▪ AbstractThe coexistence in the deep ocean of a finite, stable stratification, a strong meridional overturning circulation, and mesoscale eddies raises complex questions concerning the circulation energetics. In particular, small-scale mixing processes are necessary to resupply the potential energy removed in the interior by the overturning and eddy-generating process. A number of lines of evidence, none complete, suggest that the oceanic general circulation, far from being a heat engine, is almost wholly governed by the forcing of the wind field and secondarily by deep water tides. In detail however, the budget of mechanical energy input into the ocean is poorly constrained. The now inescapable conclusion that over most of the ocean significant “vertical” mixing is confined to topographically complex boundary areas implies a potentially radically different interior circulation than is possible with uniform mixing. Whether ocean circulation models, either simple box or full numerical ones, neither explic...

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Vertical mixing, energy, and the general circulation of the oceans

The authors describe carbon system formulation and simulation characteristics of two new global coupled carbon–climate Earth System Models (ESM), ESM2M and ESM2G. These models demonstrate good climate fidelity as described in part I of this study while incorporating explicit and consistent carbon dynamics. The two models differ almost exclusively in the physical ocean component; ESM2M uses the Modular Ocean Model version 4.1 with vertical pressure layers, whereas ESM2G uses generalized ocean layer dynamics with a bulk mixed layer and interior isopycnal layers. On land, both ESMs include a revised land model to simulate competitive vegetation distributions and functioning, including carbon cycling among vegetation, soil, and atmosphere. In the ocean, both models include new biogeochemical algorithms including phytoplankton functional group dynamics with flexible stoichiometry. Preindustrial simulations are spun up to give stable, realistic carbon cycle means and variability. Significant differences...

GFDL’s ESM2 Global Coupled Climate–Carbon Earth System Models. Part I: Physical Formulation and Baseline Simulation Characteristics

By comparing observations from six diverse sites in the mid-latitude thermocline, we find that, to within a factor of 2, 〈eIW〉=7×10‐10〈N2/N02〉〈S104/SGM4〉 W kg‐1, where 〈eIW〉 is the average dissipation rate attributable to internal waves; N0 = 0.0052 s−1 is a reference buoyancy frequency; S10 is the observed shear having vertical wavelengths greater than 10 m; and SGM is the corresponding shear in the Garrett and Munk spectrum of internal waves. The functional form agrees with estimates by McComas and Muller and by Henyey, Wright, and Flatte of the rate of energy transfer within the internal wave spectrum, provided the energy density of the internal waves is treated as a variable instead of one of the constant parameters. Following Garrett and Munk, we assume that 〈S104/SGM4〉=〈EIW2/EGM2〉, where EIW is the observed energy density and EGM is the energy density used by Garrett and Munk. The magnitude of eIW is twice that of Henyey et al. and one third that of McComas and Muller. Thus the observations agree with predictions sufficiently well to suggest that (1) a first-order understanding of the link between internal waves and turbulence has been achieved, although Henyey et al. made some ad hoc assumptions and Garrett and Munk's model does not match important features in the internal wave spectrum reported by Pinkel, and (2) the simplest way to obtain average dissipation rates over large space and time scales is to measure 〈N2/N02〉〈S104/SGM4〉. Even though the observations were taken at latitudes of 42°−11.5°, the variability in the Coriolis parameter ƒ was too limited for a conclusive test of the ƒ dependence also predicted for 〈eIW〉 by the wave-wave interaction models. An exception to the scaling occurs east of Barbados in the thermohaline staircase that is apparently formed and maintained by salt fingers. Although e in the staircase is very low compared with rates at mid-latitude sites, it is 8 times larger than predicted for e due only to internal waves.

Scaling turbulent dissipation in the thermocline

Internal tides are internal gravity waves generated in stratified waters by the interaction of barotropic tidal currents with variable bottom topography. They play a role in dissipating tidal energy and lead to mixing in the deep ocean. Key dimensionless parameters governing their generation include the tidal excursion compared with the scale of the topography, the bottom slope compared with the angle at which rays of internal waves of tidal frequency propagate, and the height of the topography compared with the depth of the ocean. Recent theoretical developments for parts of this parameter space particularly relevant to the deep ocean show that most of the energy flux is associated with low modes that propagate away from the generation region. For isolated features this energy flux is not strongly dependent on the bottom slope. Intense beams of internal tidal energy are expected near “critical slopes," bottom slopes equal to the ray slope, and lead to local mixing.

