The thermodynamic ice-ocean interaction parameterizations used by McPhee (2000) in 1-D Local Turbulence Closure (LTC) simulations of the Weddell Sea Mixed Layer have been implemented in the LES to simulate the freezing and melting of ice. A prescribed mean surface stress derived from observations is applied at the upper model domain, and the velocity boundary condition is nonslip in fluctuations with respect to the mean horizontal velocity at the surface. Heat flux through the ice is also derived from ANZFLUX measurements, and the model ocean heat flux at the upper boundary is
where the freezing point is the boundary temperature is the LES temperature in the first grid level adjacent to the boundary, and is a nondimensional Stanton number, adjusted for consistency with vertical grid size . Freezing and melting of ice is then determined by the imbalance between heat fluxes in the ice and in the ocean.
Several LES runs have been carried out to test the stability of the upper ocean under conditions observed during ANZFLUX at certain times when ocean observations were not made. In general, they agree with the LTC results of McPhee (2000), showing the upper ocean becoming unstable to a process of thermobaric parcel detrainment, but at an earlier point in time. These simulations do not yet account for cabbeling effects, as this term was omitted in the preliminary simulations for comparison with LTC results.
Two of the first simulations are presented on a separate document. Simulation 3 was performed with a domain of 128x128x64 grid points, extended to 128x128x168 after one simulated day. The time step is 4s and the grid resolution 6m. The LES was initialized from averaged typical profiles measured in 1994 on year days 216 and 217 by the Turbulent Instrument Cluster and CTD, and forced with time-dependent surface stress deduced from observations.
Potential temperature is shown on 2 vertical sections and two isothermal surfaces at 0°C (above) and 0.4°C (below) representative of the pycnocline. The animation illustrates the evolution of the plumes into a major convective cell that spreads when it reaches a level of neutral buoyancy near 300m depth.
GIF Movie (5.0MB)
Figures 1-3 below summarize some results from this most recent simulation. High wind in the first two days results in shear production of mixed layer TKE with classical forced mixed layer scaling, (Figure 1, top). Thermobarically unstable parcels are subsequently detrained from the mixed layer in plumes with with small vertical TKE, large negative skewness (Figure 1, second from top) and positive values of below . Large negative values of buoyant TKE production (Figure 1, third plot) resulting from the conversion of TKE to entrainment work, are followed by significant release of potential energy below the mixed layer as the detrained thermobaric plumes become more negatively buoyant with depth. The fourth plot in Figure 1 tracks the net buoyant production of TKE above and below separately, and demonstrates that without thermobaricity the detrained plumes would be a net sink, rather than a source of TKE. This sensitivity (lower right) to the second order terms in the expanded equation of state arises from the high level of compensation between the heat and salinity fluxes (lower left).
Including the cabbeling term in the equation of state will probably delay thermobaric instability, owing to the negative sign of for the plumes (first results of this case can now be seen as an animation here). Mean TKE below the mixed layer is relatively small, but the skewness of the thermobaric plumes is large and negative, and individual plumes (Figure 2) have large downward velocities concentrated in structures about 100m in horizontal scale.
Figure 1: The top figure shows vertical TKE integrated over depth, separately within and below the mixed layer, along with a representative one-third of the dimensional surface stress forcing scale . The profile timeseries of mean skewness is illustrated in the second plot, and buoyancy flux -the work rate for buoyant TKE production- is shown in the third plot. The fourth plot shows the net work rate due to buoyancy production of TKE separately within and below the mixed layer, both with and without thermobaricity. The lower right profile also shows the effect of thermobaricity on buoyant TKE production, averaged over the entire simulation, and the lower left plot decomposes into heat and salinity flux components.
Figure 2: Vertical cross sections of potential temperature (top plot) and vertical velocity (bottom plot), on about day 220 of the simulation, illustrating a detraining thermobaric plume.