Experiments in Fluids

, Volume 45, Issue 5, pp 899–915

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

  • Timothy J. Crone
  • Russell E. McDuff
  • William S. D. Wilcock
Research Article

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.

List of symbols

A

area of jet nozzle, m2

B

initial specific buoyancy flux, m4/s3

c1

constant in along-axis plume velocity equation

cf

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

k1

constant in along-axis jet velocity equation

lM

Morton length scale, m

lmax

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

Qi

individual nozzle flow rate measurement, l/s

Qm

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

Δt10

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

\(\bar{u}\)

flow velocity, m/s

t

time, s

up

instantaneous image-velocity, pixels/frame

\(\overline{u_p}\)

mean image-velocity, pixels/frame

Um

mean along-axis jet velocity, m/s

Up

flow rate metric, pixels/frame

W

mean flow velocity across jet nozzle, m/s

Wp

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

x

horizontal coordinate, m

xp

projected horizontal coordinate, pixels

z

vertical coordinate, m

zp

projected vertical coordinate, pixels

Greek symbols

λp

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

ρJ

density of jet fluid, kg/m3

Δρ

density difference between jet and ambient fluid, kg/m3

Supplementary material

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References

  1. Adelson EH, Bergen JR (1985) Spatiotemporal energy models for the perception of motion. J Opt Soc Am A 2(2):284–299Google Scholar
  2. Adrian RJ (2005) Twenty years of particle image velocimetry. Exp Fluid 39:159–169. doi:10.1007/s00348-005-0991-7 CrossRefGoogle Scholar
  3. Alt JC (1995) Subseafloor processes in mid-ocean ridge hydrothermal systems. In: Humphris SE, Zierenberg RA, Mullineaux LS, Thomson RE (eds) Seafloor hydrothermal systems: physical, chemical, biological, and geological interactions, Geophysical Monograph 91, American Geophysical Union, Washington DC, pp 85–114Google Scholar
  4. Anandan P (1989) A computational framework and an algorithm for the measurement of visual motion. Int J Comput Vis 2:283–310CrossRefGoogle Scholar
  5. Beauchemin SS, Barron JL (1995) The computation of optical flow. ACM Comput Surv 27(3):433–467CrossRefGoogle Scholar
  6. Bischoff JL, Rosenbauer RJ (1985) An empirical equation of state for hydrothermal seawater (3.2 percent NaCl). Am J Sci 285(8):725–763Google Scholar
  7. Butterfield DA, Jonasson IR, Massoth GJ, Feely RA, Roe KK, Embley RW, Holden JF, McDuff RE, Lilley MD, Delaney JR (1997) Seafloor eruptions and evolution of hydrothermal fluid chemistry. Phil Trans R Soc Lond A 355:369–386CrossRefGoogle Scholar
  8. Converse DR, Holland HD, Edmond JM (1984) Flow rates in the axial hot springs of the East Pacific Rise (21°N): implications for the heat budget and the formation of massive sulfide deposits. Earth Planet Sci Lett 69:159–175CrossRefGoogle Scholar
  9. Coupland JM (2000) Laser Doppler and pulsed laser velocimetry in fluid mechanics. In: Rastogi PK (ed) Photomechanics, topics in applied physics. Springer, BerlinGoogle Scholar
  10. Crone TJ, Wilcock WSD (2005) Modeling the effects of tidal loading on mid-ocean ridge hydrothermal systems. Geochem Geophys Geosyst 6:Q07001. doi:10.1029/2004GC000905 CrossRefGoogle Scholar
  11. Crone TJ, Wilcock WSD, Barclay AH, Parsons JD (2006) The sound generated by mid-ocean ridge black smoker hydrothermal vents. PLoS ONE 1:e133. doi:10.1371/journal.pone.0000133 CrossRefGoogle Scholar
  12. Davis E, Becker K, Dziak R, Cassidy J, Wang K, Lilley M (2004) Hydrological response to a seafloor spreading episode on the Juan de Fuca Ridge. Nature 430:335–338. doi:10.1038/nature02755 CrossRefGoogle Scholar
  13. Delaney JR, Robigou V, McDuff RE (1992) Geology of a vigorous hydrothermal system on the Endeavour segment, Juan de Fuca Ridge. J Geophys Res 97(B13):19663–19682CrossRefGoogle Scholar
  14. Delaney JR, Kelley DS, Lilley MD, Butterfield DA, Baross JA, Wilcock WSD, Embley RW, Summit M (1998) The quantum event of oceanic crustal accretion: impacts of diking at mid-ocean ridges. Science 281:222–230CrossRefGoogle Scholar
  15. Delaney JR, Heath GR, Howe B, Chave AD, Kirkham H (2000) NEPTUNE: Real-time ocean and earth sciences at the scale of a tectonic plate. Oceanography 13(2):71–79Google Scholar
  16. Dimotakis PE, Miake-Lye RC, Papantoniou DA (1983) Structure and dynamics of round turbulent jets. Phys Fluids 26(11):3185–3192CrossRefGoogle Scholar
  17. Draper NR, Smith H (1981) Applied regression analysis. Wiley, New YorkMATHGoogle Scholar
  18. Elderfield H, Schultz A (1996) Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean. Annu Rev Earth Planet Sci 24:191–224CrossRefGoogle Scholar
  19. Harris FJ (1978) On the use of windows for harmonic analysis with the discrete Fourier transform. Proc IEEE 66:51–83CrossRefGoogle Scholar
