Black-smoker hydrothermal plumes rise through the stratified deep ocean into ambient currents that are typically modulated by semidiurnal (M2M_2) tides, so that the plume is bent by a cross flow whose speed oscillates between near zero and several centimeters per second. Lavelle, Di Iorio and Rona (2013) simulated this situation with a three-dimensional turbulent convection model calibrated on the Dante sulfide mound (Juan de Fuca Ridge) but derived effective entrainment coefficients only for times of near-slack flow, explicitly leaving the entrainment description of strongly bent plumes 'for a later time', and asking whether the unsteadiness of the cross flow prevents plume bifurcation or plume puffing at a fixed frequency. A decade of follow-up work has not closed these questions: the direct continuation (Adams and Di Iorio 2021) again restricted its entrainment analysis to near-vertical plume conditions and reserved cross-flow effects 'for another study', and the most detailed recent near-field simulations (large-eddy simulations at centimeter scale) treat only quiescent ambient fluid. The open problem is to determine the near-source dynamics and an effective entrainment parameterization for a hydrothermal plume strongly bent by a time-variable cross flow, including the conditions on cross-flow amplitude, period, and mean flow under which bifurcation and fixed-frequency puffing occur or are suppressed, together with the effects of an Ekman boundary layer and rotation.

Background

Hydrothermal plumes form where hot (up to about 400 degrees Celsius), buoyant fluid discharges from seafloor vents ('black smokers') on mid-ocean ridges; the fluid rises tens to hundreds of meters, entraining and diluting ambient seawater, until it reaches a level of neutral buoyancy where it spreads laterally as a neutrally buoyant plume. The classical description is the integral plume model of Morton, Taylor and Turner (1956), in which the buoyant plume is assumed self-similar and the rate at which ambient fluid is mixed into the plume is parameterized by a single entrainment coefficient multiplying the local axial (upward) velocity. In a stratified ocean, integral models relate the maximum rise height to the source buoyancy flux; for hydrothermal plumes this dependence is weak, so rise height is a poor indicator of source strength. When a horizontal current (a cross flow) bends the plume, entrainment is no longer axisymmetric — fluid is drawn in preferentially from the upstream side — and the Morton–Taylor–Turner closure no longer applies directly; Devenish, Rooney, Webster and Thomson (2010) analyzed the entrainment rate of buoyant plumes in a steady crossflow in the atmospheric context. At deep-sea ridge axes the cross flow is rarely steady: currents of a few centimeters per second are modulated at the semidiurnal tidal period M2M_2 of about 12.42 hours, so a plume can bend more than 45 degrees from the vertical at peak flow and stand nearly upright at slack water. Lavelle (1997), using a three-dimensional convection model of a buoyant plume in a rotating, stratified cross flow, found that at the two largest cross-flow strengths the plume showed evidence of bifurcation — the rising column splitting into two branches. Buoyant plumes can also 'puff' at a fixed frequency: a periodic instability in which vortex structures are shed at a well-defined frequency, documented for laboratory buoyant plumes and pool fires by Cetegen and Ahmed (1993). Whether a tidally oscillating cross flow permits, prevents, or drives either behavior in a hydrothermal plume is unknown. Lavelle, Di Iorio and Rona (2013) advanced this problem with a nonhydrostatic three-dimensional turbulent convection model — nonhydrostatic meaning that the full vertical momentum equation is solved rather than assuming hydrostatic balance — with rotation and stratification included and unresolved eddy viscosities from a Smagorinsky-type closure (a standard turbulence parameterization in which the subgrid viscosity scales with the resolved velocity strain) of the plume rising from Dante, a sulfide mound in the Main Endeavour Field of the Juan de Fuca Ridge, driven by an M2M_2-modulated cross flow oscillating between near zero and about 7 cm/s. The model reproduced observed footprint sizes and vertical velocities for a source heat output of roughly 50 MW, showed that the plume pools over the source at slack flow and streams away diluted at peak flow, that plume properties at identical cross-flow speeds differ depending on whether the flow is accelerating or decelerating (a flow-history hysteresis), and that small changes in background hydrographic profiles change rise heights as much as large changes in source buoyancy flux. Cast into an entrainment framework, the simulations gave an effective entrainment coefficient αEFF\alpha_{\mathrm{EFF}} falling from about 0.11 near the source to about 0.025 at 76 m height — but only for times when the cross flow was negligible and the plume nearly upright, with inflow at the plume edge not azimuthally invariant. The authors stated that deriving effective entrainment coefficients when the plume is bent over by a cross flow 'is left for a later time', posed whether the unsteadiness of the cross flow prevents plume bifurcation or fixed-frequency puffing, called the effects of an Ekman boundary layer (the frictional, rotating boundary layer at the seafloor in which the horizontal current turns and decays with height) and of rotation 'worthy substudies', and noted that their model could not represent the current shear associated with the axial valley's variable topography. New cabled seafloor observatories — for example the Ocean Networks Canada cabled array at Endeavour, which hosts the COVIS sonar (Cabled Observatory Vent Imaging Sonar, an instrument that images the plume acoustically), and the U.S. Ocean Observations Initiative (OOI) Regional Cabled Array elsewhere on the Juan de Fuca Ridge — now deliver long, high-frequency time series of plume shape, velocity, and water properties, which these unresolved modeling questions are needed to interpret — in particular to separate source forcing, ambient hydrography, and flow history in the observed signals.

Problem Statement

For a buoyant hydrothermal plume rising through a rotating, stratified deep-ocean boundary layer into a time-variable cross flow (as at Dante in the Main Endeavour Field, where an M2M_2-modulated current oscillates between near zero and about 7 cm/s and bends the plume by more than 45 degrees at peak flow), determine the near-source dynamics in the strongly bent regime that Lavelle, Di Iorio and Rona (2013) did not model, specifically: (1) an effective entrainment description — entrainment coefficient(s) or an equivalent closure, including their dependence on cross-flow speed and on the acceleration/deceleration phase of the flow — for a plume strongly bent over by the cross flow, extending the αEFF\alpha_{\mathrm{EFF}} framework that has so far been derived only for nearly upright plumes in near-slack flow; (2) the conditions on cross-flow amplitude, oscillation period, and mean flow under which plume bifurcation (the splitting of the rising column into two branches, found at the largest steady cross-flow strengths by Lavelle 1997) and plume puffing at a fixed frequency (the periodic instability of buoyant plumes documented by Cetegen and Ahmed 1993) occur or are suppressed — that is, whether the unsteadiness of the cross flow prevents either or both; and (3) as posed substudies of the same program, the effects of an Ekman boundary layer and of Earth's rotation, and of the current shear associated with variable topography, on these dynamics. All three parts are jointly required, none optional: the problem is resolved only when all three have been addressed for the strongly bent, time-variable regime. The problem concerns the strongly bent plume under time-variable cross flow, not the near-slack or steady-flow regimes, and the results should state what they imply for separating source forcing, ambient hydrography, and flow history in time-dependent plume observations.

References

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