After mulling over the necessity for downward mixing of solar heated surface waters and thinking about coriolis forces, I arrived at the Wikipedia page on internal tides, which has some interesting things to tell us, not least about how poorly GCM’s handle ocean mixing:
http://en.wikipedia.org/wiki/Internal_tides
The surface tide propagates as a wave, in which water parcels in the whole water column oscillate in the same direction at a given phase (i.e, in the trough or at the crest, Fig. 1, top). At the simplest level, an internal wave can be thought of as an interfacial wave (Fig. 1, bottom). If there are two levels in the ocean, such as a warm surface layer and cold deep layer separated by a thermocline,then motions on the interface are possible. The interface movement is large compared to surface movement. The restoring force for internal waves and tides is still gravity but its effect is reduced because the densities of the 2 layers are relatively similar compared to the large density difference at the air-sea interface. Thus larger displacements are possible inside the ocean than at the sea surface.
Tides occur mainly at diurnal and semidiurnal periods. The principal lunar semidiurnal constituent is known as M2 and generally has the largest amplitudes. (See external links for more information.)
Where are internal tides found?
The largest internal tides are generated at steep, midocean topography such as the Hawaiian Ridge, Tahiti, the Macquarie Ridge, and submarine ridges in the Luzon Strait. [3] Continental slopes such as the Australian North West Shelf also generate large internal tides. [4] These internal tide may propagate onshore and dissipate much like surface waves. Or internal tides may propagate away from the topography into the open ocean. For tall, steep, midocean topography, such as the Hawaiian Ridge, it is estimated that about 85% of the energy in the internal tide propagates away into the deep ocean with about 15% of its energy being lost within about 50 km of the generation site. The lost energy contributes to turbulence and mixing near the generation sites. [5] [6] It is not clear where the energy that leaves the generation site is dissipated, but there are 3 possible processes: 1) the internal tides scatter and/or break at distant midocean topography, 2) interactions with other internal waves remove energy from the internal tide, or 3) the internal tides shoal and break on continental shelves.
Where do internal tides go and what happens to them along the way?
Briscoe (1975) succinctly noted that “We cannot yet answer satisfactorily the questions: ‘where does the internal wave energy come from, where does it go, and what happens to it along the way?’” [7] Although technological advances in instrumentation and modeling have produced greater knowledge of internal tide and near-inertial wave generation, Garrett and Kunze (2007) observed 33 years later that “The fate of the radiated [large-scale internal tides] is still uncertain. They may scatter into [smaller scale waves] on further encounter with islands[8] [9] or the rough seafloor [10] , or transfer their energy to smaller-scale internal waves in the ocean interior [11] ” or “break on distant continental slopes [12]”. [13] It is now known that most of the internal tide energy generated at tall, steep midocean topography radiates away as large-scale internal waves. This radiated internal tide energy is one of the main sources of energy into the deep ocean, roughly half of the wind energy input .[14] Broader interest in internal tides is spurred by their impact on the magnitude and spatial inhomogeneity of mixing, which in turn has first order effect on the meridional overturning circulation [3] [14] .[15]
The internal tidal energy in one tidal period going through an area perpendicular to the direction of propagation is called the energy flux and is measured in Watts/m2. The energy flux at one point can be summed over depth- this is the depth-integrated energy flux and is measured in Watts/m. The Hawaiian Ridge produces depth-integrated energy fluxes as large as 10 kW/m. The longest wavelength waves are the fastest and thus carry most of the energy flux. Near Hawaii, the typical wavelength of the longest internal tide is about 150 km while the next longest is about 75 km. These waves are called mode 1 and mode 2, respectively. Although Fig. 1 shows there is no sea surface expression of the internal tide, there actually is a displacement of a few centimeters. These sea surface expressions of the internal tide at different wavelengths can be detected with the Topex/Poseidon orJason-1 satellites (Fig. 2). [9] Near 15 N, 175 W on the Line Islands Ridge, the mode-1 internal tides scatter off the topography, possibly creating turbulence and mixing, and producing smaller wavelength mode 2 internal tides. [9]
Figure 2: The internal tide sea surface elevation that is in phase with the surface tide (i.e., crests occur in a certain spot at a certain time that are both the same relative to the surface tide) can be detected by satellite (top). (The satellite track is repeated about every 10 days and so M2 tidal signals are shifted to longer periods due to aliasing.) The longest internal tide wavelengths are about 150 km near Hawaii and the next longest waves are about 75 km long. The surface displacements due to the internal tide are plotted as wiggly red lines with amplitudes plotted perpendicular to the satellite groundtracks (black lines). Figure is adapted from Johnston et al. (2003).
