Published on: **Mar 4, 2016**

- 1. meso to submesoscale! horizontal wavenumber spectra ! in Drake Passage Cesar B Rocha*! Teresa K Chereskin* Sarah T Gille* Dimitris Menemenlis+ * : SIO, UC San Diego +: JPL, NASA Snapshot of surface relative vorticity from 1/48o MITgcm run visualization credit: Ryan Abernathey thanks to William R. Young
- 2. hypotheses! what do we expect for the KE spectrum at 1-200 km? Isotropic spectrum interior QG: k-3 Charney 1970; Blumen 1978; Garrett & Munk 1975; Callies & Ferrari 2013 surface QG: k-5/3 • isotropic QG turbulence: interior and surface! • inertia-gravity waves! • other motions • real ocean spectrum likely due to combined processes log10 x log10 space
- 3. hypotheses! what do we expect for the KE spectrum at 1-200 km? • isotropic QG turbulence: interior and surface! • inertia-gravity waves! • other motions • real ocean spectrum likely due to combined processes interior QG: k-3 Charney 1970; Blumen 1978; Garrett & Munk 1975; Callies & Ferrari 2013 surface QG: k-5/3 inertia-gravity waves Isotropic spectrum log10 x log10 space
- 4. hypotheses! what do we expect for the KE spectrum at 1-200 km? Isotropic spectrum ! • real ocean spectrum likely due to combined processes • Challenge: few ‘repeat’ in-situ observations are available to produce statistically meaningful spectra ! • In the Gulf Stream, Wang et al. and Callies & Ferrari ﬁnd interior QG at scales > 20 km. CF also argue for a transition into internal waves at smaller scales Wang et al. 2010; Callies & Ferrari 2013 Transition? Isotropic spectrum log10 x log10 space
- 5. interpreting 1D spectra! Batchelor 1953; Charney 1970; Rhines 1977; Callies & Ferrari 2013; Bühler et al. 2014 1D spectra • isotropic and 1D spectra follow the same power law k-n • Across-track and along-track spectra are related through the scaling exponent • Non-divergent ﬂows: Ku = n Kv • Assuming horizontal isotropy and homogeneous statistics, we can split the spectra into non-divergent and irrotational components: Bühler’s et al. decomposition log10 x log10 space
- 6. interpreting 1D spectra! • isotropic and 1D spectra follow the same power law k-n • Across-track and along-track spectra are related through the scaling exponent • Irrotational ﬂows: Kv = n Ku • Assuming horizontal isotropy and homogeneous statistics, we can split the spectra into non-divergent and irrotational components: Bühler’s et al. decomposition Batchelor 1953; Charney 1970; Rhines 1977; Callies & Ferrari 2013; Bühler et al. 2014 1D spectra log10 x log10 space
- 7. velocity measurements • US Antarctic Research and Supply Vessel Laurence M Gould! • 290 transects (1999-2012) • Underway ADCP (150 kHz) • Upper ocean currents (26-300 m) Lenn et al. JMR 2007 Lenn & Chereskin JPO 2009 mean currents and eddy KE
- 8. ADCP 1D KE spectra • Approximately follows a k-3 power law between 40-200 km • Slightly shallower spectra between 10-40 km: k-n, 2<n<3 • The across-track/along-track KE ratio is <2 between 40-200 km, and ~1 between 10-40 km • No dependence on depth in the upper 200 m (not shown) k-2 k-3
- 9. ADCP 1D KE spectra • Bühler’s et al. decomposition • Non-divergent ﬂows dominate at scales larger than 40 km • Irrotational motions account for 45% of the KE at scales between 10-40 km Bühler et al. 2014 k-3 k-2
- 10. the llc4320 MITgcm simulation ! • A 1/48o global simulation spun up from a 1/24o spun up from a 1/12o … • Forced with tides and 6-hourly ECMWF products • ~1 km in Drake Passage • “Internal-tide resolving and submesoscale-admitting” • ~80 days (Sept.-Nov. 2011) snapshot
- 11. llc4320 1D KE spectra • Model spectra are roughly consistent with ADCP spectra • Approximately follows a k-n 2<n<3 power law between 10-200 km • The across-track/along-track KE ratio is ~1.5 between 40-200 km, and <1 between 5-20 km • No dependence on depth in the upper 200 m (not shown) k-3 k-2
