Lecture 16 oceanography
Lecture Overview
This is the second lecture on tides, building upon a previous discussion that covered fundamental concepts related to sea levels and the general phenomenon of tides. It's crucial to understand the foundational aspects from the prior lecture to fully grasp today's material.
Today's focus is on the underlying physical reasons behind the existence and behavior of tides, specifically discussing two primary theoretical explanations that offer different but complementary perspectives:
Isaac Newton's explanation using gravitational forces: This classical approach highlights the Moon's and Sun's gravitational pull as the primary mechanism for tidal generation, focusing on the differential gravitational force across Earth.
The oceanographic explanation involving the balance between gravitational and centrifugal forces: This more comprehensive view considers the Earth-Moon system as a rotating pair, where both gravitational attraction and the inertial centrifugal force contribute significantly to the formation of tidal bulges.
Key Forces Involved in Tides
To understand how tides are generated, it's essential to first grasp the forces that govern the motion of celestial bodies and masses within rotating systems. These fundamental forces include:
Centripetal Force (Green Arrow):
This is a real force that acts on an object moving in a circular path, pulling it inwards towards the center of rotation. It is essential for maintaining circular motion.
Example: In a system with a ball on a string being swung in a circle, the tension in the string provides the centripetal force required to keep the ball from flying tangentially. If the string is cut, the centripetal force is removed, and the ball would fly out in a straight line tangent to its previous circular path due to its inertia.
Centrifugal Force (Red Arrow):
This is an apparent or fictitious force that is perceived to push an object outward from the center when observed from within a rotating reference frame. It arises from the inertia of the object.
Example: When driving a car rapidly around a sharp curve, you feel a push towards the outside of the curve. This sensation is the centrifugal force, which is essentially your body's inertia wanting to continue in a straight line while the car turns. From an external, non-rotating frame, there's no outward force; instead, the car provides the centripetal force that turns you.
Gravitational Attraction
Gravity is one of the four fundamental forces of nature, responsible for attraction between any two objects possessing mass. It is considered a relatively weak force compared to the electromagnetic or nuclear forces, but it dominates on astronomical scales due to the immense masses involved.
The equation for gravitational force () between two objects is given by Newton's Law of Universal Gravitation: Fg = G rac{m1 ullet m2}{r^2}
Where:
is the universal gravitational constant, approximately 6.674 imes 10^{-11} N ullet (m/kg)^2 . It's a fundamental constant that determines the strength of the gravitational interaction.
and are the masses of the two interacting objects (e.g., Earth and the Moon), measured in kilograms ().
is the distance between the centers of mass of the two objects, measured in meters ().
In the Earth-Moon and Earth-Sun systems, gravitational strength variations are critically based on both the distance () and the masses (, ) involved. Notably, the force decreases rapidly with the square of the distance, meaning that even a small change in distance can significantly alter the gravitational pull.
`Earth-Moon System and Gravitational Forces
A diagram (not provided here, but mentally visualize) illustrates the differential gravitational attraction exerted by the moon on different points of Earth. Various sized arrows depict the gravitational force:
The direction of these arrows consistently indicates the gravitational pull directly towards the moon's center.
Arrow sizes vary inversely with the square of the distance from the moon. Points on Earth closest to the moon experience the strongest pull (largest arrows), while points farthest away experience the weakest pull (smallest arrows). This differential pull is the foundation of tidal forces.
Example Calculation:
Consider two points, E and A, on Earth's surface. Point E is directly facing the Moon, while point A is on the opposite side. The gravitational force at point E will be significantly stronger than at point A because point E is approximately one Earth diameter closer to the Moon. This difference in gravitational force across Earth is what creates the tidal stretching effect.
Centrifugal Force Explained
As part of the Earth-Moon system, both bodies orbit a common center of mass, known as the barycenter. The centrifugal force, arising from this orbital motion, acts as a uniform push away from this common rotational axis on every particle of Earth.
The rotational axis mentioned here refers to the axis of the Earth-Moon barycenter, which is distinct from Earth's own daily rotational axis. The Earth-Moon barycenter, the center of their mutual orbit, resides within the Earth itself—approximately 1700 km below Earth's surface—due to the Earth's significantly greater mass compared to the Moon.
Dynamics of Tides
Tidal Forces are the true drivers of oceanic tides. They are not simply the gravitational force, but rather the resultant or differential force. They represent the vector sum of two primary components:
The gravitational forces exerted by the moon (and sun) vary across Earth (depicted by the green arrows in a typical diagram).
The uniform centrifugal force acting on every part of Earth due to the planet's revolution around the Earth-Moon barycenter (depicted by the red arrows).
The tidal force is the net vector obtained when the Moon's gravitational pull and the centrifugal force are combined. This net force is what causes the water on Earth's surface to bulge.
