Wave Height for Mass Transport Velocity to Second Order Calculator

Wave Height Formula:

\[ Hw = \frac{\lambda \times \sqrt{Uz \times \frac{2 \times \sinh^2(2\pi d/\lambda)}{C \times \cosh(4\pi(DZ + d)/\lambda)}}}{\pi} \]

Wavelength of Wave (λ):

Mass Transport Velocity (Uz):

m/s

Water Depth for Fluid Velocity (d):

Celerity of the Wave (C):

m/s

Distance above the Bottom (DZ):

Height of the Wave (Hw):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Wave Height for Mass Transport Velocity Formula?

The Wave Height for Mass Transport Velocity to Second Order formula calculates the wave height based on wavelength, mass transport velocity, water depth, wave celerity, and distance above the bottom. This second-order approximation provides more accurate results for wave dynamics analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Hw = \frac{\lambda \times \sqrt{Uz \times \frac{2 \times \sinh^2(2\pi d/\lambda)}{C \times \cosh(4\pi(DZ + d)/\lambda)}}}{\pi} \]

Where:

\( Hw \) — Height of the Wave (m)
\( \lambda \) — Wavelength of Wave (m)
\( Uz \) — Mass Transport Velocity (m/s)
\( d \) — Water Depth for Fluid Velocity (m)
\( C \) — Celerity of the Wave (m/s)
\( DZ \) — Distance above the Bottom (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula accounts for hyperbolic functions to model wave behavior in varying water depths and distances from the bottom.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for coastal engineering, sediment transport studies, offshore structure design, and understanding nearshore hydrodynamics.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length, m/s for velocity). All values must be positive, with distance above bottom being zero or positive.

5. Frequently Asked Questions (FAQ)

Q1: What is mass transport velocity?
A: Mass transport velocity refers to the net velocity at which water mass is transported by wave motion, important for sediment and pollutant transport.

Q2: How does water depth affect wave height calculation?
A: Water depth significantly influences wave behavior through the sinh and cosh functions, accounting for wave shoaling and depth-limited breaking.

Q3: What is wave celerity?
A: Wave celerity is the speed at which a wave propagates through the water, which varies with water depth and wavelength.

Q4: When is this second-order approximation most accurate?
A: This approximation works best for intermediate water depths and moderate wave conditions where nonlinear effects become significant.

Q5: What are the limitations of this formula?
A: The formula may be less accurate in very shallow water, breaking wave conditions, or for highly nonlinear wave phenomena.