Tides

Lecture 14: Tides

OCS 1005/1006
Spring 2026
Dr. Paul Miller

Characteristics and Causes of Tides

  • Definition of Tides:
      - Tides are periodic, short-term changes in the height of the ocean surface at a specific location.
      - They are caused by a combination of the gravitational forces exerted by the moon and the sun, along with the motion of the Earth.
      - Tides represent the longest of all ocean waves.
      - The wavelengths associated with tides are so extensive that even in depth as profound as the abyssal plain, the depth remains less than half of the wavelength.
      - Tides are affected by the frictional effects produced at the ocean bottom, categorizing them as shallow water waves.

Theoretical Framework

Equilibrium Theory of Tides

  • This theory explains tides by analyzing the balance between and the effects of gravitational and inertial forces that keep planets in orbit around the sun and moons in orbit around their planets.
  • The proximity of the moon to Earth grants it a more substantial influence on tides than the more distant sun.

Dynamic Theory of Tides

  • The dynamic theory considers additional factors such as:
      - Water Depth
      - Seabed Contour
      - Water Viscosity
      - Tide Wave Inertia
  • The combination of both equilibrium and dynamic theories enables predictions of tides up to several years in advance.

Forces Behind Tides

  • Gravity:
      - The gravitational force pulls Earth, the moon, and the sun toward one another.
  • Inertia:
      - The inertial force, which is the tendency of moving objects to continue in a straight line, acts to keep masses apart.
  • The interplay between gravity and inertia generates tides.

Orbital Mechanics

  1. If the planet is stationary, gravitational attraction will draw it into the sun.
  2. If the planet is in motion, the inertia of the planet keeps it moving in a linear path.
  3. In a stable orbit, the forces of gravity and inertia create a balance that allows the planet to travel along a fixed orbital path around the sun.

Factors Influencing Tidal Generation

  • Distance Matters:
      - The tide-generating force, denoted as TT, can be expressed with the formula:
    T=Gimesm1imesm2r3T = \frac{G imes m_1 imes m_2}{r^3}
        where:
        - GG = universal gravitational constant
        - m1m_1 and m2m_2 = masses of the two celestial bodies
        - rr = distance between their respective centers
  • The force of tidal generation decreases in proportion to the cube of the distance from the Earth's center to the center of the tide-generating body.
  • Example:
      - The moon, despite being 27 million times less massive than the sun, is located about 387 times closer to Earth than the sun.
      - Thus, the sun's impact on tides is only about 46% of that of the moon.

Lunar Tides

  • The gravitational pull of the moon attracts ocean water toward it.
  • The motion of the Earth around the center of mass of the Earth-moon system creates a bulge on the side opposite the moon, resulting in two tidal bulges overall.

High and Low Tides

  • The interaction of these tidal bulges with the Earth's rotation causes the rise and fall of tides:
      - As the Earth rotates on its axis, locations such as islands on the equator move through these crests and troughs (the peaks and valleys of tidal waves).
        - When an island moves through a crest, it experiences high tide.
        - Conversely, as the island transitions through a trough, it experiences low tide.

Movement of the Moon & Tidal Bulges

  • The moon's position is dynamic and it does not remain exactly over the equator.
      - Throughout the month, the moon fluctuates from a position as high as 28.5 degrees above the equator to as low as 28.5 degrees below.
  • The tidal bulges adapt and track the moon's movement throughout its monthly cycle.

Lunar Days vs. Solar Days

  • Definition of a Lunar Day:
      - A lunar day is the time interval from when the moon is highest in the sky to the next occurrence of that same position.
      - Lunar days are longer than solar days.
  • In a typical 24-hour solar day, the moon moves approximately 12.2 degrees eastward.
  • Therefore, Earth must rotate an additional 12.2 degrees, which takes about 50 minutes, to realign the moon back overhead. - Consequently, a lunar day measures roughly 24 hours and 50 minutes.
  • As a result of this time difference, lunar tides typically occur around 50 minutes later each day.

Solar Tides

  • The sun also exerts a gravitational influence on the ocean's tides, although its distance diminishes this impact compared to that of the moon.
  • Smaller solar tidal bulges are generated, which align with the sun's position as it moves above and below the equator by 23.5 degrees.
  • Unlike lunar bulges, solar bulges shift more gradually due to the Earth's annual revolution around the sun.

