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Wave–vortex decomposition of one-dimensional ship-track data

Published online by Cambridge University Press:  09 September 2014

Oliver Bühler ,
Jörn Callies  and
Raffaele Ferrari
Oliver Bühler*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Jörn Callies
Affiliation:
MIT/WHOI Joint Program in Oceanography, Cambridge/Woods Hole, MA 02139, USA
Raffaele Ferrari
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present a simple two-step method by which one-dimensional spectra of horizontal velocity and buoyancy measured along a ship track can be decomposed into a wave component consisting of inertia–gravity waves and a vortex component consisting of a horizontal flow in geostrophic balance. The method requires certain assumptions for the data regarding stationarity, homogeneity, and horizontal isotropy. In the first step an exact Helmholtz decomposition of the horizontal velocity spectra into rotational and divergent components is performed and in the second step an energy equipartition property of hydrostatic inertia–gravity waves is exploited that allows a diagnosis of the wave energy spectrum solely from the observed horizontal velocities. The observed buoyancy spectrum can then be used to compute the residual vortex energy spectrum. Further wave–vortex decompositions of the observed fields are possible if additional information about the frequency content of the waves is available. We illustrate the method on two recent oceanic data sets from the North Pacific and the Gulf Stream. Notably, both steps in our new method might be of broader use in the theoretical and observational study of atmosphere and ocean fluid dynamics.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Quasi-geostrophic flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 1007 - 1026
Copyright
© 2014 Cambridge University Press 

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Callies, J. & Ferrari, R. 2013 Interpreting energy and tracer spectra of upper-ocean turbulence in the submesoscale range (1–200 km). J. Phys. Oceanogr. 43 (11), 2456–2474.CrossRefGoogle Scholar
Charney, J. G. 1971 Geostrophic turbulence. J. Atmos. Sci. 28 (6), 1087–1095.2.0.CO;2>CrossRefGoogle Scholar
Ferrari, R. & Rudnick, D. L. 2000 Thermohaline variability in the upper ocean. J. Geophys. Res. 105 (C7), 16857–16883.Google Scholar
Ferrari, R. & Wunsch, C. 2010 The distribution of eddy kinetic and potential energies in the global ocean. Tellus A 62 (2), 92–108.Google Scholar
Lindborg, E. 1999 Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 388, 259–288.Google Scholar
Lindborg, E. 2007 Horizontal wavenumber spectra of vertical vorticity and horizontal divergence in the upper troposphere and lower stratosphere. J. Atmos. Sci. 64 (3), 1017–1025.CrossRefGoogle Scholar
Müller, P., Lien, R.-C. & Williams, R. 1988 Estimates of potential vorticity at small scales in the ocean. J. Phys. Oceanogr. 18 (3), 401–416.2.0.CO;2>CrossRefGoogle Scholar
Munk, W. H. 1981 Internal waves and small-scale processes. In Evolution of Physical Oceanography (ed. Warren, B. A. & Wunsch, C.), chap. 9, pp. 264–291. The MIT Press.Google Scholar
Nastrom, G. D. & Gage, K. S. 1985 A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci. 42 (9), 950–960.Google Scholar
Riley, J. J. & Lindborg, E. 2008 Stratified turbulence: a possible interpretation of some geophysical turbulence measurements. J. Atmos. Sci. 65 (7), 2416–2424.Google Scholar
Smith, L. M. & Waleffe, F. 2002 Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145–168.Google Scholar
Tulloch, R. & Smith, K. S. 2006 A theory for the atmospheric energy spectrum: depth-limited temperature anomalies at the tropopause. Proc. Natl Acad. Sci. USA 103 (40), 14690–14694.CrossRefGoogle ScholarPubMed
Waite, M. L. & Bartello, P. 2004 Stratified turbulence dominated by vortical motion. J. Fluid Mech. 517, 281–308.Google Scholar
Wang, D.-P., Flagg, C. N., Donohue, K. & Rossby, H. T. 2010 Wavenumber spectrum in the Gulf Stream from shipboard ADCP observations and comparison with altimetry measurements. J. Phys. Oceanogr. 40 (4), 840–844.Google Scholar
Wortham, C., Callies, J. & Scharffenberg, M. 2014 Asymmetries between wavenumber spectra of along- and across-track velocity from tandem-mission altimetry. J. Phys. Oceanogr. 44 (4), 1151–1160.Google Scholar