Image courtesy of Harper Simmons
I am interested in understanding how three-dimensional turbulence in the ocean impacts climate.
Turbulent diffusivities parameterize the effect of small-scale chaotic wave breaking in the ocean. They are characterized by a length scale, L, and a time scale, T, and have dimensional units L^2/T. In the surface and bottom boundary layers, values may easily exceed .1 m^2 /sec. Where conditions are not favorable for turbulence to develop, finite levels of mixing are maintained by the background gravity wave field with values up to 10^-4 m^2/sec.
This background value is usually given by a constant in climate models. Numerous studies have explored climate sensitivity to this parameter (see, e.g. Samelson and Vallis, 1997). Is it realistic to consider the background as being uniform in space and/or time for the purpose of simulating the long term climate of the ocean?
Variations do exist owing to environmental parameters such as bathymetry, tides, storms, and physical laws governing the behavior of internal waves. Bob Hallberg and I have a manuscript in JPO which examines the impact of a latitudinally-varying diffusivity with low values near the equator arising from internal wave dynamics (Gregg, 2003) . Critical to this research is the newly-developed GOLD isopycnal ocean model developed by Hallberg and Alistair Adcroft at NOAA's GFDL. There are 3 reasons why this model is well suited for this study:
- Diapycnal fluxes are handled explicitly. It is difficult to accurately account for cross-isopycnal fluxes in traditional z-coordinate models as they are often hidden in the numerics.
- Mixing can be controlled with extreme precision.
- The model is part of a coupled climate system which conserves heat and freshwater (FMS) and is suitable for climate study.
Internal Gravity Wave Behavior
Gravity waves in the ocean are continuously excited by tides and winds. Their intrinsic frequency in a rotating system is in the range (f,N), where f is the Coriolis parameter and N is the buoyancy frequency. The maximum frequency is N for pure gravity waves.
Through their mutual interaction (wave-wave), interaction with mesoscale or frontal features (wave-mean flow), or interaction with topography, internal waves are modulated in the frequency-wavenumber domain. Dissipation occurs at high vertical wavenumbers, so that random wave interactions may trigger turbulence.
Plane wave solutions obey the approximate dispersion relation,
k_h = k_v [ (w^2 - f^2) / (N^2 - w^2) ] ^1/2,
where k_h and k_v are the horizontal and vertical wavenumbers and w is the intrinsic frequency. Near-inertial waves have a small aspect ratio (k_h / k_v) and parcel motions are near the horizontal plane. Assuming that the internal wave spectrum follows the profile given by Garrett and Munk (GM, 1972), the energy-weighted average aspect ratio ,
(k_h/k_v) ~= f /N ln(2N /f)
We investigated wave-wave interactions of the type proposed by Henyey et al, 1986 ( HWF86). This involves the propagation of single test waves through a background flow sampled randomly from the GM wave field. As the wave encounters vertical shear, its wavenumber/frequency is randomly displaced following the dispersion relation. The rectified effect of these interactions is a net transfer of energy to dissipative scales. A fraction of the turbulent energetic dissipation drives irreversible diapycnal overturns which do work on the system to homogenize the fluid. HWF86 proposed that the rate of wave-breaking is linearly related to the horizontal wavenumber. Waves with larger horizontal wavenumber, or shorter lengthscale, break more frequently. The argument follows (see above) that in the tropics, the wave field exhibits much larger horizontal scales at a given vertical wavenumber compared to mid-latitudes, resulting in less dissipation. This is supported by microstructure data as reported by Gregg 2003
Turbulent dissipation rates below the main thermocline as measured by profiling microstructure instruments at various latitudes, along with the predicted values from Gregg et al, (2003)
Climate Model Study
We used an isopycnal ocean model , GOLD, to assess climate sensitivity to extremely low equatorial diffusivities. The minimum value at the equator is about 10^-6 m^2/sec and near 10^-5 m^2/sec in mid-latitudes.
We find that the equatorial drop-off in dissipation has a dramatic effect on the structure of the subtropical pycnocline.
- Peak stratification in the upper ocean is in better agreement with historical CTD and ARGO data, mainly along the eastern boundary and the northern ITCZ.
- Coupled model drift in the depth of Pacific sigt=26.4 decreases by about 30% in a 400 year experiment. This corresponds to cooling by 1-2 degC over much of the tropics at depths between 100 and 300 meters.
- Upwelling of Intermediate water in the Western tropics decreases by 1-2 Sv. This is balanced by increased northward inflow from the Southern Ocean at densities lighter than sigt=26.4 and increased outflow through the ITF at densities greater than sigt=26.4.
- Entrainment temperatures along the equator are warmer in the eastern equatorial Pacific upwelling region (Nino3), increasing evaporative cooling and cloud cover.
- Colder entrainment temperatures emerge along the eastern boundary (Peru, Oregon).
Top: Temperature change at 140W based on a 400 year coupled model integration with the latitudinally-varying profile for background diffusivity compared to the control case with a uniform background. Bottom: relative buoyancy frequency change at 140W.
JPO.
