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Wave Celerity (Shallow Water) Calculator

Calculates the speed of a wave in shallow water based on gravity and water depth.

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Wave Celerity

Formula first

Overview

This equation, C = √(gd), is used to determine the speed of waves in shallow water, a condition where the water depth (d) is less than 1/20th of the wave's wavelength (L/20). Unlike deep water waves, shallow water wave celerity is independent of wave period and wavelength, being solely governed by the acceleration due to gravity (g) and the water depth (d). This principle is crucial for understanding how waves slow down and transform as they approach a coastline, leading to phenomena like wave shoaling and breaking.

Symbols

Variables

g = Acceleration due to gravity, d = Water Depth, C = Wave Celerity

Acceleration due to gravity
m/s²
Water Depth
Wave Celerity
m/s

Apply it well

When To Use

When to use: Apply this formula when dealing with waves in very shallow environments, specifically when the water depth (d) is less than 1/20th of the wave's wavelength (L/20). This is common in nearshore zones, estuaries, and tidal flats, where the seabed significantly influences wave propagation.

Why it matters: Understanding shallow water wave celerity is fundamental for predicting wave breaking, coastal erosion patterns, and the design of coastal structures. It's essential for navigation in shallow channels, managing sediment transport in estuaries, and assessing tsunami propagation speeds across continental shelves.

Avoid these traps

Common Mistakes

  • Using the formula for deep or intermediate water waves.
  • Forgetting to take the square root.
  • Using wavelength or period instead of depth.

One free problem

Practice Problem

A wave is approaching a beach where the water depth is 2.5 meters. Assuming the acceleration due to gravity is 9.81 m/s², calculate the celerity (speed) of this shallow water wave. Give your answer to two decimal places.

Acceleration due to gravity9.81 m/s²
Water Depth2.5 m

Solve for:

Hint: Remember to take the square root of the product of g and d.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Introduction to Physical Oceanography by Robert H. Stewart, Texas A&M University (online textbook)
  2. Fluid Mechanics by Frank M. White, 8th Edition
  3. Wikipedia: Ocean surface wave (Shallow water waves section)
  4. NIST CODATA
  5. Bird-Stewart-Lightfoot (Transport Phenomena)
  6. Wikipedia: Standard gravity
  7. Wikipedia: Wave celerity
  8. Wikipedia: Shallow water equations