The inescapable conclusion is that energy is lost from the surface tide to the internal tide at midocean topography and continental shelves, but the energy in the internal tide is not necessarily lost in the same place. Internal tides may propagate thousands of kilometers or more before breaking and mixing the abyssal ocean.
Their importance to abyssal mixing and the meridional overturning circulation
The importance of internal tides and internal waves in general relates to their breaking, energy dissipation, and mixing of the deep ocean. If there were no mixing in the ocean, the deep ocean would be a cold stagnant pool with a thin warm surface layer. [16]While the meridional overturning circulation (also referred to as the thermohaline circulation) redistributes about 2 PW of heat from the tropics to polar regions, the energy source for this flow is the interior mixing which is comparatively much smaller- about 2 TW. [14] Sandstrom (1908) showed a fluid which is both heated and cooled at its surface cannot develop a deep overturning circulation. [17] Most global models have incorporated uniform mixing throughout the ocean because they do not include or resolve internal tidal flows.
However, models are now beginning to include spatially variable mixing related to internal tides and the rough topography where they are generated and distant topography where they may break. Wunsch and Ferrari (2004) describe the global impact of spatially inhomogeneous mixing near midocean topography: “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… 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… neither explicitly accounting for the energy input into the system nor providing for spatial variability in the mixing, have any physical relevance under changed climate conditions is at issue.” There is a limited understanding of “the sources controlling the internal wave energy in the ocean and the rate at which it is dissipated” and are only now developing some “parameterizations of the mixing generated by the interaction of internal waves, mesoscale eddies, high-frequency barotropic fluctuations, and other motions over sloping topography.”
Internal tides at the beach
Internal tides may also dissipate on continental slopes and shelves [12] or even reach within 100 m of the beach (Fig. 3). Internal tides bring pulses of cold water shoreward and produce large vertical temperature differences. When surface waves break, the cold water is mixed upwards making the water cold for surfers, swimmers, and other beachgoers. Surface waters in the surf zone can change by about 10oC in about an hour.
Tallbloke's Talkshop 
TB,
Check again where internal tides have big mixing effects. It’s a fairly small fraction of the ocean surface. You need relatively shallow water and something that will drive fairly strong currents.
The article doesn’t suggest that this is a big problem with AOGCM’s, and it’s for that reason. They assume uniform mixing. The areas that deviate from that are toward the lower range for resolution, but they are trying to resolve them now.
The reason that you don’t get these effects much in deep ocean is that they involve shearing and that requires torque. This generally requires a solid surface. Winds apply some torque, but not that much.
Gravity waves from wind (surface) or internal tides (between layers) create little shear in open sea, as shown by the fact that they can travel long distances.
Hi Nick, and thanks for dropping by.
http://en.wikipedia.org/wiki/Walter_Munk
“According to Sandström’s theorem (1908), without the occurrence of mixing in the abyssal ocean, such as may be driven by internal tides, most of the ocean would become cold and stagnant, capped by a thin, warm surface layer.”
So, how to explain the relatively uniform mixing of solar energy entering the top ~300′ of the ocean down to the thermocline, which varies in depth from 100′ in the tropics to over 3000′ at the temperate latitudes?
According to the Wiki article above:
“Garrett and Kunze (2007) observed 33 years later that “The fate of the radiated [large-scale internal tides] is still uncertain. They may scatter into [smaller scale waves] on further encounter with islands[8] [9] or the rough seafloor [10] , or transfer their energy to smaller-scale internal waves in the ocean interior [11] ” or “break on distant continental slopes [12]”. [13] It is now known that most of the internal tide energy generated at tall, steep midocean topography radiates away as large-scale internal waves. This radiated internal tide energy is one of the main sources of energy into the deep ocean, roughly half of the wind energy input ”
Scattering, mixing, it’s all meat and drink to me.
Regarding your “small fraction of the surface”, the article says:
“The inescapable conclusion is that energy is lost from the surface tide to the internal tide at midocean topography and continental shelves, but the energy in the internal tide is not necessarily lost in the same place. Internal tides may propagate thousands of kilometers or more before breaking and mixing the abyssal ocean.”
