Tidal Mixing Over Rough Topographystory by Helen Hill
This month we focus on the work of recent doctoral graduate Maxim Nikurashin (now working at GFDL) who, in a collaboration with long time user Sonya Legg, has been using a non-hydrostatic, 2-D version of the MITgcm to explore tidal mixing over rough topography (Fig. 1). The MITgcm’s elegant non-hydrostatic and topography-representing capabilities make it an ideal choice for this kind of high-resolution process study.
Taking the Mid-Atlantic Ridge (MAR) region of the Brasil Basin (Fig. 2) as the prototype for their idealised problem, Nikurashin and Legg constructed synthetic bottom boundary conditions having the same spectral characteristics as the abyssal hills observed to cluster along the long, deep canyons of the MAR. It is believed (Polzin et al., 1997) that the enhanced mixing observed within O(1km) of the bottom at this location (Fig. 3) is the result of radiation and dissipation of breaking internal waves generated by tidal flow over the especially rough local topography.
With the ultimate goal of developing physically-based parameterizations for general circulation model use, Nikurashin and Legg set about reproducing the essence of the MAR tidal mixing scenario in multiple 2D realisations of the flow associated with the barotropic M2 tide, U(t), as it interacts with MAR-like synthetic bottom topography (U(t) = Uocos(ωt), in their control u0 = 2.5cm/s, ω=1.4e-4s-1). To understand the impact of depth-varying stratification on their solutions, Nikurashin and Legg constructed two stratification scenarios one depth-independent, the other an idealisation of the observed profile. Working at very high resolution (Δx = 10 – 30 m, Δz = 5 – 10 m, viscosity = 10-3 m2s-1, diffusivity = 10-5 m2s-1), the domain was periodic and bounded by a surface sponge layer.
Figure 1, a snapshot of the wave zonal velocity deviation from the barotropic tide for their control simulation, clearly demonstrates the upward radiation and dissipation of the internal tides generated in N&L’s realizations.
As in Polzin et al’s 1997 observations, mixing is enhanced in the bottom O(1km), rising again through the thermocline (Figure 4) with the total depth-integrated energy dissipation of 3.2mWm-2 falling close to Polzin et al.’s value of 3.7mWm-2. Further analysis demonstrated both bottom energy conversion and energy dissipation departed markedly from linear theory: Predictions based on Bell (1975) over-estimating energy conversion for steep topography (Figure 5) and energy dissipation decaying much faster from the bottom than the vertical structure used in Simmons et al., 2004, recently proposed, energetically consistent mixing parameterization, relating diapycnal diffusivity to energy dissipation due to internal tides (Figure 6).
Want to find out more? – contact Max.
Polzin, K. 1997: Spatial Variability of turbulent mixing in the abyssal ocean. Science, 276, 93-96.
Simmons, H.L., S.R. Jayne, L.C. St.Laurent, and A.J. Weaver, 2004: Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modelling,6 , 245-263.