Water Surface Elevation Of Two Sinusoidal Wave Calculator

Water Surface Elevation Formula:

\[ \eta = \frac{H}{2} \cdot \cos\left(\frac{2\pi x}{L_1} - \frac{2\pi t}{T_1}\right) + \frac{H}{2} \cdot \cos\left(\frac{2\pi x}{L_2} - \frac{2\pi t}{T_2}\right) \]

Wave Height (H):

Spatial Progressive Wave (x):

Wavelength of Component Wave 1 (L₁):

Temporal Progressive Wave (t):

Wave Period of Component Wave 1 (T₁):

Wavelength of Component Wave 2 (L₂):

Wave Period of Component Wave 2 (T₂):

Water Elevation (η):

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1. What is Water Surface Elevation of Two Sinusoidal Waves?

The water surface elevation of two sinusoidal waves represents the combined vertical displacement of the water surface resulting from the superposition of two individual wave components. This is a fundamental concept in wave theory and coastal engineering.

2. How Does the Calculator Work?

The calculator uses the water surface elevation formula:

\[ \eta = \frac{H}{2} \cdot \cos\left(\frac{2\pi x}{L_1} - \frac{2\pi t}{T_1}\right) + \frac{H}{2} \cdot \cos\left(\frac{2\pi x}{L_2} - \frac{2\pi t}{T_2}\right) \]

Where:

\( H \) — Wave Height (m)
\( x \) — Spatial Progressive Wave (m)
\( L_1 \) — Wavelength of Component Wave 1 (m)
\( t \) — Temporal Progressive Wave (s)
\( T_1 \) — Wave Period of Component Wave 1 (s)
\( L_2 \) — Wavelength of Component Wave 2 (m)
\( T_2 \) — Wave Period of Component Wave 2 (s)

Explanation: The formula calculates the combined water surface elevation from two sinusoidal wave components with different wavelengths and periods.

3. Importance of Water Surface Elevation Calculation

Details: Accurate water surface elevation calculation is crucial for coastal engineering, offshore structure design, wave energy assessment, and understanding coastal processes and sediment transport.

4. Using the Calculator

Tips: Enter all wave parameters in appropriate units. Wave height, wavelengths, and wave periods must be positive values. Spatial and temporal progressive waves can be zero or positive values.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of water surface elevation?
A: Water surface elevation describes the vertical position of the water surface relative to the mean water level, which is essential for understanding wave behavior and its effects on coastal structures.

Q2: How do different wave components affect the total water elevation?
A: Different wave components with varying wavelengths and periods create complex interference patterns, leading to variations in the total water surface elevation through constructive and destructive interference.

Q3: What are typical values for wave parameters in coastal environments?
A: Wave heights can range from a few centimeters to several meters, wavelengths from meters to hundreds of meters, and wave periods from seconds to tens of seconds, depending on the coastal environment.

Q4: Are there limitations to this two-wave model?
A: Real ocean waves are typically composed of many wave components. The two-wave model provides a simplified representation that may not capture the full complexity of real wave spectra.

Q5: How is this calculation used in practical applications?
A: This calculation is used in coastal engineering for designing breakwaters, sea walls, and offshore platforms, as well as in predicting coastal flooding and erosion patterns.