Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T07:12:23.977Z Has data issue: false hasContentIssue false
  • English
  • Français

Anisotropic Helmholtz and wave–vortex decomposition of one-dimensional spectra

Published online by Cambridge University Press:  21 February 2017

Oliver Bühler Open the ORCID record for Oliver Bühler [Opens in a new window] ,
Max Kuang  and
Esteban G. Tabak
Oliver Bühler*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Max Kuang
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Esteban G. Tabak
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: obuhler@cims.nyu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an extension to anisotropic flows of the recently developed Helmholtz and wave–vortex decomposition method for one-dimensional spectra measured along ship or aircraft tracks in Bühler et al. (J. Fluid Mech., vol. 756, 2014, pp. 1007–1026). Here, anisotropy refers to the statistical properties of the underlying flow field, which in the original method was assumed to be homogeneous and isotropic in the horizontal plane. Now, the flow is allowed to have a simple kind of horizontal anisotropy that is chosen in a self-consistent manner and can be deduced from the one-dimensional power spectra of the horizontal velocity fields and their cross-correlation. The key result is that an exact and robust Helmholtz decomposition of the horizontal kinetic energy spectrum can be achieved in this anisotropic flow setting, which then also allows the subsequent wave–vortex decomposition step. The anisotropic method is as easy to use as its isotropic counterpart and it robustly converges back to it if the observed anisotropy tends to zero. As a by-product of our analysis we also found a simple test for statistical correlation between rotational and divergent flow components. The new method is developed theoretically and tested with encouraging results on challenging synthetic data as well as on ocean data from the Gulf Stream.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Quasi-geostrophic flows Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 815 , 25 March 2017 , pp. 361 - 387
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Balwada, D., LaCasce, J. H. & Speer, K. G. 2016 Scale-dependent distribution of kinetic energy from surface drifters in the gulf of mexico. Geophys. Res. Lett. 43 (20), 10856–10863.CrossRefGoogle Scholar
Bierdel, L., Snyder, C., Park, S.-H. & Skamarock, W. C. 2016 Accuracy of rotational and divergent kinetic energy spectra diagnosed from flight-track winds. J. Atmos. Sci. 73 (8), 3273–3286.CrossRefGoogle Scholar
Bühler, O., Callies, J. & Ferrari, R. 2014 Wave–vortex decomposition of one-dimensional ship-track data. J. Fluid Mech. 756, 1007–1026.Google Scholar
Callies, J., Bühler, O. & Ferrari, R. 2016 The dynamics of mesoscale flows in the upper troposphere and lower stratosphere. J. Atmos. Sci. 73 (12), 4853–4872.CrossRefGoogle 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.Google Scholar
Callies, J., Ferrari, R. & Bühler, O. 2014 Transition from geostrophic turbulence to inertia–gravity waves in the atmospheric energy spectrum. Proc. Natl Acad. Sci. USA 111 (48), 17033–17038.CrossRefGoogle ScholarPubMed
Callies, J., Ferrari, R., Klymak, J. M. & Gula, J. 2015 Seasonality in submesoscale turbulence. Nature 6.Google ScholarPubMed
Flagg, C. N., Schwartze, G., Gottlieb, E. & Rossby, T. 1998 Operating an acoustic doppler current profiler aboard a container vessel. J. Atmos. Ocean. Technol. 15 (1), 257–271.Google Scholar
Lindborg, E. 2015 A helmholtz decomposition of structure functions and spectra calculated from aircraft data. J. Fluid Mech. 762, R4.CrossRefGoogle Scholar
McIntyre, M. E. 2008 Potential-vorticity inversion and the wave-turbulence jigsaw: some recent clarifications. Adv. Geosci. 15, 47–56.Google Scholar
Merrifield, M. A., Holloway, P. E. & Johnston, T. M. 2001 The generation of internal tides at the hawaiian ridge. Geophys. Res. Lett. 28 (4), 559–562.CrossRefGoogle Scholar
Munk, W. 1981 Internal waves and small-scale processes. In The Evolution of Physical Oceanography (ed. Warren, B. & Wunsch, C.), pp. 264–291. MIT.Google Scholar
Rocha, C. B., Chereskin, T. K., Gille, S. T. & Menemenlis, D. 2016 Mesoscale to submesoscale wavenumber spectra in drake passage. J. Phys. Oceanogr. 46 (2), 601–620.Google Scholar
Stewart, K. D., Spence, P., Waterman, S., Le Sommer, J., Molines, J.-M., Lilly, J. M. & England, M. H. 2015 Anisotropy of eddy variability in the global ocean. Ocean Modell. 95, 53–65.Google Scholar
Wortham, C., Callies, J. & Scharffenberg, M. G. 2014 Asymmetries between wavenumber spectra of along- and across-track velocity from tandem mission altimetry. J. Phys. Oceanogr. 44 (4), 1151–1160.CrossRefGoogle Scholar
Wortham, C. & Wunsch, C. 2014 A multidimensional spectral description of ocean variability. J. Phys. Oceanogr. 44 (3), 944–966.Google Scholar
Yaglom, A. M. 2004 An Introduction to the Theory of Stationary Random Functions. Courier Corporation.Google Scholar
Young, W. R. & Jelloul, M. B. 1997 Propagation of near-inertial oscillations through a geostrophic flow. J. Marine Res. 55 (4), 735–766.Google Scholar
Zhang, F., Wei, J., Zhang, M., Bowman, K. P., Pan, L. L., Atlas, E. & Wofsy, S. C. 2015 Aircraft measurements of gravity waves in the upper troposphere and lower stratosphere during the start08 field experiment. Atmos. Chem. Phys. 15 (13), 7667.CrossRefGoogle Scholar