The idealized model domain (Fig. ) is a 100 km by 300 km re-entrant channel with a constant depth h=50 m, free-slip walls along the north and south boundaries, and periodic conditions along the east and west boundaries. The model is run on an f-plane (f=10-4 s⁻¹), corresponding to an inertial period of roughly 17.4 h. This bi-directional, baroclinic instability–inducing channel (Bichan) configuration, despite its simplicity and flat bottom, develops a complex ocean state with multiscale interacting submesoscale fronts and eddies. The Bichan setup is a variant of the idealized domain presented in and provides a dynamically rich environment for studying the full lifecycle of frontal eddies, from their formation and frontogenesis to the onset of frontal instabilities, arrest, and eventual decay .

Both MPAS-O and ROMS use vertical grids with 50 equally spaced levels, giving a vertical resolution of 1 m. MPAS-O employs a z* coordinate within an arbitrary Eulerian–Lagrangian framework , while ROMS uses a terrain-following coordinate with surface and bottom stretching parameters (θs,θb)=0. Because the Bichan configuration uses a flat bottom, the vertical coordinates in the two models behave similarly. As a result, differences between MPAS-O and ROMS in these experiments primarily reflect their numerical schemes and subgrid-scale parameterizations rather than vertical coordinate choice. In the realistic nGoM comparison presented in Part 2, vertical coordinate differences may play a larger role. However, because bathymetric gradients on the Texas-Louisiana shelf (where the eddies are prominent) are gentle, coordinate effects should not significantly influence overall model performance. Appendix  presents a proof-of-concept demonstration of the Bichan configuration with variable bathymetry; these simulations are not part of the primary flat-bottom comparison discussed here.

Initial tracer distributions (Fig. a–b) of temperature, T, and salinity, S, are defined by constants, N2=-g∂ρ∂zρ0-1=10-4s-2 and M2=g∂ρ∂yρ0-1=10-6s-2, that define the vertical stratification and lateral density gradients, 1T=T0+N2gαz2S=S0+M2gβy where T0=25 °C, S0=15 g kg⁻¹, α= 1.7×10-4 °C⁻¹ and β= 7.6×10-4 g⁻¹ kg are the linear thermal and haline expansion coefficients in the linearized equation of state, 3ρ=ρ0(1-αT+βS), where ρ0=1027 kg m⁻³ is the reference density. As a result, the initial salinity varies only in cross-channel direction and temperature varies only in the vertical direction. The first deformation radius, estimated as Rd=Nh/f, is approximately 5 km at the start of the simulation, similar to conditions observed on the Texas-Louisiana shelf .

The along-channel u velocity is laterally homogeneous and is gradually relaxed from 0.5 m s⁻¹ to zero towards the bottom (Fig. c). The initial cross-shore velocity is set to zero. A small perturbation to the initial u velocity with a period of 100 km in both the along- and cross-channel directions and an amplitude of 0.01 m s⁻¹ is applied to supply perturbations on which instabilities can form and grow.

Simulations are forced with near-inertial wind stress in the along-channel direction: 4τx=τ0xsin(0.9ft), where τ0x=0.1 Pa is the near-inertial wind stress amplitude, which is slightly stronger than values observed in the nGoM . The purpose of the wind stress is to provide some resonant, near-inertial forcing to make the model more similar to summer conditions in the nGoM and sharpen the fronts .

Our goal is to compare the representation of surface submesoscale dynamics between ROMS and MPAS-O across a range of resolutions ranging from mesoscale eddy-resolving to submesoscale front-resolving. To do so, we conducted a series of 50 d experiments across the following resolutions: 10, 5, 2, 1 km, 500, 200, and 100 m. Details of the model setup across resolutions are provided in the next subsections and summarized in Table .

We apply multiple techniques to compare physical dynamics for all model simulations which include surface and volume integrated energetics, measures of flow invariants, and diagnostics of physical and numerical mixing. Details for each of these are provided in the subsections below.

The representation of submesoscale dynamics varies strongly with horizontal resolution, highlighted by surface relative vorticities during a period of high kinetic energy for both models (Day 12, Fig. ) where submesoscale fronts (O 1–10 km) and eddies (O 50 km, roughly 10 times the deformation radius) emerge across all resolutions. Inter-model comparisons at each resolution shows qualitatively similar results in the representation of eddy and frontal dynamics for both MPAS-O and ROMS. At 5–10 km resolutions (Fig. a–b, h–i), which we consider eddy-permitting, the representation of submesoscale frontal processes is limited by both ocean models. At 1–2 km resolutions (Fig. c–d, j–k), which we consider to be eddy-resolving, relative vorticity magnitude increases and frontal instabilities emerge in both models – dark red areas that appear “braided”. At sub-kilometer resolutions (Fig. e–g, l–n), resolution is sufficient to resolve cross-frontal processes and frontal instabilities become more complex in both models. The imprint of gravity waves propagating away from frontal convergence zones in regions with anticyclonic vorticity becomes apparent at 100–200 m resolutions for both models (Fig. f–g, m–n).

