Wave Height Given Ursell Number Calculator

Wave Height Formula:

\[ H_w = \frac{U \times d^3}{\lambda_o^2} \]

Ursell Number (U):

dimensionless

Coastal Mean Depth (d):

meters

Deep-Water Wavelength (λₒ):

meters

Wave Height for Surface Gravity Waves (Hw):

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1. What is Wave Height Calculation?

Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level. It's a crucial parameter in coastal engineering and oceanography.

2. How Does the Calculator Work?

The calculator uses the wave height formula:

\[ H_w = \frac{U \times d^3}{\lambda_o^2} \]

Where:

\( H_w \) — Wave Height for Surface Gravity Waves (meters)
\( U \) — Ursell Number (dimensionless)
\( d \) — Coastal Mean Depth (meters)
\( \lambda_o \) — Deep-Water Wavelength (meters)

Explanation: This formula calculates wave height based on the Ursell number, coastal depth, and deep-water wavelength, accounting for wave characteristics in different water depths.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for coastal engineering, navigation safety, beach erosion studies, and offshore structure design.

4. Using the Calculator

Tips: Enter Ursell Number (dimensionless), Coastal Mean Depth in meters, and Deep-Water Wavelength in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the Ursell Number?
A: Ursell Number is a dimensionless parameter used in fluid mechanics to characterize the nonlinearity or strength of nonlinearity in the wave motion of a fluid.

Q2: What is Coastal Mean Depth?
A: Coastal Mean Depth of a fluid flow is a measure of the average depth of the fluid in a channel, pipe, or other conduit through which the fluid is flowing.

Q3: What is Deep-Water Wavelength?
A: Deep-Water Wavelength is the horizontal distance between two successive crests (or troughs) of the wave in deep water conditions.

Q4: What are typical wave height values?
A: Wave heights vary significantly depending on weather conditions, ranging from a few centimeters during calm weather to over 30 meters during extreme storms.

Q5: Are there limitations to this calculation?
A: This formula provides an estimation and may have limitations in extreme conditions or complex coastal geometries where other factors influence wave behavior.