Magneto-Rossby Dispersion Dashboard

An interactive Streamlit app for visualizing the sectoral dispersion curves of hydrodynamic Rossby waves, fast/slow magneto-Rossby waves, and Alfvén waves as a function of azimuthal order m and magnetic field strength B.

Live app: https://magneto-rossby-dashboard.streamlit.app/

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Technical Skills

• Web app development: built and deployed an interactive Streamlit application accessible via public URL
• Interactive data visualization: real-time parameter controls with dynamic plot updates, axis zoom sliders, and multi-curve overlays, which are designed for scientific exploration rather than static presentation
• Scientific computing: quadratic dispersion relation solver, Alfvén speed computation, unit conversion between physical and dimensionless quantities
• Data products: tabular data view and one-click CSV export of all plotted curves
• Deployment: hosted on Streamlit Community Cloud; reproducible environment via requirements.txt
• Libraries: streamlit, numpy, pandas, matplotlib

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What the App Does

Users can adjust physical parameters from the sidebar and immediately see how the dispersion curves respond, no coding required. This makes it useful both as a research tool for exploring parameter space and as an educational tool for understanding wave physics.

Adjustable parameters:

• Rotation rate Ω, solar radius R₀, and plasma density ρ
• Azimuthal order range m
• One or more magnetic field strengths B (via presets or a custom list)
• Axis limits for zooming into any region of m–ν space

Output:

• Live dispersion curve plot with labeled wave families and color-coded B values
• Tabular data view of all computed curves
• CSV download of the full dataset

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Physics Background

The dispersion relations implemented here follow Zaqarashvili, Oliver, Ballester & Shergelashvili 2007, with Alfvén and Hydrodynamical (HD) Rossby branches included for reference.

$$n(n+1),x^2 + x + \alpha^2\bigl[2 - n(n+1)\bigr] = 0, \quad x = \lambda/s$$

where:

• s = n = m for sectoral modes
• λ is the dimensionless eigenvalue related to mode frequency by ν = 2Ω λ
• α = v_A / (2Ω R₀) is the dimensionless magnetic parameter
• v_A = B / √(μ₀ ρ) is the Alfvén speed

The two roots correspond to the fast (closer to the HD Rossby branch) and slow magneto-Rossby branches. The Alfvén frequency is given by ν_A = (m / R₀) v_A / 2π. In the limit α → 0, the slow branch recovers the purely hydrodynamic Rossby dispersion relation.

Some notes: (1) density (ρ) has a large effect on the Alfvén speed (and thus α); (2) for very large B or low ρ, the slow magneto-Rossby branch can depart significantly from the HD Rossby baseline; (3) the Alfvén branches are symmetric about ν = 0; only the prograde branch is labeled in the legend to avoid duplication; and (4) all frequencies are in nHz, consistent with helioseismology conventions.

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Quickstart

Run locally

pip install -r requirements.txt
streamlit run dashboard_magnetorossby.py

View online

https://magneto-rossby-dashboard.streamlit.app/

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