Wave - Wave Analysis Calculator

Advanced wave analysis calculator for coastal and marine engineering calculations.

Back to Apps

Wavelength Calculator

Method & Theory

Purpose: Calculate the wavelength of water waves using the linear wave dispersion relation.

Theory: The wavelength L is related to wave period T and water depth h through the dispersion relation:

ω² = gk tanh(kh)

Where: ω = 2π/T (angular frequency), k = 2π/L (wave number), g = 9.81 m/s² (gravity)

Solution Method: Newton-Raphson iterative method with convergence tolerance of 1×10⁻¹⁰

Input Requirements

  • Water Depth (h): Positive value in meters (0.1 to 1000m typical range)
  • Wave Period (T): Positive value in seconds (1 to 25s typical range)

Wave Statistics Calculator

Method & Theory

Purpose: Analyze wave elevation time series using zero-crossing method to extract comprehensive wave statistics.

Theory: Zero-crossing analysis identifies individual waves by detecting upward zero-crossings (trough-to-crest transitions). Each wave is characterized by:

  • Wave Height (H): Maximum elevation - Minimum elevation within one wave period
  • Wave Period (T): Time between consecutive upward zero-crossings

Statistical Parameters Calculated:

  • Hs: Significant wave height (average of highest 1/3 waves)
  • Hmean: Mean wave height (average of all waves)
  • Tmean: Mean wave period (average of all wave periods)
  • H1/10: Average of highest 1/10 waves

Applications: Wave climate analysis, coastal design, marine operations planning

Input Requirements

  • Wave Data: Time series of wave elevation (CSV format, one value per line or comma-separated)
  • Sampling Frequency: Data collection rate in Hz (typical: 1-10 Hz)
  • Minimum Data: At least 10 data points (recommended: >500 for reliable statistics)

Wave Reflection Analysis (Three-Gauge Method)

Method & Theory

Purpose: Separate incident and reflected waves using three-gauge array measurements to determine reflection coefficients.

Theory: In coastal engineering, waves approaching a structure create both incident and reflected components. The total wave field at any location is:

η(x,t) = A_i cos(kx - ωt) + A_r cos(kx + ωt + φ)

Where: η = surface elevation, A_i = incident amplitude, A_r = reflected amplitude, k = wave number, ω = frequency

Solution Method:

  • 1. FFT analysis of time series from three gauges
  • 2. Frequency domain separation using least squares
  • 3. Calculate wavelength for each frequency component
  • 4. Solve matrix system for incident/reflected amplitudes

Key Parameters:

  • Hi: Incident wave height (2 × incident amplitude)
  • Hr: Reflected wave height (2 × reflected amplitude)
  • Kr: Reflection coefficient (Hr/Hi)

Applications: Breakwater design, coastal structure optimization, wave energy analysis

Input Requirements

  • Gauge Positions: Three gauge positions along wave propagation direction (e.g., 0, 0.3, 0.9 m)
  • Water Depth: Constant depth at gauge locations in meters
  • Time Step: Data sampling interval in seconds (typically 0.01-0.1 s)
  • Three-Gauge Data: Synchronized time series from all gauges (CSV format: gauge1,gauge2,gauge3)
  • Data Quality: Sufficient length for frequency analysis (recommended: >1000 points)
  • Gauge Spacing: Should capture wavelength variations (typical: L/8 to L/4 spacing)