing numerical models allow plume cap distributions and induced circulation surrounding the plume to be computed. No uniform entrainment coefficient need be assumed, though as in all fluid dynamical models a turbulent mixing closure assumption of some kind is required. Numerical models of plumes have tended to be two-dimensional [e.g., Lilly, 1962] or quasi-three-dimensional (3-D) [Golay, 1982; Zhang and Ghoniem, 1994] because of computational demands. On the other hand, models of thunderstorms [e.g., Klemp, 1987] and cumulus cloud formation [e.g., Smolarkiewicz and Clark, 1985] have shown the benefits of full 3-D approaches for some time, and those convection problems bear some commonality with point source plume problems. In some sense the oceanic convection problem is easier: source point is stationary, initial conditions are more easily prescribed, and fluid can be assumed to be incompressible.
Hydrothermal plumes result from episodic and chronic discharges of chemically anomalous, heated water at the seafloor along crustal spreading centers. Plumes are of two main types. Megaplumes appear to be the result of short-lived discharge events [Lavelle, 1995]. These plumes are kilometers in diameter and hundreds of meters in thickness and rise many hundreds to a thousand or more meters above the seafloor [e.g., Baker et al., 1995]. The plumes are characterized by thermal anomalies as large as ~0.3°C [e.g., Baker et al., 1995] and by their distinctive chemical signatures [e.g., Massoth et al., 1995]. The few observed have been associated with linear crustal ruptures brought on by episodic magmatic intrusions that rise from depth to the seafloor leaving telltale lava flows [Embley et al., 1995; Fox et al., 1995]. More commonly observed are hydrothermal plumes that result from the continuous release of heat and chemicals stripped from the underlying rock by the hot fluids. Fluxes from chronic sources individually are many orders of magnitude less than those that result in megaplumes, but in aggregate over a ridge crest segment and over a year's time, flux is comparable. Chronic discharge can emanate from sulfide chimneys, e.g., black and white smoker chimneys, more diffusely from sulfide mounds typically meters on a side [e.g., Delaney et al., 1992], or it can percolate from seafloor fissures. Heat release from single vents is estimated to range from several to tens of megawatts [e.g., Schultz et al., 1992] and from vent fields from several hundreds to several thousand megawatts [Baker et al., 1996]. Because heat release is continuous in these cases, background current flows play a major role in plume development.
Observations of effects on the thermal, chemical, and particulate environments resulting from chronic discharges at ridge crests are numerous and are summarized by Baker et al. [1995]. Plumes from chronic sources rise several hundred meters into the water column before reaching density equilibrium. Measured temperature anomalies in the nonbuoyant plume region are typically <0.05 °C [Baker et al., 1995]. Such plumes are also made distinctive by their particle [e.g., Feely et al., 1992], metal [e.g., Massoth et al., 1994], and gas content [e.g., Lupton and Craig, 1977; Mottl et al., 1995]. Transects made along the strike of ridge crests show that plumes from chronic sources can extend longitudinally for many tens of kilometers, as plumes from separate sources coalesce in background currents, which are often along ridge [Cannon et al., 1991]. The model in this paper is intended to address features of a plume from a single, somewhat broad chronic discharge site, e.g., a sulfide mound.
Until now, there have been no models for chronic discharge of hydrothermal fluids that could address the three-dimensional distributions of plume properties in the nonbuoyant region and connect them with source discharge. The challenge of dealing with open boundary conditions when background flows are superimposed on the convection has been one reason for this absence. But the need for a plume model incorporating background flow is clear. Observations typically show that background currents advect hydrothermal plumes away from their source points. Furthermore, without lateral advection, thermal equilibrium cannot be achieved in any fixed volume enclosing a chronically discharging hydrothermal vent.
The plan of the paper is to set out the design of the numerical model, show results for a reference case, and then look at variations in results for changes in single model parameters. The reference case is calculated for source buoyancy flux, cross flow, and background stratification like those expected for hydrothermal discharges on the Juan de Fuca Ridge (JDFR) in the northeast Pacific. The reference case is then compared with a nonrotational case, with results of two experiments in which turbulent mixing is reduced, and with results of two experiments where cross flow is doubled and quadrupled. The emphasis of this initial report is on the general character of model plumes rather than on specific details of their dynamics.
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