Chapter 5 Coastal Engineering: Seiche and Harbour oscillation

Chapter 5 Coastal Engineering: Seiche and Harbour oscillation#

  1. Introduction: Harbour Oscillation

  2. Simulation: Oscillation

  3. Self-Assessment

1. Introduction#

Descriptive alt text for accessibility

Fig. 27 **Figure 5.5 **: Seiches and Harbour Oscillation.#

🌊 Seiche, Open Basins, and Closed Basins#

A seiche is a long-period standing wave that oscillates within an enclosed or partially enclosed water body. It is typically caused by:

  • Atmospheric pressure changes

  • Seismic activity

  • Strong and sustained winds

The oscillation resembles water sloshing back and forth, often forming nodes and antinodes similar to a vibrating string.

Open Basin#

An open basin is a body of water that is connected to a larger water body (e.g., ocean or sea) and allows unrestricted water exchange. These basins are influenced by:

  • Tidal forces

  • Ocean currents

  • Wave action from the open sea

Example: A bay connected to the ocean.

Closed Basin#

A closed basin is a confined water body that does not share boundaries with any larger water system. It is not influenced by tides, currents, or external wave action.

Example: A shallow inland lake.

Summary#

Term

Description

Example

Seiche

Standing wave in enclosed water body due to pressure, seismic, or wind

Oscillation in a lake

Open Basin

Connected to ocean/sea; influenced by tides and currents

Bay

Closed Basin

Isolated; no tidal or wave influence from larger water bodies

Shallow lake

Wave Amplification, Harbor Oscillations & Seiche Phenomena — Overview#

This concept explores how long-period water waves interact with coastal basins, including harbors, lakes, and enclosed bays. When wave frequencies align with a basin’s natural oscillation mode, the system can undergo resonance, leading to wave amplification, harbor oscillations, or seiche formation.

What Are These Phenomena?#

🔁 Wave Amplification#

Occurs when the period of incoming waves resonates with the basin’s natural oscillation frequency, amplifying wave heights significantly. This is governed by principles of constructive interference and standing wave formation.

🌊 Harbor Oscillations (Seiche)#

A seiche is a standing wave oscillation in an enclosed or semi-enclosed water body, driven by:

  • Long-period ocean waves

  • Wind or atmospheric pressure changes

  • Seismic activity (tsunami-triggered resonance)

Seiches can persist long after the forcing event, creating hazardous fluctuations in water levels and vessel stability.

Seiche Period Equations#

Basin Types#

Type

Boundary Condition

Behavior

Closed Basin

Fully enclosed (e.g. lake)

Supports full standing waves (seiche)

Open Basin

Partially open (e.g. harbor with entrance)

Partial oscillation with damping

✅ Closed Basin (e.g. lake or reservoir):#

\[ T_{\text{closed}} = $frac{2L}{$sqrt{g h}} \]

  • \(( L \)): basin length

  • \(( h \)): average depth

  • Supports full standing wave oscillations with nodes and antinodes

✅ Open Basin (e.g. harbor with entrance):#

\[ T_{\text{open}} = \frac{4L}{\sqrt{g h}} \]

  • One end is open, modifying reflection conditions

  • Leads to partial standing wave oscillations

##$ Wave Amplification Formula

\[ A = \left| \frac{1}{1 - \left( \frac{T_i}{T_n} \right)^2} \right| \]

  • \(( A \)): Amplification Factor

  • \(( T_i \)): Incoming wave period

  • \(( T_n \)): Natural basin period

When \(( T_i \approx T_n \)), amplification spikes — a resonance condition resulting in highly elevated water levels.

