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Optical plume velocimetry: a new flow measurement technique for use in seafloor hydrothermal systems

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Abstract

Evidence suggests that fluid flow rates in mid-ocean ridge hydrothermal systems may be strongly influenced by mechanical forces such as ocean tidal loading. However, long time-series measurements of flow have not been collected in these environments. We develop a non-invasive method, called optical plume velocimetry (OPV), suitable for obtaining fluid flow rates through black smoker vents based on image analysis of effluent video. We use video from laboratory flows to evaluate three different methods for estimating the image-velocity field that are based on region-based matching, spectral-analysis of Hovmöller diagrams, and temporal cross-correlation of adjacent pixel values. We find that OPV is most sensitive and least biased when the cross-correlation method is used and conclude that OPV should not be applied to flows that are transitioning between jet-like and plume-like behavior.

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Abbreviations

A :

area of jet nozzle, m2

B :

initial specific buoyancy flux, m4/s3

c 1 :

constant in along-axis plume velocity equation

c f :

fraction of Nyquist frequency for Hovmöller cut-off

C :

temporal cross-correlation function

D :

jet nozzle diameter, m

d :

pixel separation in temporal cross-correlation method, pixels

f :

frequency, 1/s

g :

gravitational acceleration, m/s2

k 1 :

constant in along-axis jet velocity equation

l M :

Morton length scale, m

l max :

lag number at the cross-correlation maximum, frames

M :

initial specific momentum flux, m4/s2

n :

number of instantaneous image-velocity measurements used to calculate the mean

N :

number of frames in image sequence

Q :

nozzle flow rate, m3/s

Q i :

individual nozzle flow rate measurement, l/s

Q m :

mean measured nozzle flow rate, 1/s

r :

radial coordinate, m

R :

Residual for region-based matching image-velocity estimation

Re :

Reynolds number

S :

standard deviation

Δt 10 :

time for source fluid tank level to drop by 10 l, s

\(\bar{u}\) :

flow velocity, m/s

t :

time, s

u p :

instantaneous image-velocity, pixels/frame

\(\overline{u_p}\) :

mean image-velocity, pixels/frame

U m :

mean along-axis jet velocity, m/s

U p :

flow rate metric, pixels/frame

W :

mean flow velocity across jet nozzle, m/s

W p :

mean flow velocity across jet nozzle converted to pixels per second, pixels/frame

x :

horizontal coordinate, m

x p :

projected horizontal coordinate, pixels

z :

vertical coordinate, m

z p :

projected vertical coordinate, pixels

λ p :

flow feature wavelength, pixels

ν:

Hovmöller FFT wave number, 1/pixels

μ:

viscosity of jet fluid, Pa s

ρ:

density of ambient fluid, kg/m3

ρ J :

density of jet fluid, kg/m3

Δρ:

density difference between jet and ambient fluid, kg/m3

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Acknowledgments

We thank John Kumph, Eric Lindahl, and John Mickett for many helpful discussions about this work, and we thank Evelyn Lessard for the use of camera equipment. This manuscript benefited greatly from the thorough reviews of two anonymous reviewers. Support for this study was provided by the National Science Foundation under grant OCE-0623285, by the W. M. Keck Foundation through a grant to the University of Washington, and by John Delaney via the Jerome M. Paros Endowed Chair in Sensor Networks.

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Authors and Affiliations

  1. Lamont-Doherty Earth Observatory, Columbia University, 61 Route 9W, Palisades, NY, 10964-8000, USA

    Timothy J. Crone

  2. School of Oceanography, University of Washington, Box 357940, Seattle, WA, 98195-7940, USA

    Russell E. McDuff & William S. D. Wilcock

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  1. Timothy J. Crone
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  2. Russell E. McDuff
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  3. William S. D. Wilcock
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Correspondence to Timothy J. Crone.

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Crone, T.J., McDuff, R.E. & Wilcock, W.S.D. Optical plume velocimetry: a new flow measurement technique for use in seafloor hydrothermal systems. Exp Fluids 45, 899–915 (2008). https://doi.org/10.1007/s00348-008-0508-2

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