Are you familiar with this painting (Figure 1)? Do you know that you can find a similar pattern in the ocean? They are eddies, some of them appear as coherent structures (rings) while others are more irregular. Generally, eddies mean deviations from the mean (Vallis 2006).
Figure 1. The Starry Night by Vincent van Gogh.
A video made by Ryan Abernathey showing the circulation simulated by an idealised channel model representing the Southern Ocean. This video nicely visualises the generation of eddies in the Southern Ocean as the large-scale current becomes unstable gradually. Colours represent ocean temperature and white contours are constant density layers (isopycnals).
Generation of eddies
The main generation mechanism of eddies has been long known as the baroclinic instability (e.g., Gill et al. 1974). In the Southern Ocean, the baroclinicity of the Antarctic Circumpolar Current (ACC) is induced and sustained by the westerly wind and buoyancy forcing (e.g., Howard et al. 2015). Recent studies (e.g., Barthel et al. 2017; Youngs et al. 2017) have shown that eddies are actually generated by the mixed barotropic-baroclinic instability.
A video introducing the circulation in the Southern Ocean produced by National Computational Infrastructure (NCI) Australia.
Energy equilibration of eddies
The transient eddy field is a large energy reservoir in the Southern Ocean; the eddy kinetic energy (EKE) dominates the kinetic energy field in the Southern Ocean (e.g., Ferrari and Wunsch 2009). However, the energy budget of the eddy field in the ocean remains unclear (Figure 2, e.g., Wunsch and Ferrari 2004; Ferrari and Wunsch 2009). Eddies in the ocean get energy from the wind and large-scale circulation (e.g., fronts). There are several dissipation mechanisms that have been proposed for the eddy flow:
dissipation in the turbulent bottom boundary layer (TBBL) (e.g., Sen et al. 2008; Arbic et al. 2009),
interactions with the background internal wave field (e.g., Bühler and McIntyre 2005; Polzin 2008),
loss of balance (e.g., McWilliams and Yavneh 1998; Molemaker et al. 2005), and
Kelvin wave hydraulic control at large-scale topography (e.g., Hogg et al. 2011).
Figure 2. Strawman energy budget for the global ocean circulation (source: Wunsch and Ferrari 2004).
Figure 3. The source, flow and fate of energy in the oceanic general circulation (source: McWilliams 2016).
Do lee waves matter in the energy budget of eddies?
Lee waves have been suggested to extract a significant amount of energy from the eddy field. Observations have found elevated turbulent energy dissipation rates and inferred enhanced diffusivity with respect to their background values over rough topography in the Southern Ocean (Figure 4, e.g., Polzin et al. 1997; Naveira Garabato et al. 2004; St. Laurent et al. 2012; Meyer et al. 2015). Enhanced turbulent dissipation and mixing are modulated by the strength of the eddy field downstream of rough topographic features (e.g., Liang and Thurnherr 2012, Sheen et al. 2014). This modulation is likely through the generation and breaking of lee waves. The hypothesis that breaking lee waves being a major driver for vigorous mixing is supported by observations from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES) and the Southern Ocean Finestructure project (SOFine). In agreement with observations, idealised simulations also highlight the importance of lee waves in the energy pathway from eddies to turbulence (Figure 5, Nikurashin et al. 2013). However, the energy loss from eddies due to lee wave generation remains poorly estimated.
Figure 4. The spatial distribution of mixing in the Southern Ocean is exemplified by a section along the rim of the Scotia Sea (source: Naveira Garabato et al. 2004). Enhanced mixing rates (represented by light blue to red colours) are strikingly associated with strong flow and rough topography. [SAF, Subantarctic Front, the ACC’s northern boundary; PF, Polar Front and its southern boundary (SB) are marked in the upper axis. The frontal regions are where the flow is strong. These strong flows tend to be barotropic in the Southern Ocean and extend to the seafloor.]
Figure 5. Zonal sections of (a) speed and (b) energy dissipation rate (source: Nikurashin et al. 2013). These are snapshots from a super-high resolution simulation with rough bathymetry. Energy dissipation rate near the bottom is clearly elevated (indicated by red colour in b) where the flow is strong (indicated by the light blue colour in a).
In a part of my PhD work, we quantify the impacts of lee wave generation on the transient eddy flow in the Southern Ocean (Figure 6). While the eddy flow in the Southern Ocean can be dissipated by the generation of lee waves at rough topography and turbulence in the TBBL, among others, the dissipation rate due to the lee wave generation (0.12 TW) exceeds that due to TBBL processes (0.05 TW).
Figure 6. Energy conversion from (a) time-mean and (b) eddy flow to lee waves using topographic parameters from Goff (2010), (c) energy dissipation of the eddy flow in the TBBL (adapted from Yang et al., 2018).
Our results provide a quantitative evidence that lee waves effectively weaken the eddy flow in the Southern Ocean. The implication is that, the effects of (unresolved) lee waves on the (resolved) eddy flow should be included in eddy-resolving ocean models in a self-regulating way to study the sensitivity of the Southern Ocean circulation to changes in wind.
