📊 Input Data
📈 T/S Profiles
🧮 Mathematical Background
Brunt-Väisälä Frequency:
$$N^2 = -\frac{g}{\rho_0}\frac{d\rho}{dz} = \frac{g}{\rho_0}\left(\alpha\frac{dT}{dz} - \beta\frac{dS}{dz}\right)$$
Vertical Mode Equation:
$$\frac{d^2\phi_n}{dz^2} + \frac{N^2}{c_n^2}\phi_n = 0$$
Where:
- $N^2$ = Brunt-Väisälä frequency squared
- $g$ = gravitational acceleration (9.81 m/s²)
- $\rho_0$ = reference density (~1025 kg/m³)
- $\alpha$ = thermal expansion coefficient (~2×10⁻⁴ K⁻¹)
- $\beta$ = haline contraction coefficient (~7.6×10⁻⁴ PSU⁻¹)
- $\phi_n$ = vertical structure function for mode n
- $c_n$ = phase speed for mode n