GitHub

Notebooks

This repository includes Jupyter notebooks for reproducing figures and analysis from the paper. All notebooks are located in the notebooks/ directory.

Available Notebooks

Figure Generation

  • figure_1.ipynb: Generates Figure 1 from the paper (amplification factors)
  • figure_2.ipynb: Generates Figure 2 from the paper (linear stability analysis)

Results Analysis

  • Results_internal_tide.ipynb: Analysis and visualization of internal tide results
  • Results_idealized_coast.ipynb: Analysis and visualization of idealized coast results
  • Results_channel.ipynb: Analysis and visualization of channel simulation results

Stability Analysis

  • linear_stability.ipynb: Linear stability analysis for coupled barotropic-baroclinic modes

Running Notebooks

Prerequisites

Install required packages:

using Pkg
Pkg.add(["IJulia", "Plots", "CairoMakie", "JLD2"])

Starting Jupyter

using IJulia
notebook()

Or from the command line:

julia -e "using IJulia; notebook()"

Running a Notebook

  1. Navigate to the notebooks/ directory
  2. Open the desired notebook in Jupyter
  3. Ensure simulation output files are in the expected locations (see notebook comments)
  4. Run all cells

Notebook Descriptions

Figure 1: Amplification Factors

This notebook reproduces the amplification factor analysis comparing AB2 and RK schemes for linear advection. It shows how RK schemes maintain amplification factors closer to unity over a wider CFL range, indicating less implicit dissipation.

Figure 2: Linear Stability

This notebook reproduces the linear stability analysis showing eigenvalues for the coupled barotropic-baroclinic system. It demonstrates the importance of using the averaged barotropic transport velocity (w★) for tracer advection in split-explicit RK schemes.

Results Notebooks

These notebooks load simulation output and generate diagnostic plots including:

  • Time series of kinetic energy, RPE, APE
  • Vertical profiles of numerical diffusivity
  • Spatial snapshots of velocity, buoyancy, and dissipation fields
  • Power spectra
  • Mean fields and differences between timesteppers

Linear Stability Notebook

This notebook implements the modal decomposition analysis described in the paper, computing eigenvalues for different coupling strategies and demonstrating stability constraints for multi-stage schemes.

Data Requirements

Most notebooks require simulation output files. Run the simulations first:

using TimestepperTestCases

# Run simulations
internal_tide(:SplitRungeKutta3)
internal_tide(:QuasiAdamsBashforth2)

idealized_coast(:SplitRungeKutta3)
idealized_coast(:QuasiAdamsBashforth2)

channel_simulation(timestepper=:SplitRungeKutta3)
channel_simulation(timestepper=:QuasiAdamsBashforth2)

Output files should be in the directories expected by the notebooks (typically internal_tide/, idealized_coast/, and channel-simulation/).

Customization

Notebooks can be customized to:

  • Compare different timesteppers
  • Analyze different time periods
  • Generate custom visualizations
  • Compute additional diagnostics

Modify the notebook code as needed for your analysis.