Guo Formula of Linear Dispersion Relation for Wave Number Calculator

Guo Formula of Linear Dispersion Relation for Wave Number:

\[ k = \frac{(\omega_c^2 \cdot d)/[g] \cdot (1 - \exp(-(\omega_c \cdot \sqrt{d/[g]})^{5/2})^{-2/5})}{d} \]

Wave Number for Water Wave (k):

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1. What is the Guo Formula of Linear Dispersion Relation for Wave Number?

The Guo Formula of Linear Dispersion Relation for Wave Number calculates the wave number for water waves based on angular frequency and coastal mean depth. It provides an accurate representation of the dispersion relationship in coastal waters.

2. How Does the Calculator Work?

The calculator uses the Guo formula:

\[ k = \frac{(\omega_c^2 \cdot d)/[g] \cdot (1 - \exp(-(\omega_c \cdot \sqrt{d/[g]})^{5/2})^{-2/5})}{d} \]

Where:

\( k \) — Wave Number for Water Wave (rad/m)
\( \omega_c \) — Angular Frequency of Wave (rad/s)
\( d \) — Coastal Mean Depth (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \exp \) — Exponential function
\( \sqrt \) — Square root function

Explanation: The formula accounts for the complex relationship between wave frequency, water depth, and wave number in coastal environments.

3. Importance of Wave Number Calculation

Details: Accurate wave number calculation is crucial for coastal engineering, wave forecasting, and understanding wave behavior in shallow waters. It helps in designing coastal structures and predicting wave propagation.

4. Using the Calculator

Tips: Enter angular frequency in rad/s and coastal mean depth in meters. All values must be valid (angular frequency > 0, mean depth > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is wave number in wave mechanics?
A: Wave number represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance. It is typically measured in radians per meter.

Q2: How does water depth affect wave number?
A: In shallower waters, waves experience stronger dispersion effects, which affects both wave speed and wave number calculations.

Q3: What is the significance of the Guo formula?
A: The Guo formula provides a more accurate dispersion relation for waves in coastal waters compared to traditional deep-water approximations.

Q4: When is this formula most applicable?
A: This formula is particularly useful in intermediate to shallow water depths where traditional deep-water approximations become less accurate.

Q5: Are there limitations to this equation?
A: Like all wave models, the Guo formula has limitations in extremely shallow waters or when nonlinear effects become significant.