Given the uncertainties, I don’t think we should be making any categorical statements at this point.
The other big question for me is what effect changes in length of day have on the ocean. It’s only a few milliseconds change over a couple of decades, but the masses involved in the resultant sloshing are pretty enormous, and the timing of the big oceanic oscillations seems to be in step with mulltidecadal changes in LOD. (We won’t go into the planetary motion (green curve) here)
Thoughts?
Cheers
Also there is this new finding:
http://www.nature.com/nature/journal/vaop/ncurrent/full/nature10013.html
Interannual atmospheric variability forced by the deep equatorial Atlantic Ocean
Peter Brandt, Andreas Funk, Verena Hormann, Marcus Dengler, Richard J. Greatbatch & John M. Toole
Climate variability in the tropical Atlantic Ocean is determined by large-scale ocean–atmosphere interactions, which particularly affect deep atmospheric convection over the ocean and surrounding continents1. Apart from influences from the Pacific El Niño/Southern Oscillation2 and the North Atlantic Oscillation3, the tropical Atlantic variability is thought to be dominated by two distinct ocean–atmosphere coupled modes of variability that are characterized by meridional4, 5 and zonal6, 7 sea-surface-temperature gradients and are mainly active on decadal and interannual timescales, respectively8, 9. Here we report evidence that the intrinsic ocean dynamics of the deep equatorial Atlantic can also affect sea surface temperature, wind and rainfall in the tropical Atlantic region and constitutes a 4.5-yr climate cycle. Specifically, vertically alternating deep zonal jets of short vertical wavelength with a period of about 4.5 yr and amplitudes of more than 10 cm s−1 are observed, in the deep Atlantic, to propagate their energy upwards, towards the surface10, 11. They are linked, at the sea surface, to equatorial zonal current anomalies and eastern Atlantic temperature anomalies that have amplitudes of about 6 cm s−1 and 0.4 °C, respectively, and are associated with distinct wind and rainfall patterns. Although deep jets are also observed in the Pacific12 and Indian13 oceans, only the Atlantic deep jets seem to oscillate on interannual timescales. Our knowledge of the persistence and regularity of these jets is limited by the availability of high-quality data. Despite this caveat, the oscillatory behaviour can still be used to improve predictions of sea surface temperature in the tropical Atlantic. Deep-jet generation and upward energy transmission through the Equatorial Undercurrent warrant further theoretical study.
So, vertical jets are going to cause shear in horizontal internal tidal flows, which along with coriolis effects to introduce some swirling, looks like a pretty good mixing mechanism to me, No?
TB,
Gravity waves between layers can propagate long distances, but only because they don’t do much. Think of ocean waves. They produce relatively little mixing in deep water – a lot when they break (because they are then subject to torque, which produces eddies). But the fraction of the ocean that has breaking waves is small (white-tops etc are a bit different, and deep gravity waves don’t behave like that).
Circumstances that mix heat, dissolved gases etc also mix momentum, and that causes loss of kinetic energy. So you need a supply of KE. Wind provides some. This tide mechanism also provides some, but its effect is localised. The energy is created by the interaction of currents and topography (continental shelves etc); some is dissipated locally (with mixing), and some is propagated as gravity waves to places where it can break (like surf), also on topography. There’s mixing there. But if the wave propagation itself causes a lot of mixing, then it is rapidly dissipated, and the waves won’t go far.
I’ll pass on length of day.
Regards.
Thanks again Nick for your input. I’m coming at this from a logical perspective. In order for the amount of energy required to expand the ocean by the amount measured by satellite altimetry, (the steric component of sea level rise), to be present, it *must* be mixed down somehow.
That’s simple logic.
The solution is either the satellites are wrong, in which case there is no global warming and we can all go home, or the energy from the sun is mixed down, because the additional downwelling radiation from co2 isn’t either capable or sufficient.
Take your pick, or offer another logical explanation, but don’t duck the issue.
‘Malaga View’ posted this on suggestions:
ARCTIC ENVIRONMENT BY THE MIDDLE OF THIS CENTURY
At around 2040-2050 we will be in a new major Solar Minimum. It is to be expected that we will then have a new “Little Ice Age” over the Arctic and NW Europe. The past Solar Minima were linked to a general speeding-up of the Earth’s rate of rotation. This affected the surface currents and southward penetration of Arctic water in the North Atlantic causing “Little Ice Ages” over northwestern Europe and the Arctic.
