Tides Study Notes

Lecture 14: Tides

Course Information: OCS 1005/1006, Spring 2026
Instructor: Dr. Paul Miller

Characteristics and Causes of Tides

  • Definition: Tides are periodic, short-term changes in the height of the ocean surface at a particular location.
  • Causes: They are caused by a combination of the gravitational forces exerted by the moon and the sun, along with the motion of Earth.
  • Wavelengths: Tides represent the longest of all ocean waves, with wavelengths so extensive that even over the abyssal plain, the depth is less than half the wavelength of these waves.
  • Wave Interaction: Waves are influenced by the frictional effects of the ocean floor, qualifying them as shallow water waves.

Theories Explaining Tides

Equilibrium Theory

  • Tides can be explained through the balance of forces which keep the planet in its orbit around the sun and the moon in its orbit around Earth.
  • Notably, the moon's proximity to Earth gives it a more significant influence over tidal patterns compared to the sun.
  • The equilibrium theory serves to explain tides on a hypothetical planet uniformly covered by water.

Dynamic Theory

  • The dynamic theory incorporates various factors affecting tides, including:
      - Sea depth
      - Seabed contours
      - Viscosity of water
      - Tide wave inertia
  • The combination of both equilibrium and dynamic theories allows for forecasts of tidal movements for years ahead.

Forces Responsible for Tides

  • Gravity: It pulls the Earth towards the moon and the sun.
  • Inertia: Represents the tendency of moving objects to continue in a straight-line path. This force works against gravitational pull.
  • Tidal Generation: Tides are generated through the interplay of gravitational force and inertia.

Orbital Mechanics of Tides

  1. In the absence of movement, gravity would accelerate an object into the sun.
  2. When in motion, inertia propels the object to maintain a straight path.
  3. In a stable orbital scenario, gravity and inertia work together to maintain a fixed orbital path around the sun, establishing a balance between the two forces.

Distance and Tide-Generating Forces

  • The tide-generating force ( ext{T}) can be mathematically expressed as follows:
      T = G rac{m_1 m_2}{r^2}
    Where:
      - G is the universal gravitational constant
      - m1 and m2 are the masses of the respective celestial bodies
      - r is the distance between their centers.
  • Gravitational forces that generate tides vary inversely with the cube of the distance from Earth’s center to the center of the tide-generating object.
  • Notably, the sun, while being 27 million times more massive than the moon, is also approximately 387 times further away, which diminishes its overall effect on tides to only 46% of that of the moon's.

Lunar Tides

  • The gravitational force exerted by the moon attracts ocean water towards it. This gravitational pull, combined with Earth's rotational movement around the Earth-moon system’s center of mass, causes a second bulge of water on the side opposite the moon, leading to the formation of two tidal bulges.

High and Low Tides

  • As Earth rotates on its axis, locations such as an equatorial island alternately pass through these tidal bulges.
  • When the island moves into the crest of a tidal bulge, it experiences a high tide. Conversely, upon moving into the trough created, it experiences a low tide.

Movement of Tidal Bulges

  • Lunar Positioning: The moon does not maintain a fixed position above the equator; its position changes from being as high as 28.5 degrees above the equator to as low as 28.5 degrees below over the course of a month.
  • The tidal bulges are influenced by the moon's movement throughout its lunar cycle.

Lunar Days vs Solar Days

  • Definition of a Lunar Day: The duration between successive occurrences of the moon being highest in the sky.
  • Lunar days are longer than solar days.
  • During a 24-hour solar day, the moon shifts eastward approximately 12.2 degrees. To realign with the same position overhead, Earth must rotate for an additional 50 minutes, resulting in a lunar day lasting 24 hours and 50 minutes. Hence, tidal highs and lows generally occur around 50 minutes later each day.

Solar Tides

  • While the sun’s gravity does impact ocean tides, its effect is weaker due to the greater distance compared to the moon.
  • Solar Bulges: Smaller tidal bulges affected by the sun shift positions relatively slowly, as the sun’s perceived motion occurs yearly by about 23.5 degrees above and below the equator.

