BayIW_Rectan_linear — Internal Waves in a Rectangular Bay (Linear Stratification)

Master's Degree Thesis Project

This project uses the MITgcm ocean general circulation model to simulate the generation and propagation of internal waves in a rectangular bay using a linear stratification profile. It is one of three stratification cases studied in the thesis:

The simulations are run with and without the bay geometry to isolate the bay's influence on internal wave dynamics.

BayIW_Rectan_linear/
├── build/                        # MITgcm compilation directory
├── code/                         # Model configuration and size files
│   ├── SIZE.h                    # Grid decomposition parameters
│   ├── packages.conf             # Enabled MITgcm packages
│   ├── OBCS_OPTIONS.h            # Open boundary condition options
│   └── DIAGNOSTICS_SIZE.h        # Diagnostics buffer sizes
├── input/                        # Forcing, bathymetry, and preprocessing scripts
│   ├── *.bin                     # Binary input files (bathymetry, grid spacing, T/S, wind)
│   ├── profiles_2layer/          # Two-layer profile binaries (for reference)
│   ├── profiles_gradRho/         # Gradient density profile files
│   ├── STATE/                    # Reference state generation scripts
│   ├── *.ipynb                   # Jupyter notebooks for input generation and analysis
│   └── *.py                      # Python utility scripts
├── run_expand/                   # Run directory — with bay geometry
│   ├── data                      # Main model parameter file
│   ├── data.diagnostics          # Diagnostics configuration
│   ├── data.obcs                 # Open boundary condition parameters
│   ├── data.pkg                  # Package switches
│   ├── data.mnc                  # NetCDF output settings
│   └── mnc_*/                    # NetCDF output directories (one per MPI rank)
├── run_expand_nobay/             # Run directory — without bay (control case)
├── compile_and_run_expand.sh     # Script to compile and run both simulations
├── run_expands.sh                # Run-only script (no recompilation)
├── Merge_MPI_STDOUT.sh           # Merge STDOUT files from all MPI ranks
└── compress_nc.sh                # Compress NetCDF output files

Open boundaries are applied on the south, west, and east edges using Orlanski radiation conditions. A sponge layer of 10 grid cells damps spurious reflections near the boundaries. Barotropic velocity balance is applied to maintain mass conservation.

• Wind: Periodic meridional wind forcing applied in stage 1 only (period = 1200 s, cycle = 216 000 s)(make_wind_forcing_local.ipynb)
• Initial temperature: Linear stratification profile (linear_temp_50zlev_560x352.bin)
• Initial salinity: Constant (linear_salt_50zlev_560x352.bin)

The domain features a rectangular bay carved into a coastal shelf. The bay geometry is defined in input/bahia_rectan_impar_func.ipynb with the following dimensions:

The domain uses a variable horizontal grid spacing: uniform 200 m resolution in the central region containing the bay, expanding outward to reduce the domain size while minimizing boundary reflections. A previous attempt used a parabolic (semi-circular) bay profile, which produced numerical instabilities; the rectangular geometry was adopted for all stratification scenarios.

The stratification is defined by a linearly varying density profile from surface to bottom. Both temperature and salinity may vary linearly with depth, producing a constant buoyancy frequency N² throughout the water column. This is the classic idealization used in analytical internal wave theory and allows direct comparison of simulated wave characteristics (phase speed, dispersion relation) against known theoretical solutions.

Both cases share the same model executable and physical parameters, and follow the same two-stage run strategy described below.

Each simulation is run in two consecutive stages:

Stage 1 starts from rest with the linear T/S initial conditions and applies periodic wind forcing. It writes a checkpoint (ckptA) at the end. Stage 2 restarts from that checkpoint (pickupSuff='ckptA') with the wind forcing commented out, allowing the internal wave field to propagate and decay freely.

The data files committed to the repository correspond to stage 2. To run stage 1, update &PARM03 to:

startTime=0., endTime=216000., nIter0=0,
periodicExternalForcing=.TRUE., externForcingPeriod=1200., externForcingCycle=216000.,

and uncomment the meridWindFile and hydrogThetaFile lines in &PARM05.

The input/ directory contains Jupyter notebooks used to prepare all binary input files:

• MITgcm source tree (expected at ../../../ relative to this directory)
• Fortran compiler (gfortran) — build options configured for darwin_arm64_gfortran
• MPI (optional, for parallel runs)
• Python 3 with numpy, scipy, matplotlib, xarray, netCDF4 (for preprocessing and analysis)
• Jupyter Notebook

bash compile_and_run_expand.sh

The script will interactively ask whether to:

1. Clean the build/ directory before compiling
2. Enable MPI compilation
3. Clean run directories before execution
4. Run with MPI (and how many cores)

Both run_expand/ (with bay) and run_expand_nobay/ (without bay) are run sequentially.

bash run_expands.sh

cd run_expand
bash run_expand.sh

Or manually:

cp ../build/mitgcmuv .
mpirun -np 4 ./mitgcmuv > output.txt

Model output is written as NetCDF files into mnc_*/ subdirectories (one per MPI rank). The primary diagnostic field is:

• diag_rho — density anomaly (RHOAnoma), output every 900 s (15 min)

bash Merge_MPI_STDOUT.sh    # Merge STDOUT logs from all MPI ranks into one file
bash compress_nc.sh         # Compress NetCDF output to reduce disk usage

Internal waves are gravity waves that propagate along density interfaces in the ocean interior. The linear stratification case produces a constant buoyancy frequency N², which simplifies the theoretical treatment of internal waves: phase speeds, vertical mode structures, and dispersion relations all have clean analytical forms under this assumption. This makes the linear case ideal for:

1. Validating the numerical model against theoretical predictions
2. Isolating the effect of bay geometry from stratification complexity
3. Providing a reference against which the two-layer and realistic stratification results can be compared

Esteban Cruz Isidro