Neap Tides

  • Neap tides occur when the moon, Earth, and sun form a right angle relative to one another.
      - In this configuration, solar tides counteract lunar tides.
      - This results in minimal height differences in both high and low tides.
      - Neap tides typically arise a week following spring tides, occurring around two-week intervals.

Spring Tides

  • Spring tides arise when the Earth, moon, and sun are aligned in a straight line.
      - The combination of lunar and solar tides amplifies the overall tidal height.
      - Spring tides lead to exceptionally high high tides and depressingly low low tides.
      - They manifest at two-week intervals, coinciding with new and full moons.
      - The lunar month, relevant to spring tides, is approximately 27.3 days.

Tidal Patterns

  • The movement of tidal crests is governed as forced waves.
      - Their velocity is determined by the depth of the ocean, behaving similarly to shallow water waves.
  • Continental landmasses obstruct tidal crests, thus diverting, slowing, and otherwise altering their flow patterns.
  • The topography of ocean basins profoundly impacts tidal patterns and heights due to variations in geography.
  • Tides are also influenced by other types of ocean surface oscillations (e.g., meteorological tides).
  • As a result, different coastlines experience distinct tidal patterns, including semidiurnal, diurnal, and mixed tides.

Types of Tides

  • Diurnal Tides:
      - Defined as having one high and one low tide within a single lunar day.
      - Example: Gulf of Mexico exhibits diurnal tides.
  • Semidiurnal Tides:
      - Characterized by two high tides and two low tides of near-equal height each lunar day.
      - Example: Areas like Cape Cod typically show semidiurnal tides.
  • Mixed Tides:
      - This category includes both high and low tides with significantly varying heights during the tidal cycle.
      - Example: Observed along the Pacific coast, representing a blend of diurnal and semidiurnal characteristics.

No-Tide Points

  • Water moving as a tide is influenced by the Coriolis effect.
      - This causes tide movement to be counter-clockwise around a specific point known as an amphidromic point in the northern hemisphere.
      - The height of tides generally increases with the distance from the amphidromic point.

Amphidromic Systems

  • If a basin is symmetrical and wide, it can lead to a miniature amphidromic system developing.
      - However, if a basin is narrow and restricted, the tidal wave crest cannot rotate effectively around the amphidromic point.

Characterizing Tides in Various Environments

  • Tidal Datum:
      - This term refers to the reference level used for comparing tidal height.
      - Possible reference points include mean sea surface level, the mean of the lowest tides (for mixed tides), or the average of all low tides in areas experiencing semidiurnal and diurnal tides.
  • Tidal Range:
      - Refers to the height difference between high-water and low-water marks.
      - The most significant tidal ranges occur at the edges of the largest ocean basins, especially in bays and inlets.
  • Tidal Bore:
      - Defined as a high, often breaking wave created by a tidal crest that moves rapidly up an estuary or river.
      - It is frequently referred to inaccurately as a tidal wave.

Case Studies

  • Bay of Fundy:
      - Renowned for having the world's largest tidal range.
  • Tidal Power Plant on Annapolis River (USA):
      - An example of tidal energy utilization in practice.

Effects of Tides on Earth's Rotation

  • The frictional forces exerted by tides gradually slow the Earth’s rotation over time.
      - This slowing occurs at a rate of a few hundredths of a second per century.
      - Historical data:
        - Approximately 350 million years ago, a year had between 400 and 410 days, with each day being about 22 hours long.

Impact of Tidal Patterns on Marine Life

  • Organisms located in the upper intertidal zone must adapt to submergence and exposure to air/social transitions.
  • In contrast, organisms in the lower intertidal zones contend with predation challenges.

Nuisance Floods

  • Recent trends in global sea level rise have led to increased instances of spring tides flooding coastal structures under specific meteorological conditions.
      - This is particularly problematic for coastal Louisiana.
  • Example:
      - Onshore easterly winds can exacerbate flooding events, such as observed in Cocodrie, LA, on Terrebonne Bay during a spring tide (1/10/20).

Daily Quiz

  • Question: Which celestial body exerts a stronger gravitational pull on the ocean? The Moon or the Sun?
      - Answer: The Moon exerts a stronger gravitational pull on the ocean compared to the Sun due to its proximity to Earth.

Additionally, students are encouraged to engage with supplementary materials and quizzes as per the ongoing course assessments to improve understanding of tidal dynamics and their implications.