Neap Tides

  • When the moon, Earth, and sun create a right-angle configuration, the gravitational pull of the solar tide suppresses the lunar tide.
  • This phenomenon results in lower high tides and higher low tides, known as neap tides. Neap tides occur approximately one week after spring tides and follow a two-week cycle.

Spring Tides

  • When the Earth, moon, and sun align perfectly, the resulting tidal forces are cumulative, leading to exceptionally high high tides and very low low tides, referred to as spring tides.
  • These tides also follow a two-week interval corresponding with the lunar phases of new and full moons (the complete lunar month is about 27.3 days).

Tidal Patterns

  • Tidal crests, or bulges, are affected by the ocean depth, behaving as forced waves.
  • The continents obstruct these tidal movements, affecting the speed and direction of tidal waves.
  • Basin shapes significantly impact tidal height and patterns, introducing other factors like meteorological tides into the equations.
  • Consequently, coastlines can experience:
      - Diurnal Tides: One high tide and one low tide each lunar day (e.g., Gulf of Mexico)
      - Semidiurnal Tides: Two high tides and two low tides of similar levels each lunar day (e.g., Cape Cod)
      - Mixed Tides: A combination of diurnal and semidiurnal, leading to vastly differing high and low tide heights throughout the cycle (e.g., Pacific Coast).

Diurnal, Semidiurnal, and Mixed Tides

  1. Diurnal Tides: One high and one low tide.
       - Example Location: Gulf of Mexico
  2. Semidiurnal Tides: Two high and two low tides at nearly equal levels.
       - Example Location: Cape Cod
  3. Mixed Tides: Significant variation between successive high and low tides.
       - Example Location: Pacific Coast

No-Tide Point

  • The Coriolis effect influences tidal waters, where they rotate counter-clockwise around specific nodes called amphidromic points in the northern hemisphere.
  • Tidal height typically increases with distance from an amphidromic point, leading to unique tidal phenomena.

Amphidromic Systems

  • Basin conditions play a crucial role in forming amphidromic systems.
  • If a basin is wide and symmetrical, a mini amphidromic system can develop; conversely, a narrow and restricted basin may not allow for tidal wave rotations around an amphidromic point.

Characterizing Tides in Oceans, Bays, and Rivers

  • Tidal Datum: A reference level for analyzing tidal height, which may be defined as:
        - Mean sea surface level
        - Mean of the lowest observed tides (in mixed tide scenarios)
        - Mean of all low tides (in semidiurnal vs. diurnal scenarios)
  • Tidal Range: The difference in height between high-water and low-water marks.
  • The most significant tidal ranges occur at the edges of major ocean basins, particularly in coastal bays and inlets.
  • Tidal Bore: A tidal phenomenon where a high tide crest generates a forceful wave advancing up estuaries or rivers, sometimes referred to as a tidal wave.

Impact of Tides on Earth's Rotation

  • Tidal friction has gradually led to a deceleration in Earth’s rotation, estimating a gradual change of several hundredths of a second per century.
  • Notably, 350 million years ago, a year consisted of roughly 400 to 410 days, with each day lasting merely 22 hours.

Tidal Patterns' Influence on Marine Life

  • Organisms residing in the upper intertidal zones must cope with periods of submergence and susceptibility to desiccation.
  • In contrast, organisms located in the lower intertidal zones face threats from predation.

Nuisance Flooding

  • Rising global sea levels have led to the flooding of coastal infrastructure during spring tides, particularly under certain meteorological conditions.
  • An example situation is seen in coastal areas of Louisiana.

Practical Example of Nuisance Flooding

  • An instance on January 10, 2020, illustrates a spring tide flooding local infrastructure—specifically, an onshore wind event that inundated a parking lot in Cocodrie, LA, situated on Terrebonne Bay.

Daily Quiz

  • Question: Which celestial body exerts a stronger gravitational pull on the ocean? The Moon or the Sun?