Impact Area

Description

⚓ Port Operations

Extreme oscillations disrupt vessel stability

🌪️ Storm Surge Modeling

Predict water level amplifications from offshore

🏗️ Harbor Design

Shape and size should avoid resonant conditions

📡 Real-Time Monitoring

Early warning for atmospheric-driven oscillations

Summary#

  • Closed basins have shorter natural periods than open basins of equal size

  • Amplification is strongest near resonance, risking infrastructure and navigation

  • Modeling both basin types allows safer engineering of harbors and coastal systems

Applications#

  • ⚓ Harbor Design: Avoiding resonant frequencies that amplify vessel motion

  • 🌪️ Storm Surge Modeling: Simulating long-period wave intrusion into bays

  • 🧪 Wave Tank Experiments: Studying seiche formation and boundary effects

  • 🌍 Lake Oscillation Analysis: Monitoring water level fluctuations from wind or pressure events

Visualization Tool#

Use an interactive Python model to:

  • Input basin length & depth

  • Adjust incoming wave period

  • Compute natural oscillation frequency

  • Plot amplification curve

  • Identify resonance zones and safe frequency ranges

Reference#

[of Engineers, 1984] and [U.S. Army Corps of Engineers, 2008] include guidance on harbor oscillation (also known as seiche or long-period wave resonance) in enclosed basins and include formulas for basin resonance periods and design considerations for minimizing oscillation effects on harbor structures. [of Engineers, 1984] provides a foundational overview of harbor oscillations, focusing on simplified standing wave theory in closed rectangular basins (basic formulas for estimating natural periods and cautions against resonance) but lacks detailed modeling for complex geometries. In contrast, [U.S. Army Corps of Engineers, 2008] delivers a comprehensive treatment of both closed and open basin oscillations, including Helmholtz modes, damping effects, and multi-modal resonance. It supports advanced numerical modeling and offers quantitative design guidance for mitigating oscillation impacts in real-world harbor systems.

2. Simulation#

🌊 Harbor Resonance Simulator — Natural Period & Amplification#

This interactive Jupyter Notebook tool models wave resonance in open or closed harbor basins by comparing the incoming wave period to the basin’s natural oscillation period.

🧠 What It Does#

  • Calculates natural period (T_nat) using basin length, depth, and geometry (open or closed)

  • Computes amplification factor:

    • Represents how much wave energy builds up due to resonance

    • Increases sharply when incoming period ≈ natural period

  • Plots amplification across a range of wave periods

  • Flags dangerous resonance if amplification > 10

🎛️ Inputs#

Parameter

Description

L

Basin length (m)

h

Basin depth (m)

T_in

Incoming wave period (s)

basin_type

'closed' (2L mode) or 'open' (4L mode)

📊 Outputs#

  • Amplification curve vs. wave period

  • Vertical markers for:

    • Incoming wave period (red dashed line)

    • Basin’s natural period (green dotted line)

  • Amplification warning if near-resonant

  • Text summary of natural period and peak amplification

🧭 How to Interpret#

  • If incoming period ≈ natural period, amplification spikes → risk of harbor oscillations

  • Use plots to:

    • Assess resonance vulnerability

    • Guide breakwater design or tuning harbor geometry

    • Educate on harbor dynamics and period matching

High amplification = potential wave surge or harbor seiching. Use this tool to tune harbor design against resonance risk.

import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import FloatSlider, Dropdown, interact

g = 9.81  # gravity

# ⏱️ Natural period based on basin type
def natural_period(L, h, basin_type='closed'):
    factor = 2 if basin_type == 'closed' else 4
    return factor * L / np.sqrt(g * h)

# 📈 Amplification factor
def amplification(T_in, T_nat):
    if T_in == T_nat:
        return np.inf
    return abs(1 / (1 - (T_in / T_nat)**2))