Click to access Moerner_Science_environm_sea_level_3_11_Paper_534.pdf
4.5 years is a fourth of the 18 year Saros cycle -27 days = 6558 day period I use for cyclic forecasting of the weather. There are obviously many patterns of mixing in the oceans and atmosphere driven by the declinational tides of the moon, it might be wise to consider them in the research into weather forecast and climate predictions.
(It works for me, it might work for more people if they looked into it.)
“In order for the amount of energy required to expand the ocean by the amount measured by satellite altimetry, (the steric component of sea level rise), to be present, it *must* be mixed down somehow.”
That’s not really true. The amount of sea level rise is little affected by mixing. You can work that out from the volume expansion formula:
ΔV = αV ΔT = α/(ρc) ρcV ΔT = α/(ρc) ΔH
where α is coef of expansion, ρ density, c specific heat, H heat, T temp, V volume
Since α/(ρc) is pretty much constant, total ΔV, and hence sea level rise, is proportional to the heat added, but it doesn’t matter how it is distributed (as long as it doesn’t cause freezing or boiling).
It is mixed down – but the value of sea level rise doen’t depend on it.
Nick,
what you say is correct, but come on, we know from observation that temperature falls off pretty much linearly from the bottom of the well mixed surface waters to the thermocline, which is naything up to 4000′ below. I’ve done the calcs and I know how much energy was retained by the ocean between 1993 and 2003 to cause the steric component of sea level rise.
Anyway, you agree it is mixed down, but then you also say internal tides aren’t enough to account for it.
So how is it mixed down?
I want to know the answer! 🙂
By the way, I think you’re wrong that waves in open water don’t mix the water below, here’s the diagram:
So that and diurnal tides account for the mixing of the well mixed surface water down to 30′ or so, but how about the rest?
The article says internal tides do around 50% of what the wind does.
Richard:
Sounds very plausible. The Moon pulls the deep ocean around as well as the surface after all.
TB,
I didn’t say that deep sea waves do no mixing – I said “relatively little”. Relative to mixing in the breaking zone.
Mixing requires shear. The closed cycle elliptical paths of ocean waves don’t do much shearing. Mixing paint – just whirling the can around in a circular path doesn’t help. Of course the water is moving relative to calm water at depth, so there is some shear. But not much relative to the total motion.
You’re right that there is some mixing down. But not so much, which is why the oceans take time to absorb the extra CO2 we put out, and why AGW heat can build up at the surface. When you speak of penetration to hundreds of metres, the time scales are multi-decadal.
I was thinking about my earlier comment on sea rise relating simply to heat absorbed. It’s not quite true that the coefficients are constant – the volume expansion coefficient varies quite a lot with temperature, going down to near zero at 4C. That actually has the contrary effect – as heat diffuses down, the total expansion is less.
Hi Nick,
I think that with meridional flows crossing tidal flows, getting whisked by upward jets, sloshed by changes in planetary rotational velocity, and whipped by wind, there are probably plenty enough mixing opportunities for molecules of water warmed by the sun to end up in the deep. It must be so for the ocean to warm and expand on multidecadal timescales when there is a run of high solar cycles such as in the latter half of the C20th.
We had a big discussion about the relative inability of longwave radiation or ‘AGW heat’ as you call it to penetrate much beyond it’s own wavelength and get mixed down into the ocean compared with solar shortwave which penetrates tens of metres on the blog a while back, so I’ll link to that rather than go into it here:
The volume contraction as diffusion occurs undoubtedly happens as you say. I need to think about it, but my first off the cuff obs is that there is always going to be roughly the same volume of water at 4C no matter how deep it lies.
Cheers
Rog
Many years ago I did research for creation of a sea going city for a science fiction series. I determined that the city floats needed to draft about 300 ft to be below any wave caused displacement. A 10,000ft runway can’t be moving up and down under a landing 747. 😎 pg
Paper on internal tides and mixing:
http://journals.ametsoc.org/doi/pdf/10.1175/1520-0485(2002)032%3C2882%3ATROITI%3E2.0.CO%3B2
And a citation for another:
Walter Munk and Bruce Bills (February 2007), Tides And The Climate: Some Speculations, JOURNAL OF PHYSICAL OCEANOGRAPHY, vol 37, p 135-147
Tidal currents flowing over topographic irregularities on the ocean floor generate internal waves that propagate away from their source. These internal waves arise from the fact that water density increases gradually with increasing depth.