Water Bulges Due to Tidal Forces
The combined effect of these forces leads to the formation of two distinct water bulges on Earth's surface:
Bulge Towards the Moon: On the side of Earth directly facing the Moon, the Moon's gravitational pull is strongest and outward (towards the Moon), exceeding the average centrifugal force. This differential pull draws the water towards the Moon, creating a bulge.
Bulge Away from the Moon: On the side of Earth opposite the Moon, the Moon's gravitational pull is weakest. Here, the uniform centrifugal force (outward) is greater than the Moon's gravitational pull (inward), effectively pushing water away from the Earth-Moon barycenter and creating a second bulge.
Spring Tides: These are exceptionally high high tides and very low low tides that occur when the Sun, Moon, and Earth are aligned in a straight line. This configuration is known as syzygy.
During new moon and full moon phases, the gravitational pulls of the Sun and Moon combine or add together, leading to a much stronger combined tidal force.
Neap Tides: These are characterized by lower high tides and higher low tides, resulting in a smaller tidal range. They occur when the Moon and Sun are at right angles (perpendicular) relative to Earth, forming an 'L' shape. This configuration is known as quadrature.
During the first and third quarter moon phases, the gravitational pull of the Sun works against or partially cancels out the tidal effect of the Moon, diminishing the overall tidal force.
Example statistics of tides observe significant variations in tidal ranges around the world, from near-zero in enclosed seas to over 15 meters in places like the Bay of Fundy, directly influenced by these astronomical forces and local geography.
Impacts of Earth's Structure
Dynamic Theory of Tides: This theory was introduced to address the significant limitations of the simpler equilibrium theory of tides (which assumes a uniform, water-covered Earth with instantaneous response to forces). The dynamic theory provides a more realistic and accurate prediction of tidal patterns.
Earth is not completely water-covered; continents obstruct the free flow of water, channelizing tidal waves and causing complex reflections and interference patterns.
Oceanic depths vary greatly, and tidal waves behave as shallow water waves, meaning their speed is dependent on water depth . This leads to variations in wave propagation. Significant friction also occurs at the ocean floor, dissipating tidal energy and influencing wave movement.
The dynamic theory can predict tides very accurately because it incorporates these crucial physical considerations, including the actual bathymetry (ocean depth), coastline configurations, and the Earth's rotation (Coriolis effect), allowing for precise modeling of water flow and geographic formations.
Coriolis Effect on Tidal Motion
The Coriolis effect, a consequence of Earth's rotation, significantly influences the motion of large masses of water, including tidal currents.
In the Northern Hemisphere, moving water (or air) is deflected to the right of its intended path. Conversely, in the Southern Hemisphere, it's deflected to the left.
This deflection can result in circular tidal movements around specific points in ocean basins called amphidromic points. Around these points, the tidal range is effectively zero, and tidal waves rotate around them, creating a complex pattern of high and low tides that propagate like a rotating wave across the basin.
An example of the Bay of Fundy (Nova Scotia, Canada) dramatically illustrates how basin geometry and resonance, coupled with the Coriolis effect, can restrict tidal wave sweeping and amplify the tidal range to extreme levels (the highest in the world, over 16 meters).
Tides and Time
The constant friction generated by tidal currents (tidal friction) between the moving water and the Earth's seafloor has profound long-term consequences:
This friction acts as a brake, causing Earth's rotation to slow down gradually over geological timescales, increasing the length of the day. Simultaneously, it transfers angular momentum to the Moon, causing the Moon to slowly recede from Earth at an approximate rate of 4 centimeters per year.
Historical data from geological evidence such as tidal rhythmites (layered sediments showing tidal cycles) and growth rings in ancient corals can be used to infer the changing number of days per year and Earth's rotational speed in the distant past, confirming the effects of tidal braking.
Tides in Lakes and Smaller Bodies of Water
Tides, though often associated solely with oceans, can indeed be observed in exceptionally large lakes due to their immense size and volume:
Examples include the Great Lakes in North America, particularly Lake Superior, which can experience tidal ranges of a few centimeters. These lake tides are significantly smaller than oceanic tides because the smaller water body cannot effectively resonate with the astronomical tidal forces over such short distances.
Tidal characteristics become negligible or virtually undetectable in smaller bodies of water unless they are subject to other non-astronomical forces that produce significant size and volume fluctuations, such as strong winds (which can cause seiches) or rapid changes in atmospheric pressure.
Conclusion and Next Steps
This lecture has provided a comprehensive overview of the fundamental principles of tidal generation, focusing on the interplay of gravitational and centrifugal forces, and the dynamic factors that shape tidal behavior across the globe.
We've emphasized the accuracy of tidal predictions through the application of dynamic theories, which are primary subjects of oceanographic study.
Preparation for Quiz: Review key concepts such as the distinction between centripetal and centrifugal forces, the detailed explanations of spring and neap tides, the workings of the gravitational force equation, and the implications of the dynamic theory of tides including the Coriolis effect and amphidromic systems.