Oceanography | Early Online Release
Tus, it is likely that the mode-1 and mode-2 internal tides inter-
fere constructively at the locations of the patches where their
velocities are in phase and increase the tidal amplitude, steepen
the internal tide, and enhance the energy transfer to higher har-
monics. Te locations of these patches are modulated by the
slowly varying subtidal current and the spring-neap cycle, with
greater energy available to transfer to higher- harmonics during
spring tides (Solano et al., 2023).
Impacts of Horizontal and Vertical Grid Spacing
on IGWs in Global Models
Ocean model grid spacing, both horizontal and vertical, deter-
mines how bathymetry and the wavelengths of IGW modes are
resolved. For example, a decrease in HYCOM horizontal grid size
from 8 km to 4 km can increase the IGW generation and energy
density by about 50%, largely because it increases the number of
internal wave modes resolved (Buijsman et al., 2020).
We examined what diurnal, semidiurnal, and supertidal ver-
tical wave modes could be resolved in a global, 1/25° tidally
forced global HYCOM simulation with 41 layers (Figure 2c).
Horizontal spacing and IGW wavelengths vary spatially in global
ocean models. Earth’s sphericity causes grid spacing to decrease
poleward, while wavelengths of tidally generated IGWs increase
poleward with the increase of the Coriolis frequency (Buijsman
et al., 2025). We used the criterion that a vertical mode could be
resolved if there were at least six to eight horizontal grid spac-
ings per wavelength (Stewart et al., 2017). A similar criterion was
applied for the vertical resolution, called vertical criterion CZA.
However, this criterion was designed for z-coordinate models,
whereas HYCOM is an isopycnal model below the mixed layer.
Terefore, an additional criterion was developed to account for
the changes in vertical and horizontal velocity structure caused
by isopycnals, called vertical criterion CZB.
In the horizontal, internal wave modes with lower frequen-
cies (longer wavelength) were better resolved. For example, K1
had eight modes resolved at the equator and 20 modes near the
K1 turning latitude of about 30° (Figure 2c). (Poleward of this
latitude, the tidal frequency is lower than the Coriolis frequency,
and diurnal IGWs cannot exist.) Te shorter wavelength, M2,
had fewer modes resolved, with only about four modes resolved
at the equator. For supertidal waves, M4, which has the most
energy globally (Buijsman et al., 2025), only two modes were
resolved. Te number of resolved modes was sensitive to the ver-
tical resolution criteria. CZB appeared to be a more appropriate
FIGURE 3. At the Amazon Shelf and the Mascarene Ridge: (a,b) time-mean and depth-integrated kinetic energy transfer (‹Π(τ=9hr)›); (c,d) time-mean,
depth-integrated divergence of supertidal energy flux ( ∙‹FHH›); (e,f) time-mean surface kinetic energy (KE) for the superposition of modes 1 and 2.
Panels (a–f) were modified from Solano et al. (2023). (g) Mean sound speed and (h) standard deviation of sound speed for each the tidally and non-tid-
ally forced HYCOM simulations from May 20–29, 2019, in the Amazon region, plotted by latitude along the dotted line shown in (a). The star and radial
(dashed black line) in (a) are noted for reference in Figure 6. In (b), a short, dashed line indicates the transect used in Figure 5b,c.