Particle Velocities Given Free Surface Elevation Of Solitary Waves Calculator

Particle Velocity Formula:

\[ u = \eta \times \sqrt{[g] \times d_c} \times \frac{H_w}{d_c} \div H_w \]

Free Surface Elevation (η):

Water Depth for Cnoidal Wave (d_c):

Height of the Wave (H_w):

Particle Velocity (u):

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1. What is Particle Velocity in Solitary Waves?

Particle velocity refers to the velocity at which water particles move as a result of the passage of waves or currents. In the context of solitary waves, it represents the instantaneous speed of water particles at a specific location and time.

2. How Does the Calculator Work?

The calculator uses the particle velocity formula for solitary waves:

\[ u = \eta \times \sqrt{[g] \times d_c} \times \frac{H_w}{d_c} \div H_w \]

Where:

\( u \) — Particle velocity (m/s)
\( \eta \) — Free surface elevation (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( d_c \) — Water depth for cnoidal wave (m)
\( H_w \) — Height of the wave (m)

Explanation: The formula calculates particle velocity based on free surface elevation, water depth, wave height, and gravitational acceleration.

3. Importance of Particle Velocity Calculation

Details: Understanding particle velocities is crucial for coastal engineering, sediment transport studies, wave energy assessment, and predicting wave impact on marine structures.

4. Using the Calculator

Tips: Enter free surface elevation in meters, water depth in meters, and wave height in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What are typical particle velocity values in ocean waves?
A: Particle velocities can range from a few cm/s in gentle swells to several m/s in storm waves and breaking waves near shore.

Q2: How does water depth affect particle velocities?
A: In shallower water, particle velocities generally increase due to wave shoaling and the conservation of wave energy.

Q3: What is the difference between particle velocity and wave celerity?
A: Particle velocity refers to the movement of water particles, while wave celerity is the speed at which the wave form propagates.

Q4: Are particle velocities the same throughout the water column?
A: No, particle velocities typically decrease with depth below the water surface and vary with wave phase.

Q5: How accurate is this formula for real-world applications?
A: This formula provides a theoretical estimate. For precise engineering applications, field measurements or more complex numerical models may be required.