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Benjamin Boster.
Today's episode is from a Wikipedia article titled,
Tide.
Tides are the rise and fall of sea levels caused by the combined effects of gravitational forces exerted by the moon,
And to a much lesser extent the sun,
And are also caused by the earth and moon orbiting one another.
Tide tables can be used for any given locale to find the predicted times and amplitude or tidal range.
The predictions are influenced by many factors including the alignment of the sun and moon,
The phase and amplitude of the tide,
Pattern of tides in the deep ocean,
The amphidromic systems of the oceans,
And the shape of the coastline and nearshore basymetry.
They are,
However,
Only predictions.
The actual time and height of the tide is affected by wind and atmospheric pressure.
Many shorelines experience semi-diurnal tides,
Two nearly equal high and low tides each day.
Other locations have a diurnal tide,
One high and low tide each day.
A mixed tide,
Two uneven magnitude tides a day,
Is a third regular category.
Tides vary on timescales ranging from hours to years,
Which determine the lunatidal interval.
To make accurate records,
Tide gauges at fixed stations measure water level over time.
Gauges ignore variations caused by waves with periods shorter than minutes.
These data are compared to the reference or datum level,
Usually called mean sea level.
While tides are usually the largest source of short-term sea level fluctuations,
Sea levels are also subject to change from thermal expansion,
Wind,
And barometric pressure changes,
Resulting in storm surges,
Especially in shallow seas and near coasts.
Tidal phenomena are not limited to the oceans,
But can occur in other systems whenever a gravitational field that varies in time and space is present.
For example,
The shape of the solid part of the earth is affected slightly by earth tide,
Though this is not as easily seen as the water tidal movements.
Four stages in the tidal cycle are named.
The water stops falling,
Reaching a local minimum called low tide.
Sea level rises over several hours,
Covering the intertidal zone,
Flood tide.
The water stops rising,
Reaching a local maximum called high tide.
Sea level falls over several hours,
Revealing the intertidal zone,
Ebb tide.
Oscillating currents produced by tides are known as tidal streams or tidal waves.
Oscillating currents produced by tides are known as tidal streams or tidal currents.
The moment that the tidal current ceases is called slack water or slack tide.
The tide then reverses direction and is said to be turning.
Slack water usually occurs near high water and low water,
But there are locations where the moments of slack tide differ significantly from those of high and low water.
Tides are commonly semi-diurnal,
Two high waters and two low waters each day,
Or diurnal,
One tidal cycle per day.
The two high waters on a given day are typically not the same height,
The daily inequality.
These are the higher high water and the lower high water in tide tables.
Similarly,
The two low waters each day are the higher low water and the lower low water.
The daily inequality is not consistent and is generally small when the moon is over the equator.
The following reference tide levels can be defined from the highest level to the lowest.
Highest Astronomical Tide,
HAT,
The highest tide which can be predicted to occur.
Note that meteorological conditions may add extra height to the HAT.
Mean High Water Springs,
MHWS,
The average of the two high tides on the days of spring tides.
Mean High Water Neeps,
MHWN,
The average of the two high tides on the days of neap tides.
Mean Sea Level,
MSL,
This is the average sea level.
The MSL is constant for any location over a long period.
Mean Low Water Neeps,
MLWN,
The average of the two low tides on the days of neap tides.
Mean Low Water Springs,
MLWS,
The average of the two low tides on the days of spring tides.
Lowest Astronomical Tide,
LAT,
The average of the two low tides on the days of neap tides.
The lowest tide which can be predicted to occur.
Tidal Constituents are the net result of multiple influences impacting tidal changes over certain periods of time.
Primary constituents include the earth's rotation,
The position of the moon and sun relative to the earth,
The moon's altitude,
Elevation above the earth's equator,
And bathymetry.
Variations with periods of less than half a day are called harmonic constituents.
Conversely,
Cycles of days,
Months,
Or years are referred to as long-period constituents.
Tidal forces affect the entire earth,
But the movement of solid earth occurs by mere centimeters.
In contrast,
The atmosphere is much more fluid and compressible,
So its surface moves by kilometers in a sense of the contour level of a particular low pressure in the outer atmosphere.
