That is, using ζ=0ζ=0, setting k   and m   according to the grid spacing and holding M2,f,νhM2,f,νh, and νvνv constant, the growth rates can be plotted purely as a function of N2N2. Furthermore, beginning with an initial state where Ri=0.25Ri=0.25, it is known a priori   that N2N2 must increase by a factor of 4 to reach the stable state of Ri=1Ri=1. Then the growth rates can be calculated for a discrete set of values of N2N2 between N02 and

4N02 to predict the SI-stable value of N2N2 that will be reached, and by extension the stable value of Ri  . Note that (23) and (24) require both M2M2 and N2N2 to be constant in space and time and GSI-IX in vitro the perturbations to be small in amplitude, and are approximations to the instantaneous growth rate found by holding N2N2 fixed at each instant in time. The grid spacing ΔxΔx is varied from simulation to simulation to test the hypothesis that the amount of restratification depends on how well the SI modes are resolved. The pseudo-spectral numerical solver uses a IWR1 Two-Thirds Rule de-aliasing (Orszag, 1971) to prevent aliasing of high-wavenumber modes, making the shortest resolved wavelength in the model λ=3Δxλ=3Δx. The higher-resolution

simulations (subscripts 1 through 5) are meant to demonstrate that the restratification can be limited by the stratification and viscosity, not necessarily the model resolution. The lowest-resolution simulations do not resolve the most-restratifying mode, and demonstrate restratification that is limited (subscript 6) and completely negated (subscript 7) due to the model resolution. The dimensional width of the domain varies according to the choice of ΔxΔx for each individual simulation, but the depth of the mixed layer is set to be 300 m in all cases. A uniform grid of size (Ny,Nz)=(128,80)(Ny,Nz)=(128,80) points is used, with the vertical grid spacing set to a constant Δz=5Δz=5 m. Using this number of points in the horizontal ensures that the domain is wide

enough to resolve Immune system multiple SI overturning cells in all cases, and that the largest SI modes will not be excluded even in the finest-resolution runs. The vertical diffusivity κv=1×10-6κv=1×10-6 m2 s−1 was set to be very small to prevent highly stratified fluid from diffusing up from the thermocline, and for simplicity in the stability analysis (Appendix A) the vertical viscosity was set to match this value. At higher values (i.e. κv⩾1×10-4κv⩾1×10-4 m2 s−1), diffusion caused the lowest parts of the mixed layer to become stabilized to SI before the instability became nonlinear. This effectively reduced the lengthscale of the gravest vertical mode and reduced the amount of restratification that could occur.