Internal Tide Generation in the Deep Ocean

A patch of sulfur hexafluoride was released in May 1992 in the eastern North Atlantic on an isopycnal surface near 300 m depth and was surveyed over a period of 30 months as it dispersed across and along isopycnal surfaces The diapycnal eddy diffusivity K estimated for the first 6 months was 012±002 cm2/s, while for the subsequent 24 months it was 017±002 cm2/s The vertical tracer distribution remained very close to Gaussian for the full 30 months, as the root mean square (rms) dispersion grew from 5 to 50 m Lateral dispersion was measured on several scales The growth of the rms width of the tracer streaks from less than 100 m to approximately 300 m within 2 weeks implies an isopycnal diffusivity of 007 m2/s at scales of 01 to 1 km, larger than expected from the interaction between vertical shear of the internal waves and diapycnal mixing Teasing of the overall patch, initially about 25 km across, into streaks with an overall length of 1800 km within 6 months supports predictions of exponential growth by the mesoscale strain field at a rate of 3±05 × 10−7 s−1 The rms width of these streaks, estimated as 3 km and maintained in the face of the streak growth, indicates an isopycnal diffusivity of 2 m2/s at scales of 1 to 10 km, much greater than expected from internal wave shear dispersion The patch was painted in, albeit streakily, by 12 months, confirming expectations from analytical and numerical models Homogenization of the patch continued during the subsequent 18 months, while the patch continued to spread with an effective isopycnal eddy diffusivity on the order of 1000 m2/s, acting at scales of 30 to 300 km

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JC01738

Mixing of a tracer in the pycnocline

The energy and action flow through the small-scale part of the oceanic internal wave field is modeled by use of the eikonal technique, which is not subject to a weak interaction assumption. Both Monte Carlo calculations and a simplified model are presented and found to agree. It is found that the action flows toward slightly higher frequency (and thus the waves gain energy), in striking contrast to weak interaction predictions of a strong frequency decrease. The energy dissipation scales with depth as N2 cosh−1 (N/f), in agreement with measurements. The overall level is, however, a factor of 4 smaller than measurements. Possible sources of this discrepancy are discussed. A comparison is made with previous theoretical approaches for the depth dependence of dissipation.

Energy and action flow through the internal wave field: An eikonal approach

The net integrated energy flux into a train of internal waves is evaluated in a two-layer model. The nonzero value for this integral results from the difference in the stratification between the initial and final state, similar to the energy supply to a surface bore. We apply this expression to waves measured by Wesson and Gregg [1988] in the Strait of Gibraltar and to waves measured by Farmer and Smith [1980] in Knight Inlet. We find the energy supply to be important to the energetics, but the data do not allow a definitive test of the conjecture that the primary energy balance is between this supply and dissipation. We contrast our conjecture to the solitary-wave considerations of Bogucki and Garrett [1993].

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/96JC03558

Energetics of borelike internal waves

A series expression is developed for the fourth moment of a beamed field incident on a random phase screen or an extended medium. The series has a symmetry that allows its first few terms to generate useful approximations at both low and high spatial frequency. The parabolic wave equation, the Markov approximation, and Gaussian refractive index fluctuations are assumed. The result for the phase screen is obtained by Green's function techniques. The extended-medium result is derived in an analogous manner by using path integral methods. The same results are also derived by moment-equation methods. The behavior of the leading terms is compared to previous results for plane-wave and point-source geometries.

Solution for the fourth moment of waves propagating in random media

Calcul de la dynamique des petites ondes a l'aide d'une formulation hamiltonienne canonique. Resultats similaires a ceux de Longuet-Higgins (1987)

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112088001090

The energy and action of small waves riding on large waves

Examples of gauge transform pairs of fields $\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}(x)$, ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}}^{\ensuremath{'}}(x)$ in non-Abelian gauge theories are constructed in which (1) both are in the Coulomb gauge, (2) both have zero topological charge, (3) both fall faster than $\frac{1}{r}$ at large $r$, and therefore occur in the compactified theory. These examples illustrate the fact that the Gribov ambiguity encompasses a larger variety of phenomena than those described by instantons.

Frank S. Henyey

Papers

Energy and action flow through the internal wave field: An eikonal approach

Energetics of borelike internal waves

Solution for the fourth moment of waves propagating in random media

The energy and action of small waves riding on large waves

Gribov ambiguity without topological charge