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Baroclinic Instability of Curved Fronts — Numerical Test

Nonlinear primitive-equation simulations validating and extending Singh, Buckingham & Tandon (2025), Dynamics of Atmospheres and Oceans.

What's here

baroclinic_curvature/
├── Project.toml                  # dependencies
├── src/BaroclinicCurvature.jl    # module: grid, base flow, model, output
├── run_straight.jl               # Step 1 driver — straight Charney front
├── run_meander.jl                # Step 2 driver — sinusoidal meander
├── tinker.jl                     # parameter playground for REPL workflow
└── plot_results.jl               # postprocessing: dispersion, wb, movies

Setup

From this directory:

julia --project=. -e 'using Pkg; Pkg.instantiate()'

First instantiate will take a while (CUDA, Oceananigans, Makie all compile).

Tinkering with parameters

Don't re-launch Julia for each run — startup is slow. Keep one REPL open and use tinker.jl as the parameter playground.

julia> using Pkg; Pkg.activate(".")
julia> using Revise                # picks up edits to src/ without restart
julia> include("tinker.jl")        # runs whatever's in the EDIT block

# Edit the params block in tinker.jl in your editor, then:
julia> include("tinker.jl")        # re-runs with new parameters

Or just construct parameters and run directly at the prompt:

julia> p = ProblemParams(R_c = 80e3, Nx = 64, stop_time_days = 10,
                         output_prefix = "test1")
julia> sim = build_simulation(p; arch = GPU())
julia> run!(sim)

A few convenience functions are defined in tinker.jl:

julia> smoke_test()                          # ~10 min sanity check, tiny grid
julia> run_experiment(R_c = 100e3, Nx = 96)  # any kwargs override defaults
julia> sweep_Rc([300, 150, 100, 80])         # sequence of meander cases

All parameters with defaults are listed in ProblemParams inside src/BaroclinicCurvature.jl. The most useful knobs:

Knob Effect
Nx, Ny, Nz grid resolution (linear in time cost)
stop_time_days how long to integrate
R_c Inf for straight, finite (m) for meander
L_m meander wavelength (m); keep ≫ Charney λ for scale separation
Λs, N² shear and stratification — change the dominant λ and σ
f₀, β latitude (changes Charney depth scale)
perturbation_amplitude bump up if energy doesn't grow cleanly
adjust_phase_days longer if the meander adjustment looks unfinished

Tip: Always do smoke_test() first after any change to the module file — catches API errors in ~10 minutes instead of after a 4-hour run.

Step 1 — verification

Reproduces classical Charney results. Target: most-unstable wavelength ~180 km, amplitude growth rate ~0.025 day⁻¹.

julia --project=. run_straight.jl
julia --project=. plot_results.jl straight

Outputs:

  • straight_snapshots.jld2, straight_wbprofile.jld2, straight_midslice.jld2
  • straight_energy.pdf — perturbation KE vs time, log axis. Should be a clean straight line between roughly t=5 and t=25 days.
  • straight_dispersion.pdf — σ(λ). Peak should be near 180 km at 0.025/day.
  • straight_wb.pdf — ⟨w'b'⟩(z) profile. Compare to Fig. 8 dashed line.
  • straight_surface_b.mp4 — surface buoyancy movie.

Step 2 — validation

Meandering front with R_c set at the crests. Sweep R_c by running multiple cases:

for Rc in 300 150 100 80; do
    julia --project=. run_meander.jl $Rc
    julia --project=. plot_results.jl meander_Rc${Rc}km
done

The first 5 days are an adjustment phase with strong Rayleigh damping (tapers quadratically). Treat any analysis as starting at t > 10 days.

Physical parameters (defaults)

Quantity Value
f₀ 10⁻⁴ s⁻¹ (45°N)
β 1.62 × 10⁻¹¹ m⁻¹ s⁻¹
N² 10⁻⁴ s⁻² (N/f = 100)
Λs 10⁻⁴ s⁻¹ (vertical shear)
Lz 2000 m

Straight front: Lx = 1000 km, Ly = 400 km, 128 × 64 × 64. Meander: Lx = 1200 km (2·L_m), Ly = 500 km, 256 × 96 × 64.

Meander geometry: y_f(x) = A sin(2πx/L_m), L_m = 600 km, A = L_m²/(4π²·R_c). At R_c = 80 km, A ≈ 121 km, crest slope dy/dx ≈ 1.27.

Hardware

Default architecture is GPU; falls back to CPU if CUDA isn't functional. On an RTX 3060 Ti (8 GB), the meander grid (256 × 96 × 64 ≈ 1.6 M cells) fits comfortably. Expect ~3–6 hours wall time for a 70-day meander run.

Known caveats / to-do

  1. Grid coordinate keys in JLD2 — plot_results.jl uses xᶜᵃᵃ etc; if your Oceananigans version uses different keys, inspect with jldopen(fn, "r") |> keys. The fallback is hard-coded range(...).
  2. No gradient-wind balance at init. The meander base flow is geostrophic only. The adjustment phase (5 days, exponential damping with quadratic taper) is meant to absorb the unbalanced centrifugal term. For a clean gradient-wind initialization, replace build_forcing with an iterative pressure solver before model construction.
  3. WENO advection of buoyancy. Default is WENO(order=5) on momentum and centered on tracers via the model defaults. For sharper fronts, set tracer_advection = WENO(order=5) explicitly.
  4. Output is full 3D snapshots every 6 hours. Storage budget for the default meander run is ~3–5 GB. Reduce output_interval_hours or subset fields if needed.