# 🔧 Interactive model
def harbor_model(L, h, T_in, basin_type):
    T_nat = natural_period(L, h, basin_type)
    amp = amplification(T_in, T_nat)

    periods = np.linspace(0.1, 2*T_nat, 500)
    amps = [amplification(T, T_nat) for T in periods]

    plt.figure(figsize=(10, 4))
    plt.plot(periods, amps, label="Amplification Curve", color='royalblue')
    plt.axvline(T_in, color='red', linestyle='--', label=f'Incoming Wave Period: {T_in:.2f} s')
    plt.axvline(T_nat, color='green', linestyle=':', label=f'{basin_type.capitalize()} Basin Natural Period: {T_nat:.2f} s')
    plt.title(f"Wave Amplification in {basin_type.capitalize()} Basin")
    plt.xlabel("Incoming Wave Period (s)")
    plt.ylabel("Amplification Factor")
    plt.grid(True)
    plt.legend()
    plt.tight_layout()
    plt.show()

    if amp > 10:
        print(f"⚠️ Near Resonance! Amplification: {amp:.2f}")
    else:
        print(f"📊 Amplification Factor: {amp:.2f}")
    print(f"🌊 Natural Period ({basin_type} basin): {T_nat:.2f} s")

# 🎛️ Interactive Controls
interact(harbor_model,
         L=FloatSlider(value=500, min=100, max=2000, step=50, description='Basin Length (m)'),
         h=FloatSlider(value=10, min=2, max=50, step=1, description='Basin Depth (m)'),
         T_in=FloatSlider(value=200, min=20, max=400, step=5, description='Wave Period (s)'),
         basin_type=Dropdown(options=['closed', 'open'], value='closed', description='Basin Type'));

3. Self-Assessment#

Quiz: Seiche, Harbor Oscillations & Wave Amplification#

This conceptual and reflective quiz is designed to deepen your understanding of the physics behind wave resonance phenomena in coastal basins. It covers closed vs open basin behavior, amplification mechanisms, and harbor oscillation dynamics.

Conceptual Questions#

1. What is the primary cause of a seiche in a closed basin?#

  • Wind or atmospheric pressure changes

  • Tidal forces

  • Earth’s rotation (Coriolis effect)

  • Wave diffraction at the basin entrance
    ✅ Answer: Wind or atmospheric pressure changes

2. How does the natural period of oscillation differ between a closed basin and an open basin?#

  • Shorter in open basin due to energy dissipation

  • Longer in open basin due to doubled oscillation factor

  • Same for both types of basins

  • Shorter in closed basin due to amplification
    ✅ Answer: Longer in open basin due to doubled oscillation factor

3. What happens when the incoming wave period matches the natural period of a harbor basin?#

  • Wave energy is dissipated completely

  • Wave amplification occurs due to resonance

  • Basin oscillates at a lower frequency

  • Basin becomes stable and motionless
    ✅ Answer: Wave amplification occurs due to resonance

4. Which factor most influences the natural period of a basin?#

  • Basin width

  • Basin depth

  • Salinity of water

  • Water temperature
    ✅ Answer: Basin depth

5. What is the role of damping in wave amplification?#

  • Increases amplitude

  • Reduces amplitude through energy dissipation

  • Has no effect

  • Increases natural period
    ✅ Answer: Reduces amplitude through energy dissipation

🔍 Reflective Questions#

  • 🔸 In what real-world situations could seiche oscillations pose a danger to coastal infrastructure?

  • 🔸 How would you design a harbor to minimize resonance risk?

  • 🔸 Why do higher modes of oscillation matter when modeling wave behavior in large basins?

  • 🔸 How might climate change affect the frequency or intensity of resonance-driven events?

📈 Amplification & Resonance Formula Review#

\[ A = \left| \frac{1}{1 - \left( \frac{T_i}{T_n} \right)^2} \right| \quad \text{(without damping)} \]
\[ T_{\text{closed}} = \frac{2L}{\sqrt{g h}} \quad , \quad T_{\text{open}} = \frac{4L}{\sqrt{g h}} \]

Where:

  • \(( T_i \)): Incoming wave period

  • \(( T_n \)): Natural period of basin

  • \(( L \)): Basin length

  • \(( h \)): Water depth

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