Scaling issues:

Real hydrothermal fluid rises into the Northeast Pacific, a stratified fluid body effectively without edges. In studying fluid flow that rises above the confines of the axial valley, I will have to limit my observations of entrainment to larger, 3 dimensional tanks, and to the period between plume initiation and the moment when the plume contacts and edge of the tank. Examination of 2-dimensional flow for sustained periods is also of interest, however, in understanding the velocity fields down within the axial valley -- essentially a shallow, sloping trough (100 m deep, 1 km wide), open at the ends, and full of buoyancy and momentum sources.

Based on my qualitative observations (to date) of entrainment by both focussed and diffuse sources, the balance between buoyancy forces and fluid momentum (which determines whether flow is a plume or jet) is a strong governor of how and to what extent ambient fluid is drawn in toward the axis of flow. In considering how to legitimately scale my laboratory experiments, I have examined non-dimensional numbers that ratio buoyancy flux (B) and momentum flux (M). For turbulent plumes and jets from focussed (near-point) sources, the Richardson number (Ri = QB1/2M-5/4) is an appealing discriminant.

Examination of distributed flow, however, has suggested that geometry of the source also has a strong influence on the nature of the entrainment. A black smoker atop a sulfide structure can draw in ambient fluid from its entire perimeter, and thus is in dramatic contrast with a microplume positioned in the center of a circular tube worm bed; the central microplume -- surrounded by similar microplumes -- will not be able to entrain denser fluid until its cohorts' densities begin to increase -- dense fluid can only be entrained sequentially from the perimeter inwards. The behavior of diffuse sources' fluid seems to depend strongly on the areal extent of the source (A), and a non-dimensional number that promises to differentiate between plume-like and heated-plate-like behavior is that suggested by McDuff (1995), which I call the McDuff number (Mc = B1/2N-3/2A-1).

Indeed, my intuition leads me to venture that Ri and Mc could predict scales and structures of turbulence. Even the 5 cm diameter column of fluid exiting a black smoker "feels" the ambient fluid from the outside in through the phenomena of turbulence. If that initial flow is laminar, strong shear (relative to the ambient fluid) must be present (at the perimeter of a column rising through initially still fluid), but because turbulence (of a threshold scale?) is absent, the entrainment is very slight. At the other extreme, I've observed dramatic "necking" of the (apparently) laminar trajectories of microplumes from a circular distributed source. Is this because the scale of turbulence associated with the flow of a particular Reynolds number is large relative to the diameter of the rising column?

The conical, time-averaged shape of a turbulent plume is dramatically different from the RneckedS total trajectories of laminar columns of fluid rising from a distributed source. Do we expect a laminar column of diameter 20 cm to neck, as we do a field of laminar microplumes with the same diameter? How about a turbulent plume of that diameter, versus a field of turbulent microplumes from the same basal area?

It seems there is a strong interplay between M, B, A, and/or a scale of turbulence. My latest (quantitative) response has been to look first flow from a point source with a Richardson number similar to the real black smokers. Matching the Richardson number dictates the exit velocity and density anomaly for a fixed exit radius (L). Here arises an interesting interplay with the ReynoldUs number, also a function of Uexit and Lorifice. Comparing video footage of black smokers (which shows that the flow is highly turbulent upon entering the ocean) with the initial laminar flow of the laboratory aparatus of similar Richardson number, I worry that the laboratory entrainment is not truly similar to the real flow at the orifice of a black smoker. The initial laminar jet has a the scale of turbulence that is tiny compared to the exit diameter, but as the jet wavers and breaks up, the ratio of turbulence scale to the diameter of the rising fluid increases greatly, as evidenced by the presence of strong concentration gradients along the centerline. Consequently I have been attempting to monitor entrainment beyond the jet-plume transition, especially during the first motions after the flow has been initiated.

Scales considered in combining diffuse and focussed sources:

                                Real            Lab             Real            Lab
                                Diffuse         Diffuse         Focussed	Focussed

U -- exit velocity              10-2 m/s?       10-2 m/s        3x10-1 m/s      10-1 m/s
D -- diameter of source 	10 m            10-1 m          10-1 m          10-2 m
v -- dynamic viscosity          10-6 m2/s       10-6 m2/s       10-6 m2/s       10-6 m2/s
K -- permeability               ?               ?

Re = UD/v                       10^5             10^3             3x10^4           10^3

Laboratory stratification: 0ppt - 5ppt salinity (variable...)
N -- Buoyancy frequency 	2x10-3 s-1      0.5             2x10-3 s-1      0.5
Fr = ND/U                       0.2 to 2        0.5 to 5        6x10-4       	5x10-2

Q = U*pi*D2 (~circular) 	pi*1 m3/s        pi*10-4 m3/s   ~10-2 m3/s       pi*10-5
M = U*Q                 	10-2 m4/s2      10-6 m4/s2      3x10-3 m4/s2    pi*10-6
Richardson # =          	27              ?                0.3             0.3
z* = rise height = 5.0*B1/4N-3/4