Ratio Of Wave Group Speed And Phase Speed Calculator

Formula Used:

\[ n = \frac{S_{xy} \times 8}{\rho \times [g] \times H^2 \times \cos(\alpha) \times \sin(\alpha)} \]

Radiation Stress Component (Sxy):

N/m

Mass Density (ρ):

kg/m³

Wave Height (H):

Wave Crest Angle (α):

radians

Ratio of Wave Group Speed and Phase Speed (n):

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1. What is the Ratio of Wave Group Speed and Phase Speed?

The ratio of wave group speed and phase speed (n) represents the relationship between the speed at which wave energy propagates (group speed) and the speed at which wave crests move (phase speed). This ratio is important in understanding wave energy transport and dispersion characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ n = \frac{S_{xy} \times 8}{\rho \times [g] \times H^2 \times \cos(\alpha) \times \sin(\alpha)} \]

Where:

\( S_{xy} \) — Radiation stress component (N/m)
\( \rho \) — Mass density (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( H \) — Wave height (m)
\( \alpha \) — Wave crest angle (radians)

Explanation: This formula calculates the ratio of wave group speed to phase speed based on radiation stress, fluid density, wave characteristics, and wave angle.

3. Importance of Wave Speed Ratio Calculation

Details: Understanding the ratio between group speed and phase speed is crucial for wave energy transport studies, coastal engineering design, and predicting wave behavior in various water depths and conditions.

4. Using the Calculator

Tips: Enter radiation stress component in N/m, mass density in kg/m³, wave height in meters, and wave crest angle in radians. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this ratio?
A: The ratio indicates how wave energy propagates relative to wave phase movement, which is important for understanding wave dispersion and energy transport in water bodies.

Q2: What are typical values for this ratio?
A: For deep water waves, the ratio is typically 0.5, meaning group speed is half the phase speed. In shallow water, the ratio approaches 1.

Q3: How does wave angle affect the ratio?
A: Wave angle influences the radiation stress components and thus affects the calculated ratio, particularly in directional wave fields.

Q4: Are there limitations to this formula?
A: This formula assumes linear wave theory and may have limitations for extreme wave conditions, breaking waves, or highly nonlinear wave systems.

Q5: What units should be used for input values?
A: Use consistent SI units: N/m for radiation stress, kg/m³ for density, meters for wave height, and radians for wave angle.