References
Arbic, B.K., Shriver, J.F., Hogan, P.J., Hurlburt, H.E., McClean, J.L., Metzger, E.J., Scott, R.B., Sen, A., Smedstad, O.M. and Wallcraft, A.J., 2009. Estimates of bottom flows and bottom boundary layer dissipation of the oceanic general circulation from global high‐resolution models. Journal of Geophysical Research: Oceans, 114(C2).
Barthel, A., McC. Hogg, A., Waterman, S. and Keating, S., 2017. Jet–Topography Interactions Affect Energy Pathways to the Deep Southern Ocean. Journal of Physical Oceanography, 47(7), pp.1799-1816.
Bühler, O. and McINTYRE, M.E., 2005. Wave capture and wave–vortex duality. Journal of Fluid Mechanics, 534, pp.67-95.
Ferrari, R. and Wunsch, C., 2009. Ocean circulation kinetic energy: Reservoirs, sources, and sinks. Annual Review of Fluid Mechanics, 41.
Gill, A.E., Green, J.S.A. and Simmons, A.J., 1974, July. Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies. In Deep Sea Research and Oceanographic Abstracts (Vol. 21, No. 7, pp. 499-528). Elsevier.
Goff, J.A., 2010. Global prediction of abyssal hill root‐mean‐square heights from small‐scale altimetric gravity variability. Journal of Geophysical Research: Solid Earth, 115(B12).
Hogg, A.M., Dewar, W.K., Berloff, P. and Ward, M.L., 2011. Kelvin wave hydraulic control induced by interactions between vortices and topography. Journal of Fluid Mechanics, 687, pp.194-208.
Howard, E., McC. Hogg, A., Waterman, S. and Marshall, D.P., 2015. The injection of zonal momentum by buoyancy forcing in a Southern Ocean model. Journal of Physical Oceanography, 45(1), pp.259-271.
Liang, X. and Thurnherr, A.M., 2012. Eddy-modulated internal waves and mixing on a midocean ridge. Journal of Physical Oceanography, 42(7), pp.1242-1248.
McWilliams, J.C. and Yavneh, I., 1998. Fluctuation growth and instability associated with a singularity of the balance equations. Physics of Fluids, 10(10), pp.2587-2596.
McWilliams, J.C., 2016, May. Submesoscale currents in the ocean. In Proc. R. Soc. A (Vol. 472, No. 2189, p. 20160117). The Royal Society.
Meyer, A., Sloyan, B.M., Polzin, K.L., Phillips, H.E. and Bindoff, N.L., 2015. Mixing variability in the Southern Ocean. Journal of Physical Oceanography, 45(4), pp.966-987.
Molemaker, M.J., McWilliams, J.C. and Yavneh, I., 2005. Baroclinic instability and loss of balance. Journal of physical oceanography, 35(9), pp.1505-1517.
Naveira Garabato, A.C., Polzin, K.L., King, B.A., Heywood, K.J. and Visbeck, M., 2004. Widespread intense turbulent mixing in the Southern Ocean. Science, 303(5655), pp.210-213.
Nikurashin, M., Vallis, G.K. and Adcroft, A., 2013. Routes to energy dissipation for geostrophic flows in the Southern Ocean. Nature Geoscience, 6(1), p.48.
Polzin, K.L., Toole, J.M., Ledwell, J.R. and Schmitt, R.W., 1997. Spatial variability of turbulent mixing in the abyssal ocean. Science, 276(5309), pp.93-96.
Polzin, K.L., 2008. Mesoscale eddy–internal wave coupling. Part I: Symmetry, wave capture, and results from the Mid-Ocean Dynamics Experiment. Journal of Physical Oceanography, 38(11), pp.2556-2574.
Sen, A., Scott, R.B. and Arbic, B.K., 2008. Global energy dissipation rate of deep‐ocean low‐frequency flows by quadratic bottom boundary layer drag: Computations from current‐meter data. Geophysical Research Letters, 35(9).
Sheen, K.L., Garabato, A.N., Brearley, J.A., Meredith, M.P., Polzin, K.L., Smeed, D.A., Forryan, A., King, B.A., Sallée, J.B., Laurent, L.S. and Thurnherr, A.M., 2014. Eddy-induced variability in Southern Ocean abyssal mixing on climatic timescales. Nature Geoscience, 7(8), p.577.
St. Laurent, L., Naveira Garabato, A.C., Ledwell, J.R., Thurnherr, A.M., Toole, J.M. and Watson, A.J., 2012. Turbulence and diapycnal mixing in Drake Passage. Journal of Physical Oceanography, 42(12), pp.2143-2152.
Vallis, G. K., 2006. Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp
Wunsch, C. and Ferrari, R., 2004. Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, pp.281-314.
Yang, L., Nikurashin, M., Hogg, A.M. and Sloyan, B.M., 2018. Energy loss from transient eddies due to lee wave generation in the Southern Ocean. Journal of Physical Oceanography, 48(12), pp.2867-2885..
Youngs, M.K., Thompson, A.F., Lazar, A. and Richards, K.J., 2017. ACC Meanders, Energy Transfer, and Mixed Barotropic–Baroclinic Instability. Journal of Physical Oceanography, 47(6), pp.1291-1305.