Wave Height for Simplified Horizontal Fluid Particle Displacement Calculator

Wave Height Formula:

\[ H = \varepsilon \times 2 \times \frac{\sinh(2\pi D/\lambda_{hp})}{\cosh(2\pi (DZ + d)/\lambda_{hp})} \times \sin(\theta) \]

Fluid Particle Displacement (ε):

Water Depth (D):

Wavelength of Horizontal Fluid Particle (λ_hp):

Distance above Bottom (DZ):

Phase Angle (θ):

rad

Wave Height (H):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Wave Height Formula?

The Wave Height formula calculates the vertical distance between the trough and crest of a wave based on fluid particle displacement, water depth, wavelength, distance above bottom, and phase angle. This formula is essential for understanding wave behavior in fluid dynamics.

2. How Does the Calculator Work?

The calculator uses the Wave Height formula:

\[ H = \varepsilon \times 2 \times \frac{\sinh(2\pi D/\lambda_{hp})}{\cosh(2\pi DZ/\lambda_{hp})} \times \sin(\theta) \]

Where:

\( H \) — Wave Height (m)
\( \varepsilon \) — Fluid Particle Displacement (m)
\( D \) — Water Depth (m)
\( \lambda_{hp} \) — Wavelength of Horizontal Fluid Particle (m)
\( DZ \) — Distance above Bottom (m)
\( \theta \) — Phase Angle (rad)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: The formula accounts for hyperbolic functions to model wave behavior in different water depth conditions and phase relationships.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for coastal engineering, navigation safety, offshore operations, and understanding oceanographic phenomena.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, radians for angles). Ensure all values are positive and valid for accurate calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is fluid particle displacement?
A: Fluid particle displacement refers to the movement of individual water particles as waves pass through, describing their orbital motion.

Q2: How does water depth affect wave height?
A: Water depth significantly influences wave behavior. In shallow water, waves slow down and increase in height, while in deep water, they maintain more consistent characteristics.

Q3: What is the significance of phase angle?
A: Phase angle determines the position of the wave at a specific point in time relative to a reference point, affecting the instantaneous wave height calculation.

Q4: Are there limitations to this formula?
A: This simplified formula works well for linear wave theory but may have limitations for extreme wave conditions, nonlinear effects, or complex bathymetry.

Q5: What practical applications use this calculation?
A: Coastal engineering, ship design, offshore platform construction, wave energy conversion, and marine forecasting all utilize wave height calculations.