We would like to thank four anonymous reviewers for their helpful suggestions. This work was supported by the Office of Naval Research Grant N00014-09-1-0202 and the National Science Foundation Grant OCE-0961714.
Alford, M., 2003: Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature, 423, 159–163.
Balmforth, N. J., S. G. Llewellyn Smith, and W. R. Young, 1998: Enhanced dispersion of near-inertial waves in an idealized geostrophic flow. J. Mar. Res., 56, 1–40.
Bender, C., and S. Orszag, 1978: Advanced Mathematical Methods for Scientists and Engineers. McGraw Hill, 607 pp.
Booker, J. R., and F. P. Bretherton, 1967: The critical layer for internal gravity waves in a shear flow. J. Fluid Mech., 27, 513–539.
Chuang, W., and D. Wang, 1981: Effects of density front on the generation and propagation of internal tides. J. Phys. Oceanogr., 11, 1357–1374.
Colin de Verdiere, A., 2012: The stability of short symmetric internal waves on sloping fronts: Beyond the traditional approximation. J. Phys. Oceanogr., 42, 459–475.
D’Asaro, E., C. Lee, L. Rainville, R. Harcourt, and L. Thomas, 2011: Enhanced turbulence and energy dissipation at ocean fronts. Science, 332, 318–322.
Federiuk, J., and J. S. Allen, 1996: Model studies of near-inertial waves in flow over the Oregon continental shelf. J. Phys. Oceanogr., 26, 2053–2075.
Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources and sinks. Annu. Rev. Fluid Mech., 41, 253–282.
Fomin, L. M., 1973: Inertial oscillations in a horizontally inhomogeneous current velocity field. Izv. Atmos. Ocean. Phys., 9, 75–83.
Gerkema, T., and V. I. Shrira, 2005a: Near-inertial waves in the ocean: Beyond the “traditional approximation.” J. Fluid Mech., 529, 195–219.
Gerkema, T., and V. I. Shrira, 2005b: Near-inertial waves on the “non-traditional” β plane. J. Geophys. Res., 110, C01003, doi:10.1029/2004JC002519.
Hoskins, B., 1974: The role of potential vorticity in symmetric stability and instability. Quart. J. Roy. Meteor. Soc., 100, 480–482.
Inoue, R., M. C. Gregg, and R. R. Harcourt, 2010: Mixing rates across the Gulf Stream, Part 1: On the formation of Eighteen Degree Water. J. Mar. Res., 68, 643–671.
Klein, P., and B. L. Hua, 1988: Mesoscale heterogeneity of the wind-driven mixed layer: Influence of a quasigeostrophic flow. J. Mar. Res., 46, 495–525.
Kunze, E., R. W. Schmidt, and J. M. Toole, 1995: The energy balance in a warm core ring’s near-inertial critical layer. J. Phys. Oceanogr., 25, 942–957.
Leaman, K., and T. Sanford, 1975: Vertical energy propagation of inertial waves: A vector spectral analysis of velocity profiles. J. Geophys. Res., 80, 1975–1978.
Lee, D., and P. Niiler, 1998: The inertial chimney: The near-inertial energy drainage from the ocean surface to the deep layer. J. Geophys. Res., 103 (C4), 7579–7591.
Lighthill, J., 1978: Waves in Fluids. Cambridge University Press, 524 pp.
Magaard, L., 1968: Ein Beitrag zur Theorie der internen Wellen als Störungen geostrophischer Strömungen. Deut. Hydro. Zeit., 21, 241–278.
Marshall, J., and Coauthors, 2009: The CLIMODE field campaign: Observing the cycle of convection and restratification over the Gulf Stream. Bull. Amer. Meteor. Soc., 90, 1337–1350.
Mooers, C. N. K., 1970: The interaction of an internal tide with the frontal zone in a coastal upwelling region. Ph.D. thesis, Oregon State University, 480 pp.
Mooers, C. N. K., 1975: Several effects of a baroclinic current on the cross-stream propagation of inertial-internal waves. Geophys. Fluid Dyn., 6, 245–275.