In most locations,
The largest constituent is the principal lunar semidiurnal,
Also known as the M2 tidal constituent.
Its period is about 12 hours and 25.
2 minutes,
Exactly half a tidal lunar day,
Which is the average time separating one lunar zenith from the next,
And thus is the time required for the earth to rotate once relative to the moon.
Simple tide clocks track this constituent.
The lunar day is longer than the earth day because the moon orbits in the same direction the earth spins.
This is analogous to the minute hand on a watch,
Crossing the hour hand at 12,
And then again at about 1.
05 and a half,
Not at 1.
The moon orbits the earth in the same direction as the earth rotates on its axis,
So it takes slightly more than a day,
About 24 hours and 50 minutes,
For the moon to return to the same location in the sky.
During this time,
It is passed overhead,
Culmination,
Once and underfoot once,
At an hour angle of 0 and 12 respectively.
So in many places,
The period of strongest tidal forcing is the above-mentioned about 12 hours and 25 minutes.
The moment of highest tide is not necessarily when the moon is nearest to zenith or nadir,
But the period of the forcing still determines the time between high tides.
Because the gravitational field created by the moon weakens with distance from the moon,
It exerts a slightly stronger than average force on the side of the earth facing the moon,
And a slightly weaker force on the opposite side.
The moon thus tends to stretch the earth slightly along the line connecting the two bodies.
The solid earth deforms a bit,
But ocean water being fluid,
Is free to move much more in response to the tidal force,
Particularly horizontally.
As the earth rotates,
The magnitude and direction of the tidal force at any particular point on the earth's surface change constantly.
Although the ocean never reaches equilibrium,
There is never time for the fluid to catch up to the state it would eventually reach if the tidal force were constant.
The changing tidal force nonetheless causes rhythmic changes in sea surface height.
When there are two high tides each day with different heights,
And two low tides also of different heights,
The pattern is called a mixed semi-diurnal tide.
The semi-diurnal range,
The difference in height between high and low waters over about a half a day,
Varies in a two-week cycle.
Approximately twice a month around new moon and full moon,
When the sun,
Moon,
And earth form a line,
The tidal force due to the sun reinforces that due to the moon.
The tide's range is then at its maximum.
This is called the spring tide.
It is not named after the season,
But like that word,
Derives from the meaning jump,
Burst forth,
Rise,
As in a natural spring.
Spring tides are sometimes referred to as syzygy tides.
When the moon is at first quarter or third quarter,
The sun and moon are separated by 90 degrees when viewed from the earth,
And the solar tidal force partially cancels the moon's tidal force.
At these points in the lunar cycle,
The tide's range is at its minimum.
This is called the neap tide or neaps.
Neap is an Anglo-Saxon word meaning without the power,
Or forthcognis neap,
Forthgoing without the power.
Neap tides are sometimes referred to as quadrature tides.
Spring tides result in high waters that are higher than average,
Low waters that are lower than average,
Slack water,
Time that is shorter than average,
And stronger tidal currents than average.
Neaps result in less extreme tidal conditions.
There's about a seven-day interval between springs and neaps.
The changing distance separating the moon and earth also affects tide heights.
When the moon is closest at perigee,
The range increases,
And when it is at apogee,
The range shrinks.
Six or eight times a year perigee coincides with either a new or full moon,
Causing perigeean spring tides with the largest tidal range.
The difference between the height of a tide at perigeean spring tide and the spring tide when the moon is at apogee depends on location,
But can be large as a foot higher.
These include solar gravitational effects,
The obliquity tilt of the earth's equator,
And rotational axis,
The inclination of the plane of the lunar orbit,
And the elliptical shape of the earth's orbit of the sun.
A compound tide or overtide results from the shallow water interaction of its two parent waves.
Because the M2 tidal constituent dominates in most locations,
The stage or phase of a tide,
Denoted by the time in hours after high water,
Is a useful concept.
Tidal stage is also measured in degrees,
With 360 degrees per tidal cycle.
Lines of constant tidal phase are called cotidal lines,
Which are analogous to contour lines of constant altitude on topographical maps,
And,
When plotted,
Form a cotidal map or cotidal chart.
High water is reached simultaneously along the cotidal lines extending from the coast out into the ocean,
And cotidal lines,
And hence tidal phases,
Advance along the coast.
