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EadyModel_3D

Spectral and Finite Difference 3D Code for Solving the Eady Problem in Potential Vorticity Formulation. Supervisor: Antonio Segalini

Overview

EadyModel_3D is a Python-based repository that implements numerical techniques to solve the Eady problem, a fundamental model in geophysical fluid dynamics. This model describes baroclinic instability in the atmosphere and ocean, providing insight into the dynamics of mid-latitude weather systems.

The code utilizes spectral methods and finite-difference schemes to address the problem in a 3D potential vorticity framework, ensuring both precision and computational efficiency.

Features

  • Spectral Transforms: Efficient Fourier-based algorithms for spatial derivatives.
  • Finite Difference Schemes: Methods to compute derivatives in the vertical direction.
  • Dealiasing: Implementation of spectral dealiasing to avoid aliasing errors.
  • Configurable Parameters: Adjustable grid resolution, domain size, and initial conditions.
  • Comprehensive Analysis: Includes tools for growth rate computation, visualization, and velocity profile studies.

Code Structure

eady.py

The main module that:

  • Sets up the Eady problem.
  • Defines the grid and physical parameters.
  • Solves the equations in the potential vorticity formulation using spectral and finite-difference methods.

functions.py

A utility module with functions for Fourier transforms, derivative calculations, and wavenumber generation.

Key Functions:

  • transform and inverse_transform: Perform forward and inverse Fourier transforms.
  • X_derivative and Y_derivative: Compute spatial derivatives in spectral space.
  • wavenumbers: Generate wavenumbers for Fourier transforms.

main.py

The primary script for running simulations, performing analyses, and visualizing results. It integrates with eady.py and functions.py for exploring the Eady problem.

Key Functions:

  • eady_analysis: Core function for running the Eady model and computing results.
  • plot_growth_rate_setups: Visualizes growth rates across multiple setups.
  • analyze_and_plot_growth_rates: Examines growth rates for various perturbations or random initial conditions.
  • plot_contour_of_v: Generates contour plots of the velocity field.
  • analyze_growth_rate_vs_perturbation: Studies the relationship between growth rates and perturbation modes.