- 12. llc4320 1D KE spectra • Daily-averaging the ﬁelds suppresses high wavenumber KE (dashed lines) • KE spectra are steeper: k-3 power law between 10-200 km • The across-track/along-track KE ratio is ~3 between 10-200 km • No dependence on depth in the upper 200 m (not shown) k-3 k-2
- 13. llc4320 isotropic KE spectra • Approximately follow a k-3 power law between 40-200 km; shallower between 10-40 km (~ k-2) • Surface velocity estimated from SSH assuming geostrophy are consistent with total ﬁeld between 40-200 km, but departs dramatically at scales < 40 km k-3 k-2
- 14. llc4320 isotropic KE spectra • A Helmholtz decomposition of the 2D velocity ﬁeld is consistent with Bühler’s et al. decomposition of the 1D spectra • Irrotational motions dominate at scales < 20 km • M2 internal tide: peak in irrotational spectrum at ~150 km k-3 k-2
- 15. llc4320 isotropic SSH variance spectra • Ageostrophic motions signiﬁcantly project onto the sea surface • Transition from k-5 to k-3 at ~40 km! • Daily-averaging the SSH ﬁelds suppresses high wavenumber variance k-3 k-5
- 16. summary • KE spectra are consistent with isotropic interior QG turbulence masked by ageostrophic ﬂows • KE spectra show no signature of isotropic surface QG turbulence • KE spectra are typically steeper than k -2 • No depth dependence in the upper 200 m • Ageostrophic ﬂows, likely dominated by inertia-gravity waves, account for at least 45% of the surface KE and SSH variance between 10-40 km! • Implication: what will altimeters observe at O(10) km scales? Details and caveats in Rocha et al.: Drake Passage kinetic energy and sea-surface height horizontal wavenumber spectra in the submesoscale range (10-200 km), in prep. for JPO, 2015. Please, e-mail me for a copy: crocha@ucsd.edu In Drake Passage… k-3 k-2
- 17. extra slides
- 18. ADCP 1D KE spectra • Approximately follows a k-3 power law between 40-200 km • Slightly shallower spectra between 10-40 km: k-n, 2<n<3 • The across-track/along-track KE ratio is <2 between 40-200 km, and ~1 between 10-40 km • No dependence on depth in the upper 200 m
- 19. llc4320 1D KE spectra • Approximately follows a k-n 2<n<3 power law between 10-200 km • Slightly shallower spectra between 10-40 km: k-n, 2<n<3 • The across-track/along-track KE ratio is ~1.5 between 40-200 km, and <1 between 5-20 km • No dependence on depth in the upper 200 m
- 20. llc4320 isotropic KE spectra • A Helmholtz decomposition of the 2D velocity ﬁeld is consistent with Bühler et al. decomposition of the 1D spectra • Daily-averaging the ﬁelds suppresses high wavenumber KE • Spectra are consistent with isotropic interior QG turbulence k-3 k-2
- 21. SSH variance spectra from AlTiKa! • Spectra are steep: k-4 and k-5 down to about 60 km
- 22. ADCP 1D KE spectra • Spectra based on small subtransects north and south of the 1-std envelope of the Polar Front from Sallée et al. 2008 • Basic characteristics are the same: steep spectra (~k-3) and across-track/along-track ratio < 2
- 23. how isotropic is the ﬂow in Drake Passage? • The ratio <u2>/<v2> is typically close to 1 • White pixels denote ratio <u2>/<v2> between larger than 1.5 • The ﬂow is only slightly anisotropic • There is no obvious pattern
- 24. llc4320 1D KE spectra • Bühler’s et al. decomposition • Non-divergent ﬂows dominate at scales larger than 40 km • Irrotational motions dominate at scales between 5-20 km
- 25. llc4320 1D KE spectra • Bühler et al. decomposition • Non-divergent ﬂows dominate daily-averaged ﬁelds at scales larger than 10 km • Irrotational motions are efﬁciently removed by daily- averaging the ﬁelds
- 26. SQG spectrum depth dependence • Spectra following k-5/3 at the surface • Signiﬁcant depth dependence in the upper 200 m • Both ADCP and model spectra lack such depth dependence