Ursell Number Calculator

Ursell Number Formula:

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

Ursell Number:

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1. What is the Ursell Number?

The 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. It helps determine whether linear wave theory is applicable or if nonlinear effects must be considered.

2. How Does the Calculator Work?

The calculator uses the Ursell Number formula:

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

Where:

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

Explanation: The formula relates wave characteristics to water depth to quantify the degree of nonlinearity in wave behavior.

3. Importance of Ursell Number

Details: The Ursell Number is crucial for determining when nonlinear wave theories should be applied. Small Ursell Numbers (U < 26) indicate that linear wave theory is appropriate, while larger values suggest significant nonlinear effects that require more complex modeling approaches.

4. Using the Calculator

Tips: Enter wave height and wavelength in meters, coastal mean depth in meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Ursell Number indicate?
A: A high Ursell Number indicates strong nonlinear effects in wave behavior, meaning that linear wave theory may not accurately describe the wave motion.

Q2: What is the typical range of Ursell Numbers?
A: Ursell Numbers can range from very small values (linear regime) to very large values (highly nonlinear regime), with U < 26 typically indicating linear behavior.

Q3: How does water depth affect the Ursell Number?
A: The Ursell Number is inversely proportional to the cube of water depth, meaning that waves in shallower water tend to have higher Ursell Numbers and exhibit more nonlinear behavior.

Q4: Can the Ursell Number be applied to all wave types?
A: The Ursell Number is primarily used for surface gravity waves and may not be appropriate for other wave types like capillary waves or internal waves.

Q5: What are the limitations of using the Ursell Number?
A: The Ursell Number provides a general indication of nonlinearity but doesn't capture all aspects of wave behavior. It should be used as a guideline rather than an absolute measure.