I decided to focus this Mathematical Exploration on the math behind oceanic tides. I began by looking at the generic possibilities set out by my teacher. Among them was the idea of math being applied to water. In my initial search I found nothing that seemed interesting to me, however, I wanted to stick to the broad topic of water. After continued search I decided to focus on a subject important to me the ocean, specifically oceanic tides. Every year my family takes a trip to California for a week at the beach and since I was a little kid I was perplexed that the water would come up the beach at night and recede during the day. As I grew older and I learned this movement was called the tide and was caused by the moon and the sun’s gravity affecting the ocean. Thus I decided to take the exploration as a chance to further my knowledge of this subject and tides became my subject for this.
I thus decided to explore geographical and gravitational effects on tides along with solar and lunar tides and finally predicting the tides.
With the 39% of Americans living in counties on the shore line of the ocean, tides are forces of nature that many people deal with on a day-to-day basis. But what do we know about the tides? We know that the tides are the rising and falling of the ocean levels because of the gravitational pull from the sun and moon. There are also generally four tides in a day two lunar tides and two solar tides.
In order to explore the tides one must first deduce the big ideas needed to understand them. These include factors that can affect the tides such as the geography of an area and gravitational pulls. Also a separate look at solar and lunar tides will be taken. Finally tidal predictions will be taken under consideration...
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...e highest and lowest tides occur when h’(t)=0
Using this we can predict that the lowest tide of the first week occurred at t_min= 124.58 hrs and h(t_min) = −0.86 ft. This predicts there is a low tide at 4:35 am on Sept. 6 of -.86 ft. The actual low tide occurred at 3:35 am on Sept. 6 of -1.0 ft. The prediction was off by 60 minutes and 0.14 ft. Using the same process we can predict the highest tide of the first week. Here we get the max occurring at t_max= 142.56 hrs and h(t_max) = 6.40 ft or Sept. 6 at 10:33 pm with a height of 6.4 ft. The actual is a tide of 6.7 ft at 9:36 pm on Sept. 6. This time we were off by 0.3 ft and 57 minutes off. This model proved to not be 100% accurate, however, only 4 cosine functions were used to predict the tides while most models use up to 12 and the addition of more functions and parameters would create more accurate predictions.
On average a given spot will experience two high tide and two low tides in a day. The tides are experienced due to the moon gravitational pull. The low tides are experienced when we are facing 90 and 180 degrees away from the moon. Then the high tides are found when we are facing the moon and when we are facing away from the moon.
approximately tides and not at high or low water as would be the case at other
In Longfellow’s poem, The Tide Rises, the Tide Falls, Longfellow states “The little waves, with their soft white hands, / Efface the footprints in the sands.” By personifying the waves in the ocean, longfellow reveals the truth that all humans eventually die and their mark on the world is erased, like the waves wash away the footprints. In this imaginative way, Longfellow shows how no one lasts forever. Multiple times in other parts of the poem, Longfellow writes “And the tide rises, the tide falls.” Longfellow is expressing that the ocean is continuous, regardless of what happens. After losing his second wife, Longfellow was very depressed, and in this poem he is accepting that life goes on after someone dies. Using his imagination, Longfellow states the truth of the inevitability of death and the fact that life does not stop in the event of
Figure 6 - How longshore drift works (Brief). Source: Classwork image (originally from Google images)
Carson has written this essay to provide insight about the tide currents of the deep waters. She also raises insight awareness on planetary forces and physical dimensions. Carson’s main focus consists on informing the readers about the size, timing, and occurrences the tides correlated with. Statistics and studies are given to further elaborate and assist Rachel’s theory that states “In every country the moon keeps ever the rule of alliance with the sea which-it once for all has agreed upon." From the tone of the essay, it can be seen that the theme contains educational content that has significant importance to the global being.