The persistence in the location of fronts is evident in the ROMS simulations as spatial resolution is refined from 1 km to 100 m (Fig. k–n). Generally, better defined frontal structures result in greater variability at finer spatial resolutions within the front itself. Similarities in the locations of fronts in MPAS-O at the same time are much less apparent compared to the ROMS simulations, although there is greater spatial coherence in MPAS-O among some of the fine-scale (100–200 m) simulations at earlier time periods (see animations of both simulations in the data archive). This relative lack of spatial coherence in MPAS-O is likely due to unavoidable highly nonlinear grid-scale processes (further elaborated on in the discussion) that help define early differences in initial conditions that then rapidly evolve. Like the fine-scale ROMS simulations (Fig. m–n), comparable MPAS-O results show greater variability within frontal regions (Fig. f–g).

Grid-scale noise emerges in MPAS-O at sub-kilometer resolutions (Fig. e–g), where it organizes into wave-like structures similar to Gibbs phenomenon. This noise is much weaker in the 500 m simulation and increases with increasing resolution. These results suggest that the biharmonic viscosity, which dissipates energy at the smallest resolved scales and is controlled by the grid Reynolds number, requires retuning at sub-kilometer resolutions for the new second-order Adams-Bashforth time-stepping scheme. A grid Reynolds number of 20 was tuned for the original split-explicit time stepping and is commonly used in various MPAS-O configurations. A systematic retuning is beyond the scope of this study due to the substantial computational and storage costs of the 100–200 m simulations; for example, the 100 m simulation requires nearly six days of wall-clock time on 4096 cores and produces 11 TB of output. The impacts of this grid-scale noise are discussed throughout the paper.

The emergence of energetic submesoscale frontal processes occurs more rapidly in ROMS than MPAS-O, evidenced by time series of surface domain-averaged kinetic energy (KE) and depth-integrated eddy kinetic energy (EKE) across all resolutions (Fig. ). Low levels of KE and EKE are simulated during the first 4–5 d for both MPAS-O and ROMS simulations. At approximately Day 5, however, the mean surface KE in the ROMS model domain rapidly increases, peaking around Day 10 at 0.65 m² s⁻² for all sub-kilometer resolution scenarios (Fig. b). This average peak in MPAS-O mean surface KE occurs 4 d later than ROMS, at similar levels (Fig. a). MPAS-O simulations also decrease surface KE more rapidly but reach approximately the same endpoint as ROMS simulations over the remainder of the 50 d period, although both 10 km model scenarios decay most rapidly and reach a lower stable endpoint (Fig. a–b). This pattern, however, does not hold for EKE time series, which peak at higher levels for coarser resolutions in MPAS-O than ROMS, with generally less stability for most resolutions (Fig. c–d). Generally, there is greater variability in the absolute value of surface KE across model resolutions for ROMS than MPAS-O over the first half of the simulation period. For EKE, the trend towards a lower stable configuration is more variable for a greater number of spatial resolutions in ROMS, but MPAS-O has a noticeable uptick in the highest resolution (100 m) simulation, likely a spurious mode that emerges as grid-scale tracer variance becomes more important. A key detail not reflected in Fig.  is that there is there is much less structure within and surrounding fronts in MPAS-O compared to ROMS beyond the halfway point in the simulations (∼ Day 25, see data archive animations). We return to this point again in Sect. .

The kinetic energy spectra (Fig. ) computed over the entirety of the simulation also reinforces that ROMS has slightly greater levels of regular high frequency variability compared to MPAS-O. Both ocean models show a clearly defined subinertial peak in their spectra, closely matching the imposed periodic wind forcings. At lower frequencies, the two models are highly similar at 1 km resolution; generally differences in the KE spectra distributions between the two ocean models are smaller than the differences in distribution for an ocean model across multiple spatial resolutions. While the amplitude of high-frequency (near daily) variability in surface KE is greater for ROMS than MPAS-O in the first month of the simulation, this difference is diminished by Day 40 (a–b), as both models converge to surface KE levels that are only slightly greater than initial conditions as the strong salinity gradients are progressively eroded. The average 10 d periods of maximum surface KE for both models (Day 8–18) are banded in gray (Fig. a–b) and these subsets of the simulations are used for calculations in the remaining analyses.

