Distance From Bottom To Wave Trough Calculator

Formula Used:

\[ y_t = d_c \times \left( \frac{y_c}{d_c} - \frac{H_w}{d_c} \right) \]

Water Depth for Cnoidal Wave (d_c):

Distance from the Bottom to the Crest (y_c):

Height of the Wave (H_w):

Distance from the Bottom to the Wave Trough (y_t):

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1. What is Distance from Bottom to Wave Trough?

Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave in cnoidal wave theory. It represents the minimum water level point in a wave cycle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ y_t = d_c \times \left( \frac{y_c}{d_c} - \frac{H_w}{d_c} \right) \]

Where:

\( y_t \) — Distance from the Bottom to the Wave Trough (m)
\( d_c \) — Water Depth for Cnoidal Wave (m)
\( y_c \) — Distance from the Bottom to the Crest (m)
\( H_w \) — Height of the Wave (m)

Explanation: This formula calculates the distance from the seabed to the wave trough by considering the water depth, crest distance, and wave height in cnoidal wave theory.

3. Importance of Wave Trough Calculation

Details: Calculating the wave trough distance is crucial for coastal engineering, offshore structure design, and wave energy conversion systems. It helps determine wave characteristics and their impact on marine structures.

4. Using the Calculator

Tips: Enter water depth, distance to crest, and wave height in meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a cnoidal wave?
A: Cnoidal waves are exact periodic wave solutions of the Korteweg-de Vries equation, characterized by their rounded crests and relatively flat troughs, often used to model shallow water waves.

Q2: How does this differ from regular wave calculations?
A: Cnoidal wave theory provides more accurate results for waves in shallow water conditions compared to linear wave theory, especially for waves with finite amplitude.

Q3: What are typical values for wave trough distance?
A: The distance varies significantly based on water depth and wave characteristics, but typically ranges from near-zero in shallow breaking waves to substantial distances in deep water conditions.

Q4: When is cnoidal wave theory most applicable?
A: Cnoidal wave theory is most accurate for waves in relatively shallow water where the water depth is small compared to the wavelength (typically d/L < 0.1).

Q5: Are there limitations to this calculation?
A: This calculation assumes ideal cnoidal wave conditions and may not account for complex bathymetry, wave breaking, or other nonlinear effects in extreme conditions.