  20. Holzbecher EO (1998) Modeling density-driven flow in porous media. Springer, BerlinGoogle Scholar
  21. Horn BKP, Schunck BG (1981) Determining optical flow. Artif Intell 17:185–203CrossRefGoogle Scholar
  22. Hovmöller E (1949) The trough-and-ridge diagram. Tellus 1(2):62–66CrossRefGoogle Scholar
  23. Johnson HP, Hutnak M, Dziak RP, Fox CG, Urcuyo I, Cowen JP, Nabelek J, Fisher C (2000) Earthquake-induced changes in a hydrothermal system on the Juan de Fuca mid-ocean ridge. Nature 407:174–177CrossRefGoogle Scholar
  24. Jupp TE (2000) Fluid flow processes at mid-ocean ridge hydrothermal systems. PhD Thesis, Pembroke College, University of CambridgeGoogle Scholar
  25. Kelley DS, Baross JA, Delaney JR (2002) Volcanoes, fluids, and life at mid-ocean ridge spreading centers. Annu Rev Earth Planet Sci 30:385–491. doi:10.1146/annurev.earth.30.091201.141331 CrossRefGoogle Scholar
  26. Kraus NC, Lohrmann A, Cabrera R (1994) New acoustic meter for measuring 3D laboratory flows. J Hydraul Eng 120(3):406–412CrossRefGoogle Scholar
  27. Larson BI, Olson EJ, Lilley MD (2007) In-situ measurement of dissolved chloride in high temperature hydrothermal fluids. Geochim Cosmochim Acta 71:2510–2523. doi:10.1016/j.gca.2007.02.013 CrossRefGoogle Scholar
  28. List EJ (1982) Turbulent jets and plumes. Annu Rev Fluid Mech 14:189–212CrossRefGoogle Scholar
  29. McDuff RE (1995) Physical dynamics of deep-sea hydrothermal plumes. In: Humphris SE, Zierenberg RA, Mullineaux LS, Thomson RE (eds) Seafloor hydrothermal systems: physical, chemical, biological, and geological interactions, Geophysical Monograph 91, American Geophysical Union, Washington DC, pp 357–368Google Scholar
  30. McDuff RE, Delaney JR (1995) Periodic variability in fluid temperature at a seafloor hydrothermal vent. Eos Trans AGU 76(46), Fall Meet. Supl., F710Google Scholar
  31. Meynart R (1983) Speckle velocimetry study of vortex pairing in a low-Re unexcited jet. Phys Fluids 26:2074–2079CrossRefGoogle Scholar
  32. Morton BR, Taylor G, Turner JS (1956) Turbulent gravitational convection from maintained and instantaneous sources. Proc R Soc Lond Math Phys Sci 234(1196):1–23MATHMathSciNetGoogle Scholar
  33. Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9:62–66CrossRefGoogle Scholar
  34. Papanicolaou PN, List EJ (1988) Investigations of round vertical turbulent bouyant jets. J Fluid Mech 195:341–391CrossRefGoogle Scholar
  35. Pruis MJ, Johnson HP (2004) Tapping into the sub-seafloor: examining diffuse flow and temperature from an active seamount on the Juan de Fuca Ridge. Earth Planet Sci Lett 217:379–388. doi:10.1016/S0012-821X(03)00607-1 CrossRefGoogle Scholar
  36. Rodi W (ed) (1982) Turbulent buoyant jets and plumes, HMT—the science & applications of heat and mass transfer, vol 6. Pergamon, New YorkGoogle Scholar
  37. Ruden P (1933) Turbulente Ausbreitungsvorgänge im Freistrahl. Die Naturwissenschaften 21:375–378CrossRefGoogle Scholar
  38. Schultz A, Dickson P, Elderfield H (1996) Temporal variations in diffuse hydrothermal flow at TAG. Geophys Res Lett 23(23):3471–3474CrossRefGoogle Scholar
  39. Shabbir A, George WK (1994) Experiments on a round turbulent buoyant plume. J Fluid Mech 275:1–32CrossRefGoogle Scholar
  40. Spiess FN, Macdonald KC, Atwater T, Ballard R, Carranza A, Cordoba D, Cox C, Diaz Garcia VM, Francheteau J, Guerrero J, Hawkins J, Haymon R, Hessler R, Juteau T, Kastner M, Larson R, Luyendyk B, Macdougall JD, Miller S, Normark W, Orcutt J, Rangin C (1980) East Pacific Rise: hot springs and geophysical experiments. Science 207(4438):1421–1433CrossRefGoogle Scholar
  41. Tokumaru PT, Dimotakis PE (1995) Image correlation velocimetry. Exp Fluid 19:1–15CrossRefGoogle Scholar
  42. Tolstoy M, Vernon FL, Orcutt JA, Wyatt FK (2002) Breathing of the seafloor: tidal correlations of seismicity at Axial volcano. Geology 30(6):503–506CrossRefGoogle Scholar
  43. Turner JS (1986) Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J Fluid Mech 173:431–471CrossRefGoogle Scholar
  44. Wilcock WSD, Fisher AT (2004) Geophysical constraints on the sub-seafloor environment near mid-ocean ridges. In: Wilcock WSD, DeLong EF, Kelley DS, Baross JA, Cary SC (eds) The subseafloor biosphere at mid-ocean ridges, Geophysical Monograph 144, American Geophysical Union, Washington DC, pp 51–74Google Scholar
  45. Wilcock WSD, Toomey DR (1991) Estimating hypocentral uncertainties for marine microearthquake surveys: a comparison of the generalized inverse and grid search methods. Mar Geophys Res 13:161–171Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Timothy J. Crone
    • 1
  • Russell E. McDuff
    • 2
  • William S. D. Wilcock
    • 2
  1. 1.Lamont-Doherty Earth ObservatoryColumbia UniversityPalisadesUSA
  2. 2.School of OceanographyUniversity of WashingtonSeattleUSA

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