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Idealized Coastal Baroclinic Adjustment

The idealized coast test case simulates baroclinic adjustment in a coastal domain with a sloping bottom and initial meridional salinity gradient. This configuration introduces nonlinearities and demonstrates how numerical mixing can suppress submesoscale variability.

Configuration

The domain is 192 km × 192 km × 103 m with a linearly sloping bathymetry (5 m deep at the southern edge, reaching full depth at 96 km). The initial hydrography features a meridional salinity gradient that drives baroclinic instabilities.

Parameters

using TimestepperTestCases

# Run with default settings (forced, high resolution)
sim = idealized_coast(:SplitRungeKutta3)

# Low resolution version
sim = idealized_coast(:SplitRungeKutta3; lowres=true)

# Unforced version (no wind stress)
sim = idealized_coast(:SplitRungeKutta3; forced=false)

Key parameters:

  • Domain: 192 km × 192 km × 103 m
  • Grid: 250 × 250 × 40 points (high res) or 96 × 96 × 40 (low res)
  • Bottom slope: Linear from 5 m to 103 m depth
  • Initial stratification: N² = 10⁻⁴ s⁻²
  • Meridional gradient: M² = 1.2×10⁻⁶ s⁻² (for y < 50 km)
  • Time step: 5 minutes (AB2) or 10 minutes (RK3)
  • Simulation duration: 40 days
  • Wind forcing: Oscillatory stress after 4-day spin-up (if forced=true)

Running the Simulation

using TimestepperTestCases

# Standard forced case
sim = idealized_coast(:SplitRungeKutta3; forced=true, lowres=false)

# Customize free surface
sim = idealized_coast(:SplitRungeKutta3; 
                      free_surface=ImplicitFreeSurface(grid))

Output Fields

The simulation outputs:

  • u, v, w: Velocity components
  • T, S: Temperature and salinity
  • b: Buoyancy
  • η: Free surface elevation
  • Abx, Aby, Abz: Advective buoyancy dissipation (x, y, z)
  • ATx, ATy, ATz: Advective temperature dissipation
  • ASx, ASy, ASz: Advective salinity dissipation
  • Gbx, Gby, Gbz: Buoyancy gradient squared
  • GTx, GTy, GTz: Temperature gradient squared
  • GSx, GSy, GSz: Salinity gradient squared
  • κu, κc: CATKE diffusivities (if forced)

Expected Results

As shown in the paper:

  • RK3-SE maintains sharper stratification and stronger submesoscale variability
  • AB2-SE shows reduced eddy activity and weaker stratification
  • Horizontal dissipation dominates over vertical dissipation
  • RK3-SE preserves more kinetic energy variance across scales

Loading and Analyzing Results

# Load results
case = load_idealized_coast("output_folder/", "CATKE", "split_free_surface_", "SplitRungeKutta3")

# Access diagnostics
case[:KE]   # Kinetic energy
case[:MKE]  # Mean kinetic energy
case[:RPE]  # Reference potential energy
case[:APE]  # Available potential energy
case[:abx], case[:aby], case[:abz]  # Volume-averaged dissipation
case[:gbx], case[:gby], case[:gbz]  # Volume-averaged gradient squared

Physical Interpretation

This test case demonstrates that numerical mixing can suppress physical instabilities. The reduced dissipation in RK3-SE allows baroclinic instabilities to develop more fully, preserving submesoscale variability that AB2-SE suppresses. The horizontal dissipation dominates because eddy activity occurs primarily at the surface where horizontal gradients are strongest.