June 2025 | Oceanography
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criterion than CZA. Accounting for the isopycnal layering in
HYCOM, as in CZB, a maximum of 12 diurnal modes could be
resolved at the equator.
Vertical Grid Spacing in Idealized Models
Recent discussions among the oceanography community
resolve that global models can achieve a more accurate ocean
state if they include tidal forcing and have a horizontal grid spac
ing on the order of 1/50° or finer (the most up-to-date global
HYCOM has 1/25° grid spacing). However, the optimal num
ber of vertical layers needed in submesoscale resolving mod
els to resolve internal tides and their energetics is unknown.
To explore this question, we used an idealized HYCOM con
figuration with 1/100° horizontal grid spacing (~1 km), forced
only by the semidiurnal (M2) tides over a centrally spaced
ridge, and varied the number of layers in the simulations from
8 to 128 (Figure 4; Hiron et al., 2025). The idealized configu
ration allowed the problem to be isolated from contamination
by ocean eddies and currents while resolving all the physics
allowed in HYCOM.
Each idealized simulation was initialized with a climatologi
cal temperature profile averaged over the Cape Verde area and
constant salinity. The domain size, approximately 8,000 km in
the zonal direction, was large enough to prevent the reflection
of internal tides at the boundaries. The vertical grid discretiza
tion was chosen based on characteristic wavelengths of differ
ent IGW modes. To generate internal tides, a steep ridge with a
Gaussian shape was added in the center of the domain. The crit
icality of the slope, which is a measure of the ridge steepness
normalized by the ray slope of the internal waves, was larger
than one, allowing for nonlinear waves and wave beams to be
generated (Garrett and Kunze, 2007).
The wave beams were the strongest near the ridge (Figure 4a).
The depth-integrated vertical KE of the 8- and 16-layer sim
ulations differed from the others in amplitude and phase
(Figure 4b). As the number of layers increased, the simulations
became more similar. For the 48- to the 128-layer simulations,
amplitude and phase were similar across simulations. When
integrated from 0–2,000 km, the tidal barotropic-to-baroclinic
energy conversion, the vertical kinetic energy, and the turbu
lent dissipation were greatest in the 128-layer simulation and
decreased with coarser vertical grid spacing (Hiron et al., 2025).
These variables converged for the simulations with greater than
48 layers, showing that the number of vertical layers can deter
mine the IGW energy transfer; however, these results may differ
at other horizontal grid spacings.
A Final Word on Grid Spacing: Interaction of
IGWs and Eddies
The IGW spectrum covers the transfer of energy between IGWs
and the transfer of KE from its injection at large scales in eddies,
near-inertial waves, and tides to the smallest scales. It is applica
ble globally but uses free parameters to account for regional and
seasonal variations of the ocean state, such as the slowly varying
background circulation and surface forcing. Ongoing research
focuses on what determines these parameters and any devia
tion from this spectral form; nonlinear interactions involving
IGWs, such as those on display in the Amazon basin and near
Mascarene Ridge, are thought to be of particular importance.
Previous work on IGW-IGW interactions has identified
some important processes that move energy to smaller scales
(McComas and Bretherton, 1977; Dematteis et al., 2022). These
FIGURE 4. (a) Snapshot of the vertical velocity for the 128-layer simulation, zoomed in to the ridge centered at 40°W, where the domain is symmetric
about the ridge. The black triangles indicate the location of the sound speed profiles in (c,d). (b) Time-averaged, depth-integrated vertical kinetic energy
(½ ∫w2dz), where w is the vertical velocity, for different vertical discretization: 8, 16, 32, 48, 64, 96, and 128 layers. (c) Mean and (d) standard deviation
of sound speed 83 km from the ridge for the 8-, 16-, 32-, 48-, and 96-layer simulations.