Surface relative vorticity and divergence dynamics demonstrate similar shifts in their distributions due to increasing resolution for both MPAS-O and ROMS (Fig. ) over the 10 d period when surface mean KE is maximized (Fig. ). At coarse spatial resolutions, the PDF of relative vorticity (Fig. a–b) is slightly positively skewed with a shorter positive tail, indicating lower levels of frontogenesis. In both models, this skew also becomes more positive at higher spatial resolutions, and is slightly more peaked in negative vorticity for MPAS-O than ROMS at equivalent resolutions with the exception of the 100 m scenario. This elevated peak in MPAS-O negative ζ/f is indicative of a sharper division between eddies and frontal regions in ROMS simulations at higher spatial resolutions compared to smoother gradients found in MPAS-O. Both models also show a distinctive asymmetric shift leftwards at resolutions finer than 5 km, with the highest peak in negative vorticity occurring for both models' 500 m simulations.

The distributions of normalized divergence within fronts (where ζf-1>1, Fig. c–f) again emphasize that inter-model differences between MPAS-O and ROMS are smaller than intra-model spatial resolution differences. In both models, coarser spatial resolutions produced a lesser amount of fronts (locations where ζf-1>1), resulting in lower levels of divergence (positive x axis) and convergence (negative x axis) than more highly spatially resolved simulations. There is also a marked change in the distributions of divergence as spatial resolution decreases below 1 km, where the distribution is severely flattened and extends outwards beyond -1<δf-1<1. Both models show that the vast majority (> 96 %) of convergent flows fall within ±1 at spatial resolutions of 10 and 5 km (Fig. e).

The relative fractions of convergent flow along fronts (ζf-1>1) in ROMS and MPAS-O are approximately equal across all simulations ≥ 1 km (Fig. e). At highly resolved (100–200 m) resolutions, MPAS-O has slightly greater amounts of strongly convergent flow, suggesting a growing influence of grid-scale noise. The fraction of strongly divergent flows are also similar between models across all spatial resolutions (Fig. f). At spatial resolutions of 100 m, the percentage of strongly divergent and convergent flows along fronts (|δf-1|>1 where ζf-1>1) in MPAS-O and ROMS (the sum of the left-most values in panels e and f) are equal to 55 % and 50 %, respectively.

Joint PDFs of vorticity versus strain rate (Fig. ) and divergence (Fig. ), following that described by , demonstrate similar behavior under periodic wind stress conditions for MPAS-O and ROMS. In both models, increasing spatial resolution increases the strength of the relationship between increasing positive vorticities and strain rates, centered around the dashed gray line at 45° highlighting regions of pure shear that are characterized by strong cyclonic vorticity (Fig. ). As spatial resolution increases, the relationship along this line of pure shear becomes less distinctive in both MPAS-O and ROMS. However, a clear divide between relative vorticity values at -1 (where ζ is equal to -f at the zero potential vorticity boundary) remains apparent across resolutions, although this is more visible within ROMS than MPAS-O. This is most clearly exemplified by a clear increase in shear associated with low negative relative vorticities at high spatial resolutions in MPAS-O (Fig. d) that is also present but substantially diminished in ROMS (Fig. h).

Relationships between normalized divergence and relative vorticity for MPAS-O and ROMS are also similar, but again highlight differences in the distributions of divergence between the two models (Fig. ). Reflecting the differences in the shape of the PDFs (Fig. c–d), the distribution of divergence vs. vorticity is more narrowly focused about the x axis for MPAS-O than ROMS, which has a greater negative skew in divergence. However a clear barrier point at ζ values that are equal to -f remains evident in both models at resolutions > 100 m.

Joint PDFs of along- and cross-frontal divergence within frontal coordinates at the surface were also computed in regions where ζf-1>1, following the approach introduced by (Fig. ). The distributions in both MPAS-O and ROMS show a clear rotation towards a more vertically aligned distribution (greater frontal compression and decreased shear) for both ocean models as spatial resolution increases. Ellipses fit to the model variation using principal component analysis reinforce that the rotation is increasingly aligned along the axis of cross-frontal divergence as the component parallel to the major axis becomes more closely aligned with the y axis (Table ). With smaller spatial scales, flows in both MPAS-O and ROMS become more convergent, as the primary axis of variability lies in the along-front direction of elevated vorticity regions. Differences in levels of divergence between MPAS-O and ROMS are also shown in Table , where the ratio of major to minor components of principal component analysis (PCA) variability show a somewhat consistent increase from coarser to finer scale ROMS simulations but mixed trends for MPAS-O simulations. This reinforces what is evident in Fig. , that the distribution of cross- versus along-frontal divergence values are more diffuse in MPAS-O than ROMS at all resolutions ≥ 500 m. Despite some differences in the angle of rotation of the primary axis of variability, the average of the distributions (∂ũ/∂x̃) is remarkably similar (within ±0.06) for cross-frontal divergence values between MPAS-O and ROMS across all resolutions.