Semi-diurnal and long-phase constituents are measured from high water,
Diurnal from maximum flood tide.
This and the discussion that follows is precisely true only for a single tidal constituent.
For an ocean in the shape of a circular basin enclosed by a coastline,
The cotidal lines point radially inward and must eventually meet at a common point,
The amphidromic point.
The amphidromic point is at once cotidal with high and low waters,
Which is satisfied by zero tidal motion.
The rare exception occurs when the tide encircles an island,
As it does around New Zealand,
Iceland,
And Madagascar.
Tidal motion generally lessens moving away from continental coasts,
So that crossing the cotidal lines are contours of constant amplitude,
Half the distance between high and low water,
Which decrease to zero at the amphidromic point.
For a semi-diurnal tide,
The amphidromic point can be thought of roughly like the center of a clock face,
With the hour hand pointing in the direction of the high water cotidal line,
Which is directly opposite the low water cotidal line.
High water rotates about the amphidromic point once every 12 hours,
In the direction of rising cotidal lines,
And away from ebbing cotidal lines.
This rotation,
Caused by the Coriolis effect,
Is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere.
The difference of cotidal phase from the phase of a reference tide is the epoch.
The reference tide is the hypothetical constituent equilibrium tide on a landless earth measured at zero degrees longitude,
The Greenwich meridian.
In the North Atlantic,
Because the cotidal lines circulate counterclockwise around the amphidromic point,
The high tide passes New York Harbor approximately an hour ahead of Norfolk Harbor.
South of Cape Hatteras,
The tidal forces are more complex,
And cannot be predicted reliably based on the North Atlantic cotidal lines.
Investigation into tidal physics was important in the early development of celestial mechanics,
With the existence of two daily tides being explained by the moon's gravity.
Later,
The daily tides were explained more precisely by the interaction of the moons and the sun's gravity.
Seleucus of Seleucia theorized around 150 BC that tides were caused by the moon.
The influence of the moon on bodies of water was also mentioned in Ptolemy's Tetrabiblos.
In the Reckoning of Time of 725 Bede,
Linked semidiurnal tides and the phenomenon of varying tidal heights to the moon and its phases.
Bede starts by noting that the tides rise and fall four-fifths of an hour later each day,
Just as the moon rises and sets four-fifths of an hour later.
He goes on to emphasize that in two lunar months,
59 days,
The moon circles the earth 57 times and there are 114 tides.
Bede then observes that the height of tides varies over the months.
Increasing tides are called malony and decreasing tides letanies,
And that the month is divided into four parts of seven or eight days,
With alternating malony and letanies.
In the same passage,
He also notes the effects of winds to hold back tides.
Bede also records that the time of tides varies from place to place.
To the north of Bede's location,
The tides are earlier.
To the south,
Later.
He explains that the tide deserts these shores all the more to be able to flood other shores when it arrives there,
Noting that the moon which signals the rise of tide here signals its retreat in other regions far from this quarter of the heavens.
Later medieval understanding of the tides was primarily based on works of Muslim astronomers,
Which became available through Latin translation starting from the 12th century.
Abu Ma'shar al-Balkhi,
Circa 886,
In his Introductorium in Astronomium taught that ebb and flood tides were caused by the moon.
Abu Ma'shar discussed the effects of wind and moon's phases relative to the sun on the tides.
In the 12th century,
Al-Bitruji,
Circa 1204,
Contributed the notion that the tides were caused by the general circulation of the heavens.
Simon Stephen,
In his 1608,
The Theory of Ebb and Flood,
Dismissed a large number of misconceptions that still existed about ebb and flood.
Stephen pleaded for the idea that attraction of the moon was responsible for the tides and spoke in clear terms about ebb,
Flood,
Spring tide,
And neap tide,
Stressing that further research needed to be made.
In 1609,
Ioannis Kepler also correctly suggested that the gravitation of the moon caused the tides,
Which he based upon ancient observations and correlations.
Galileo Galilei,
In his 1632 Dialogue Concerning the Two Chief World Systems,
Whose working title was Dialogue on the Tides,
Gave an explanation of the tides.
