Near-inertial wave propagation between stratified and homogeneous layers: Conclusions and References

22 May 2024


(1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands.

Abstract and Intro



Simulating Transition


Conclusions and References

6 Conclusions

Acknowledgments I thank the crews of the R/V Thethys II and Le Suroît for the sea operations, G. Rougier and C. Millot for preparing the ‘GYROSCOP-2’ mooring, and T. Gerkema for providing the model results. I gratefully acknowledge support from the Netherlands organisation for the advancement of scientific research, NWO, and Centre National de la Recherche Scientifique, CNRS, under the (alas no longer existing) French Dutch scientific collaboration.


Abarbanel HDI, Holm DD, Marsden JE, Ratiu T (1984) Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Phys Rev Lett 52:2352-2355

Dengler M, Quadfasel D (2002) Equatorial deep jets and abyssal mixing in the Indian Ocean. J Phys Oceanogr 32:1165-1180

Gascard J-C (1973) Vertical motions in a region of deep water formation. Deep-Sea Res 20:1011-1027

Gerkema T, Shrira VI (2005) Near-inertial waves on the “nontraditional”  plane. J Geophys Res 110:C01003. doi:10.1029/2004JC002519

Gerkema T, Exarchou E (2008) Internal-wave properties in weakly stratified layers. J Mar Res 66:617-644

Gerkema T, Zimmerman JTF, Maas LRM, van Haren H (2008) Geophysical and astrophysical fluid dynamics beyond the traditional approximation. Rev Geophys 46:RG2004. doi:10.1029/2006RG000220

Gill AE (1982) Atmosphere-Ocean Dynamics. Academic Press, San Diego, pp 1-680

Gonella J (1972) A rotary-component method for analysing meteorological and oceanographic vector time series. Deep-Sea Res 19:833-846

Howard LN (1961) Note on a paper of John W. Miles. J. Fluid Mech 10:509-512

LeBlond PH, Mysak LA (1978) Waves in the ocean. Elsevier, Amsterdam, pp 1-602

Marshall J, Schott F (1999) Open-ocean convection: observations, theory, and models. Rev Geophys 37:1-64

Matsuno T, Endoh T, Hibiya T, Sengyu T, Watanabe M (2015) Formation of the well‑mixed homogeneous layer in the bottom water of the Japan Sea. J Oceanogr 71:441-447

Miles JW (1961) On the stability of heterogeneous shear flows. J Fluid Mech 10:496-508

Millot C (1999) Circulation in the Western Mediterranean Sea. J Mar Sys 20:423-442

Millot C, Monaco A (1984) Deep strong currents and sediment transport in the Northwestern Mediterranean Sea. Geo-Mar Lett 4:13-17

Morozov EG, Velarde MG (2008) Inertial oscillations as deep ocean response to hurricanes. J Oceanogr 64:495-509

Munk WH (1980) Internal wave spectra at the buoyant and inertial frequencies. J Phys Oceanogr 10:1718-1728

Saint-Guily B (1970) On internal waves, effects of the horizontal component of the Earth’s rotation and of a uniform current. D Hyd Z 23:16-23

Schott F, Leaman K (1991) Observations with moored acoustic Doppler current profilers in the convection regime in the Golfe du Lion. J Phys Oceanogr 21:558-574

Shay LK, Elsberry RL (1987) Near-inertial ocean current response to hurricane Frederic. J Phys Oceanogr 17:1249-1269

Sheremet VA (2004) Laboratory experiments with tilted convective plumes on a centrifuge: a finite angle between the buoyancy and the axis of rotation. J Fluid Mech 506:217-244

Straneo F, Kawase M, Riser SC (2002) Idealized models of slantwise convection in a baroclinic flow. J Phys Oceanogr 32:558-572

Talley LD, Lohmov V, Ponomarev V, Salyuk A, Tishchenko P, Zhabin I, Riser S (2009) Deep convection and brine rejection in the Japan Sea. Geophys Res Lett 30:1159. doi: 10.1029/2002GL016451