Nagai, T., A. Tandon, H. Yamazaki, and M. J. Doubell, 2009: Evidence of enhanced turbulent dissipation in the frontogenetic Kuroshio front thermocline. Geophys. Res. Lett., 36, L12609, doi: 10.1029/2009GL038832.
Plougonven, R., and V. Zeitlin, 2005: Lagrangian approach to geostrophic adjustment of frontal anomalies in a stratified fluid. Geophys. Fluid Dyn., 99, 101–135.
Pollard, R. T., and R. C. Millard, 1970: Comparison between observed and simulated wind-generated inertial oscillations. Deep-Sea Res., 17, 813–821.
Rainville, L., and R. Pinkel, 2004: Observations of energetic high-wavenumber internal waves in the Kuroshio. J. Phys. Oceanogr., 34, 1495–1505.
Sawyer, J., 1956: The vertical circulation at meteorological fronts and its relation to frontogenesis. Proc. Roy. Soc. London, A234, 346–362.
Shcherbina, A. Y., L. D. Talley, E. Firing, and P. Hacker, 2003: Near-surface frontal zone trapping and deep upward propagation of internal wave energy in the Japan East Sea. J. Phys. Oceanogr., 33, 900–912.
Thomas, L., 2012: On the effects of frontogenetic strain on symmetric instability and inertiagravity waves. J. Fluid Mech.,711, 620–640, doi:10.1017/jfm.2012.416.
Thomas, L., and T. Joyce, 2009: Subduction on the northern and southern flanks of the Gulf Stream. J. Phys. Oceanogr., 40, 429–438.
Thomas, L., C. Lee, and Y. Yoshikawa, 2010: The subpolar front of the Japan/East Sea. Part II: Inverse method for determining the frontal vertical circulation. J. Phys. Oceanogr., 40, 3–25.
Weller, R. A., 1982: The relation of near-inertial motions observed in the mixed layer during the Jasin (1978) experiment to the local wind stress and to quasi-geostrophic flow field. J. Phys. Oceanogr., 12, 1122–1136.
Whalen, C. B., L. D. Talley, and J. A. Mackinnon, 2012: Spatial and temporal variability of global ocean mixing inferred from Argo profiles. Geophys. Res. Lett., 39, L18612, doi:10.1029/2012GL053196.
Winkel, D. P., M. C. Gregg, and T. B. Sanford, 2002: Patterns of shear and turbulence across the Florida Current. J. Phys. Oceanogr., 32, 3269–3285.
Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281–314.
Young, W. R., and M. Ben-Jelloul, 1997: Propagation of near-inertial oscillations through a geostrophic flow. J. Mar. Res., 55, 735–766.
Zeitlin, V., G. M. Reznik, and M. Ben Jelloul, 2003: Nonlinear theory of geostrophic adjustment. Part 2. Two layer and continuously stratified primitive equations. J. Fluid Mech., 491, 207–228.
Geostrophic flows with extremely high baroclinicity can develop enhanced shear and dissipation parallel to isopycnals even without significant inertial wave activity. Frontogenetic strain, in particular, can play an important role in this process and can also modify any internal waves in the front (Thomas 2012). However, frontogenesis does not appear to be important in the observations presented here and is not the focus of the present paper. See Winkel et al. (2002), Nagai et al. (2009), Thomas et al. (2010), and D’Asaro et al. (2011) for other examples of enhanced shear parallel to isopycnals due to waves and other phenomena.
The selected frequencies are somewhat arbitrary but, when ω is not too far from f and the flow is baroclinic, the observed separation between ωmin and F is typical. The qualitative nature of the results does not change for slightly different frequencies [i.e., (0.95 ± 0.05)f]. However, waves with much larger frequencies are not trapped whereas waves with much smaller frequencies cannot exist.
The theory of Young and Ben-Jelloul (1997) used in, for example, Balmforth et al. (1998) and Zeitlin et al. (2003) depends on an asymptotic expansion in small