Coastal Internal Wave Analysis Platform

📊 Water Column Stratification Analysis

Brunt-Väisälä Frequency:

$$N^2(z) = -\frac{g}{\rho_0}\frac{d\rho}{dz} = \frac{g}{\rho_0}\left(\alpha\frac{dT}{dz} - \beta\frac{dS}{dz}\right)$$

Stratification Parameter:

$$S = \frac{1}{H}\int_0^H N(z) dz$$

🌡️ Temperature Profile

Surface Temperature (°C):

Bottom Temperature (°C):

Thermocline Depth (m):

Thermocline Thickness (m):

🧂 Salinity Profile

Surface Salinity (psu):

Bottom Salinity (psu):

Halocline Depth (m):

Halocline Thickness (m):

🌊 Environmental Parameters

Total Water Depth (m):

Latitude (degrees):

Season:

🌀 Internal Wave Properties Calculator

Internal Wave Dispersion Relation:

$$\omega^2 = N^2\frac{k_h^2}{k_h^2 + k_z^2} + f^2\frac{k_z^2}{k_h^2 + k_z^2}$$

Phase Speed: $c = \frac{\omega}{k_h}$

Group Speed: $c_g = \frac{\partial\omega}{\partial k_h}$

🌊 Wave Parameters

Wave Amplitude (m):

Wave Period (hours):

Horizontal Wavelength (km):

Vertical Mode Number:

🎯 Stratification Input

Average N (rad/s):

Maximum N (rad/s):

Pycnocline Depth (m):

Latitude (degrees):

⚡ Internal Wave Generation Mechanisms

Select Generation Mechanism:

Tidal Generation over Topography:

$$E = \frac{1}{2}\rho_0 N^2 U_0^2 h_0^2 \frac{k_h^2}{k_h^2 + k_z^2}$$

Conversion Rate:

$$P = \rho_0 N^2 U_0^2 h_0^2 k_h \sin(k_h x)$$

🌊 Tidal Parameters

Tidal Velocity U₀ (m/s):

Tidal Period (hours):

Topography Height h₀ (m):

Topography Length (km):

📊 Environmental Conditions

Buoyancy Frequency N (rad/s):

Water Depth (m):

Criticality Parameter:

🏄 Wave Propagation & Shoaling Analysis

Shoaling Coefficient:

$$K_s = \sqrt{\frac{c_{g0}}{c_g}} = \sqrt{\frac{N_0 H_0}{N H}}$$

Amplitude Evolution:

$$A(x) = A_0 K_s \exp\left(-\int_0^x \alpha dx'\right)$$

Ray Tracing:

$$\frac{dk_x}{dx} = -\frac{\partial\omega}{\partial x}, \quad \frac{dk_z}{dz} = -\frac{\partial\omega}{\partial z}$$

🌊 Initial Conditions

Initial Amplitude (m):

Initial Depth (m):

Initial N (rad/s):

Propagation Angle (degrees):

🏔️ Bathymetry Profile

Shelf Break Depth (m):

Shelf Depth (m):

Slope Length (km):

Damping Coefficient (1/km):

💥 Internal Wave Breaking Analysis

Breaking Criteria:

$$Ri = \frac{N^2}{(\partial u/\partial z)^2} < Ri_c = 0.25$$

Convective Instability:

$$\frac{\partial\rho}{\partial z} > 0 \quad \text{(unstable)}$$

Shear Instability:

$$|u_z| > \frac{N}{2} \quad \text{(Miles-Howard criterion)}$$

🌊 Wave Characteristics

Wave Amplitude (m):

Wavelength (km):

Background N (rad/s):

Breaking Depth (m):

⚡ Instability Parameters

Maximum Shear (1/s):

Density Gradient (kg/m⁴):

Breaking Type:

🌪️ Turbulent Mixing from Internal Waves

Dissipation Rate:

$$\varepsilon = \frac{1}{2}\nu\left\langle\left(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}\right)^2\right\rangle$$

Diapycnal Diffusivity:

$$K_\rho = \Gamma\frac{\varepsilon}{N^2}$$

Thorpe Scale:

$$L_T = \sqrt{\langle d^2 \rangle}$$

📊 Turbulence Measurements

Dissipation Rate ε (W/kg):

Buoyancy Frequency N (rad/s):

Thorpe Scale LT (m):

Mixing Efficiency Γ:

🌊 Wave-Induced Mixing

Wave Energy Density (J/m³):

Breaking Fraction:

Mixing Layer Depth (m):

Mixing Time Scale (hours):

📈 Field Data Analysis Tools

📊 Data Input

Data Type:

Sampling Rate (Hz):

Record Length (hours):

🔍 Analysis Parameters

Filter Type:

Low Frequency (cph):

High Frequency (cph):

📋 Analysis Summary Table

Parameter	Value	Units	Status	Notes
Dominant Frequency	-	cph	Normal	Within internal wave band
Wave Amplitude	-	m	Moderate	Typical for coastal waters
Richardson Number	-	-	Stable	Above critical value
Mixing Rate	-	m²/s	Low	Background mixing

🌊 Coastal Internal Wave Analysis Platform