Timmermans M-L, Melling H, Rainville L (2007) Dynamics in the deep Canada Basin, Arctic Ocean, inferred by thermistor chain time series. J Phys Oceanogr 37:1066-1076

van Haren H (2006) Asymmetric vertical internal wave propagation. Geophys Res Lett 33:L06618. doi:10.1029/2005GL025499

van Haren H (2008) Abrupt transitions between gyroscopic and internal gravity waves: the mid-latitude case. J Fluid Mech 598:67-80

van Haren H, Millot C (2004) Rectilinear and circular inertial motions in the Western Mediterranean Sea. Deep-Sea Res I 51:1441-1455

van Haren H, Millot C (2005) Gyroscopic waves in the Mediterranean Sea. Geophys Res Lett 32:L24614. doi:10.1029/2005GL023915

van Haren H, Millot C (2009) Slantwise convection: a candidate for homogenization of deep newly formed dense waters. Geophys Res Lett 36:L12604. doi:10.1029/2009GL038736

van Haren H, Millot C, Taupier-Letage I (2006) Fast deep sinking in Mediterranean eddies. Geophys Res Lett 33:L04606. doi:10.1029/2005GL025367

Voorhis AD, Webb DC (1970). Large vertical currents observed in a winter sinking region of the northwestern Mediterranean. Cah océanogr 22:571-580

Fig. 1 Site and hydrography. a) Western-Mediteranean Sea with observational site *. Depth contours every 500 m for [500, 2500] m and 2750 m. b) Typical local density anomaly profiles referenced to a pressure of 2000 dbar observed using shipborne CTD in April 2005 (blue; stopped at z = -2500 m) and February 2006 (red) during mooring deployment and recovery cruises, respectively. For reference, particular density gradient slopes are given (see text). To the left, the mooring is given schematically, with current meter (CM) depths (same colours as in Figs 2a,b, 3a,b; light-blue: only Tdata) and range of upward looking ADCP (yellow). The local seafloor is at the x-axis.

Fig. 2 Time-series for the entire 10-month mooring period (a,b) and for the 5.5-month period of ADCP-data (c,d). Yeardays in 2006 are +365. a) Current amplitude at ADCP's bin 5 (z = -2025 m) and CM (-1990 m) using the instruments’ colour coding in Fig. 1b. The horizontal bar indicates the period of Fig. 6. The ADCP record ends before a change in the time series' characteristics (days 260-270, indicated by thick black bar) that defines two different periods. b) T-time-series from the same instruments as in a), but at z = -2090 m for the ADCP. T-data are calibrated using CTD-profiles at recovery. During the 10-month period, the local homogeneous-adiabatic T raised by 0.013C, which is approximately the T-sensors' resolution. c) Mooring-line tilt measured by the ADCP and reflecting water-flow drag. d) Vertical current-component (black) and error velocity (light-blue) measured at ADCP’s bin 5 (z = -2025 m) and smoothed using a 3- h running mean. The horizontal black line indicates the period of Fig. 6.

Figure 4. Spectra from ADCP-data at z = -2025 m. Horizontal kinetic energy (black), vertical current (red) and error velocity (light-blue). Vertical lines as in Fig. 3.

Figure 7. Simulation results of vertical current amplitudes |w| for internal wave ‘beams’ in a vertical-horizontal plane with the seafloor at z = -2000 m. The upper two panels show a transition (dashed line) between a weakly stratified layer above a homogeneous one. The lower two panels show a transition between a stratified layer below a homogeneous one. The left two panels are for super-inertial motions, the right two for sub-inertial motions. The left panels show amplitude enhancement and trapping in the homogeneous N=0 layer, while the right panels show enhancement and trapping in the stratified layer. Note the two different angles to the horizontal of up- and down-going rays, which is typical for the non-traditional approach (Gerkema et al. 2008).

This paper is available on arxiv under CC 4.0 license.