Plan-view plots of surface numerical mixing for both models across all resolutions are shown in Fig. , at the same time as Fig. . Numerical mixing is generally largest at fronts for all resolutions due to elevated salinity gradients, consistent with previous studies . At 1–10 km resolutions (Fig. a–d, h–k), numerical mixing is noisy at the grid scale, with the spatially-averaged mixing generally decreasing as resolution increases, particularly within eddies. At sub-kilometer resolutions in MPAS-O (Fig. e–g), regions with grid-scale noise in the vorticity field coincide with regions of higher numerical mixing. This is most prevalent in the 200 m simulation (Fig. f). Significant patches of negative numerical mixing are visible in both models, with MPAS-O showing slightly more organized patches. The negative patches indicate tracer variance production, rather than destruction, and may reflect either anti-diffusive or dispersive numerical errors associated with the advection schemes. However, we cannot precisely determine the quantity of numerical mixing occurring at the grid scale that directly results from the tracer advection scheme or noise generated by the DVD algorithm.

To further quantify these differences, we examine time series of volume-averaged physical (Fig. a–b) and numerical (Fig. c–d) mixing for both models across all resolutions. The volume-averaging operator is defined as V-1∭{.}dV, where V is the domain volume. The volume-averaged physical mixing is correlated with the time series of mean surface kinetic energy (Fig. ), growing later in MPAS-O (Fig. a) than in ROMS (Fig. b). Since the models were initialized with vertically uniform salinity, physical mixing is strongly influenced by restratification due to mixed-layer instabilities , which generates vertical salinity variance that can be destroyed by mixing. In MPAS-O, the volume-averaged physical mixing reaches a steady, periodic state that exceeds ROMS by the end of the simulation. Physical mixing generally increases with resolution, particularly when kinetic energy is near its maximum.

Volume-averaged numerical mixing (Fig. c–d) partially follows the distribution of kinetic energy, peaking during eddy formation but decreasing much faster than physical mixing. This is likely because strongly convergent ageostrophic motions during frontogenesis sharpen horizontal salinity gradients. As the simulation evolves through the later phases of the frontal life cycle (instability, arrest, and decay), the destruction of salinity gradients reduces numerical mixing. For both models, volume-averaged numerical mixing generally decreases with increasing resolution, with notable exceptions. MPAS-O exhibits higher peak numerical mixing in the 2, 5, and 10 km cases than ROMS, and oscillates between positive and negative values at all resolutions. The 100–200 m simulations, especially the 100 m run, show much more tracer variance production, likely due to excessive grid-scale noise. Peak instances of negative numerical mixing for the 100 m simulation occur between Days 15–20 and Days 25–30. The behavior may be phenomenologically similar to fossil turbulence in that small-scale variance persists after the energetic phase, but in this case arises from numerical rather than physical processes. In ROMS, volume-averaged numerical mixing remains positive at all resolutions and consistently decreases with increasing resolution.

To summarize differences between models and across resolutions, we compute bulk mixing quantities (Fig. ), defined as the time-summed volume-averaged mixing. We normalize horizontal resolution by the initial deformation radius (5 km) to produce a dimensionless metric which may be useful for future studies. For MPAS-O, the absolute value of numerical mixing is taken at each time step to prevent negative values from artificially reducing bulk mixing. This is preferable to taking the absolute value of numerical mixing at the grid scale because the noise from the DVD algorithm would contaminate the bulk mixing estimates. The ratio of bulk numerical to physical mixing decreases with increasing resolution (Fig. a), except for the 100 m MPAS-O case. In MPAS-O, this ratio decreases from 42 % at 10 km to 2.8 % at 200 m, but rises to 40 % at 100 m. In ROMS, the ratio decreases from 131 % at 10 km to 4 % at 100 m. Bulk numerical (Fig. b) and physical mixing (Fig. c) trends reflect these ratios.

As suggested by the time series, bulk numerical mixing in ROMS exceeds MPAS-O at most resolutions. Bulk numerical mixing decreases by 90 % in ROMS from 10 km to 100 m, and by 89 % in MPAS-O from 10 km to 200 m (we exclude the 100 m MPAS-O case due to the massive increase in numerical mixing). Physical mixing increases with resolution in both models: MPAS-O shows a 52 % increase from 10 km to 100 m, while ROMS increases by nearly 200 %. At 5–10 km resolutions, MPAS-O exhibits over 50 % more physical mixing than ROMS, though differences diminish at finer resolutions. Total bulk mixing, defined as |Mnum+Mphy|, is shown in Fig. d. Greater levels of physical mixing in MPAS-O offer a partial explanation as to why there is noticeably less frontal structure than ROMS beyond the halfway point in the simulations. At 5–10 km, ROMS has smaller total mixing than MPAS-O due to lower physical mixing; between 200 m and 2 km, total mixing estimates between both models are within 5 % of each other. For the 100 m MPAS-O simulation, total mixing increases by over 30 % due to the large rise in numerical mixing.