The resulting theory,
However,
Was incorrect as he attributed the tides to the sloshing of water caused by the earth's movement around the sun.
He hoped to provide mechanical proof of the earth's movement.
The value of his title theory is disputed.
Galileo rejected Kepler's explanation of the tides.
Isaac Newton was the first person to explain tides as the product of the gravitational attraction of astronomical masses.
His explanation of the tides and many other phenomena was published in his Principia,
1687,
And used this theory of universal gravitation to explain the lunar and solar attractions as the origin of the tide-generating forces.
Newton and others before Pierre-Simon Laplace worked the problem from the perspective of a static system,
Equilibrium theory,
That provided an approximation that described the tides that would occur in a non-inertial ocean evenly covering the whole earth.
A tide-generating force,
Or its corresponding potential,
Is still relevant to tidal theory,
But as an intermediate quantity-forcing function,
Rather than as a final result.
Theory must also consider the earth's accumulated dynamic tidal response to the applied forces,
Which response is influenced by ocean depth,
The earth's rotation,
And other factors.
In 1740,
The Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides.
Daniel Bernoulli,
Leonard Euler,
Colin McLaurin,
And Antoine Cavalieri shared the prize.
McLaurin used Newton's theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a prolate spheroid,
Essentially a three-dimensional oval,
With major axis directed toward the deforming body.
McLaurin was the first to write about the earth's rotational effects on motion.
Euler realized that the tidal force's horizontal component,
More than the vertical,
Drives the tide.
In 1744,
Jean-Laurent de Lambert studied tidal equations for the atmosphere,
Which did not include rotation.
In 1770,
James Cook's Bark HMS Endeavour grounded on the Great Barrier Reef.
Attempts were made to refloat her on the following tide,
Which failed,
But the tide after that lifted her clear with ease.
While she was being repaired in the mouth of the Endeavour River,
Cook observed the tides over a period of seven weeks.
At neap tides,
Both tides in a day were similar,
But at springs,
The tides rose seven feet in the morning,
But nine feet in the evening.
Pierre-Simone Laplace formulated a system of partial differential equations relating the ocean's horizontal flow to its surface height,
The first major dynamic theory for water tides.
The Laplace tidal equations are still in use today.
William Thomson,
1st Baron Kelvin,
Rewrote Laplace's equations in terms of vorticity,
Which allowed for solutions describing tidally driven coastally trapped waves,
Known as Kelvin waves.
Others,
Including Kelvin and Henri Poincaré,
Further developed Laplace's theory.
Based on these developments and the lunar theory of E.
W.
Brown describing the motion of the moon,
Arthur Thomson Dudeson developed and published,
In 1921,
A first modern development of the tide generating potential in harmonic form.
Dudeson distinguished 388 tidal frequencies.
Some of his methods remain in use.
From ancient times,
Tidal observation and discussion has increased in sophistication,
First marking the daily recurrence,
Then tide's relationship to the sun and moon.
Pythias traveled to the British Isles about 325 BC and seems to be the first to have related spring tides to the phase of the moon.
In the 2nd century BC,
The Hellenistic astronomer Seleucus of Seleucia correctly described the phenomenon of tides in order to support his heliocentric theory.
He correctly theorized that tides were caused by the moon,
Although he believed that the interaction was mediated by the pneuma.
He noted that tides varied in time and strength in different parts of the world.
According to Strabo,
Seleucus was the first to link tides to the lunar attraction and that the height of the tides depends on the moon's position relative to the sun.
The Naturalis Historia of Pliny the Elder collates many tidal observations,
E.
G.
The spring tides are a few days after or before new and full moon and are highest around the equinoxes,
Though Pliny noted many relationships now regarded as fanciful.
In his Geography,
Strabo described tides in the Persian Gulf having their greatest range when the moon was furthest from the plane of the equator.
All this despite the relatively small amplitude of Mediterranean basin tides.
Phylostratus discussed tides in Book 5 of The Life of Apollonius of Tiana.
Phylostratus mentions the moon,
But attributes tides to spirits.
In Europe,
Around 730 A.
D.
,
The Venerable Bede described how the rising tide on one coast of the British Isles coincided with the fall on the other and described the time progression of high water along the Northumbrium coast.