One of the greater messages conveyed through An Ocean Apart, A World Away, pertains to the eradication of sexism, encouraging equality between all genders, and re-establishing the independence of women in many cultures. The author demonstrates the struggles of one individual assimilating into a foreign culture. The difference between the Chinese and American culture is evident as are the attempts of the main character to assimilate, and adapt to his/her new surroundings. The novel compares the stereotypes women face in both the Chinese and American culture and clearly regards it as an issue. An Ocean Apart, A World Away is a unique story with an important message, providing great insight into the history of China while maintaining a subtle sense of humour to keep the story entertaining. It also has a strong female protagonist but failed to successfully develop secondary characters. Other female characters could have aided the story in giving a stronger message as well as creating a more interesting plot. The plot lacked many details during the events, causing the plot to seem rushed. Although the story is lacking in some aspects, readers will find themselves fully engrossed into the daily lives of Chinese women during the early 1900s.
Sara M. Evans, in her book, Tidal Wave: How Women Changed America at Century’s End, chronicles feminist activities over several decades from just before the beginning of the women’s liberation movement in the 1960’s through the 1990’s. Doctor Evans was born in 1943 and currently teaches at the University of Minnesota in the history department after receiving both her B.A. and M.A. at Duke University and then later her PhD from the University of North Carolina Chapel Hill.
The Sun’s radiation heats the upper atmosphere, sending the energy toward the earth’s surface and finally mixes with the planet’s counter-rotational currents, creating jetstream flows. The winds flow over the ocean’s surface creating friction that spawns chops, pushing up the seas forming perfect bands of open ocean swell. Pushed on by gravitational forces, the swells speed away from the winds that they came from, moving across the deeps until they feel the drag of the shallows near the coast. As the swells rise up out of themselves, they peak, curling into the liquid dreams that we surfers ride (Kampton 4).
In the article “A Tsunami, Where?” (2015). On June 2013 a storm have hit the East Coast in the U.S that results in tsunami. Over 30 tide gauges have reported similar tsunami conditions. The highest capacity was recorded in Newport located in Rhode Island. In addition, Conditions showed a conceivable torrent, even to the individuals who did not have the guide of the tide gages. Brian Coen was spearfishing at Barnegat Inlet in Ocean County, New Jersey he saw a solid outrush of water as the tide went out. Outrush conveyed jumpers over submerged rocks that serve as a barrier, the strong waves carried the three drivers but only two were harmed. However, Ebersole reviewed that before long, the current switched at the same pace. A close-by gage recorded
The area of the Atlantic Ocean popularly referred to as the Bermuda Triangle is a complete enigma and has proven to be so for much of recorded history. Many seemingly inexplicable occurrences and disappearances have taken place in this particular area. No rational explanation that will satisfy the materialistic parameters of the typical scientist has been offered that would account for all the mysterious happenings that have taken place in the Bermuda Triangle during the course of many thousands of years.
Ocean currents are horizontal or vertical movement of both surface and deep water throughout the world’s oceans (Briney, n.d.). The primary generating forces are wind and differences in water density caused by variations in temperature and salinity. Currents generated by these forces are modified by factors such as the depth of the water, ocean floor topography and deflection by the rotation of the Earth. Horizontal currents are wind driven, fast moving and carries small amount of water; while, vertical currents are slow moving, density driven and carries large bodies of water. In this paper I will describe horizontal and vertical currents, their importance and some of the tools used to measure ocean currents.
That is causing tides just like the oceans on earth. A push pull effect of the water underneath the moon or planet. (Robert H. Tyler, cellphone August, 27th, 2015). Dr. Tyler has to use scientific method to help prove his theories to be correct. First Dr.Tyler will found his problem (why are there oceans under 50 miles of think oceans.).
The evolution story of Ocean Basket has the hallmarks of early humble beginnings to now being a seafood franchise restaurant playing in the big leagues.
Tides are common features of the ocean. Tides occur when large bodies water rise and fall, because of the gravitational pull of the moon and the sun. Spring tides are especially strong tides; in spite of the name they have nothing to do with the season spring. They occur when the Earth, the sun, and the moon are in a line. Spring tides occur during the full moon and the new moon. Neap tides are especially weak tides. They occur when the gravitational forces of the moon and the sun are perpendicular to one another. When water moves from side to side, it is called a current. Currents move warm and cold water to different parts of the ocean.