Tidal Ellipse Analysis

Advanced harmonic analysis of tidal currents with ellipse parameter calculation, constituent identification, and comprehensive visualization by Claudio Iturra

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Tidal Velocity Data Input

Enter your tidal velocity time series and location parameters

Input Configuration

📍 Location Parameters

Analysis Options

Tidal Ellipse Parameters

🔄 Ellipse Geometry

  • • Semi-major axis (a): Maximum current speed
  • • Semi-minor axis (b): Minimum current speed
  • • Inclination (θ): Orientation of major axis
  • • Eccentricity (e): Shape parameter (0=circle, 1=line)

🌊 Tidal Properties

  • • Phase (φ): Time of maximum current
  • • Sense: Clockwise or counterclockwise rotation
  • • Amplitude: Vector magnitude of tidal current
  • • Greenwich phase: Referenced to Greenwich

📊 Major Constituents

M2: 12.42h (Principal lunar)
S2: 12.00h (Principal solar)
N2: 12.66h (Lunar elliptic)
K1: 23.93h (Lunar diurnal)
O1: 25.82h (Lunar diurnal)
K2: 11.97h (Lunisolar)

Tidal Ellipse Analysis Results

Comprehensive harmonic analysis and ellipse visualization

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Enter your tidal velocity data and perform analysis to see ellipse results

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Tidal Ellipse Theory

Mathematical foundations and harmonic analysis principles

Harmonic Analysis

Tidal currents are decomposed into harmonic constituents:

u(t) = Σ [Aᵢ cos(ωᵢt + φᵢ)]
v(t) = Σ [Bᵢ cos(ωᵢt + ψᵢ)]

Where:

  • ωᵢ = angular frequency of constituent i
  • Aᵢ, Bᵢ = amplitudes in u, v directions
  • φᵢ, ψᵢ = phase lags

Ellipse Parameters

From complex representation w = u + iv:

w = W⁺e^(iωt) + W⁻e^(-iωt)

Ellipse parameters:

a = |W⁺| + |W⁻| (semi-major)
b = ||W⁺| - |W⁻|| (semi-minor)
θ = ½arg(W⁺W⁻*) (inclination)
φ = arg(W⁺) (phase)

Nodal Corrections

Account for 18.6-year lunar nodal cycle:

A'ᵢ = fᵢ × Aᵢ
φ'ᵢ = φᵢ + uᵢ

Where fᵢ and uᵢ are nodal amplitude and phase corrections.

Critical for long-term predictions and accurate constituent separation.

Applications

Navigation

Current predictions for safe passage planning

Engineering

Design loads for offshore structures

Oceanography

Understanding tidal mixing and transport

Climate

Long-term tidal energy dissipation studies