Fig. 1 shows the spectra in x for potential density σ and nitrate N computed at a single depth within the nutricline (150-165 m, depending on the model) over a latitudinal band between 22°N and 24°N, 157.5°W and 150°W. The spectra shown are the average over that domain and either a snapshot is shown or a two-mean mean when available.

The slopes of the spectra have been estimated for zonal wavelengths between 25 and 166 km. We find -2.701 and -2.583 for the nitrate, mean and snapshot, respectively, and -2.318, -2.164, -2.842, -2.365 and -2.721 for σ in the same downward order as in the legend. Thus, the spectrum slope in nitrate and σ are relatively the same in all models and, according to literature (see below), it is the slope expected for the density field in a typical geostrophic turbulent regime.

The spectrum slopes are closed to the slope -2.77 of the spectrum in density in the numerical simulations of Levy and Klein (2004). Especially, the slope for nitrate is larger than the slope from the theoretical value of -1.1 in 2D turbulence (Kraichman 1977; Levy and Klein 2004) and the slope for the phytoplankton, -1.5 ± 0.2, in Levy and Klein’s simulations. Also, according to Levy *et al*. 2001, “it is also known that any tracer field forced by such w-structures is characterized by a spectrum with a -2 slope, i.e., by mesoscale structures much more energetic than small-scale structures (Klein et al., 1998)”. In their numerical simulations, “[t]he production of nitrate sub-mesoscale structures in the upper layers [...] shows that the nitrate spectrum slope is much flatter at 130 m (-1.5) than that at 500 m (-3)”. The different slope between the two depths “result from the different w-features that drive the nitrate distributions at those two depths: quadripolar at 500 m and bipolar at 130 m.”

See `spectrum_x_sigma_ntr_1_10_1_30_HYCOM_snap_year.mat` in `RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/OFES/link_ntr_ntr_grad_dens_SSH` on `ipu1`.