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# Ocean Circulation and Waves (Week/Day 7) GEOLOGY103

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GPA 3.819

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This 9 page Class Notes was uploaded by Monica Weisenbach on Saturday January 24, 2015. The Class Notes belongs to GEOLOGY103 at University of Massachusetts taught by Peter Panish in Fall. Since its upload, it has received 218 views. For similar materials see Intro Oceanography in Geoscience at University of Massachusetts.

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Date Created: 01/24/15

Exam Study Guide Stuff to Remember Just in case fX gX fgX f gX fX gX fgx input x into g take that new value place into f gfx input x into f take that new value place into g Equations of lines ymxb linear yyomxxo pointslope yax2bxc quadratic Quadratic Formula x b xb24ac2a SOHCAHTOA For sine function asinbx a is the amplitude 2nb is the period LogabX xlogab Logabc logab logac Logabc logab logac X Xquot12 Rate of change fx fXoXXo lim fxh fx f x hgtgtO h What are the derivatives The derivative is the slope of the line at a point For linear lines the slope is the same For nonlinear lines the slope changes at each point Technically the derivative is the slope of the tangent line at said point f x dydx ddx all ways to write the derivative List of Derivatives Power functions xn nxn1 Exponential functions nX nXnn Sine functions sinx cosx Cosine functions cosx sinx Natural logarithm functions lnx 1x eX eX ekx kekx Number n O The Manipulation of Derivatives Manipulations fg X f X 9 X af X af X Product rule fg f g fg Quotient rule fg f g fg g2 Chain rule AB where B is a function acting on A ddx A ddx B Concept Question Answer derivative Power 3x2 6x Exponential 7X 7 Natural log ln8x 18x Chain rule 5ln1e 5e Product rule xeX eX Chain rule ln2x 10ln2x Quotient rule lnxx 1 lnxx First derivative the derivative of the original equation The zeroes of this equation equate to minimums and maximums on the graph Positive graph is increasing negative graph is decreasing O maximum O minimum Second derivative the derivative of the first derivative The zeroes of this equation equate to points of inflection on the graph Positive concave up negative concave down O and O changes in the value of the second derivative show that the graph is changing shape in it s curve 0 Max5 mln 0 0 o Revenue Functions Revenue pricequantity Marginal revenue derivative of revenue equation Cost cost of producing itemquantity initial fixed cost Marginal cost derivative of cost function Profit revenue cost Profit is maximized when R 0 when marginal revenue and cost is equal If 0 Cql pro l P flit Ir cap gt Roi loSS crash0 c Logistic Growth Curve The equation is L1Ceki L limit k is the growth rate L i L2 is the inflection point for the curve 7392 1quot quotquotrquot The greatest rate of change is at the inflection point Integral The integral is the area under the graph shown by the symbol f It s units are the units of y times the units of x It can be estimated with lower and upper estimates using rectangles I I 1 l a 1in quot 1 To find an estimate of the integral between 1 and 2 on this graph find the values x 1 54 32 74 2 y 1 45 8 23 67 47 59 12 5 The lower estimate uses the left hand points of the rectangles In this case it s 14186759 The right estimate uses the right hand points of the rectangles In this case it s 14867592 Add those up find the average divide by 2 and you have a Close estimate Another way to remember this is that both upperlower estimates have the same number of terms as there are intervals the above example has 4 intervals so 4 terms per estimate and the lower starts on the lowest value while the upper ends on the highest value Definite Integral is fab fXdX a is the lower xvalue b is the xvalue dx is the size of the interval The area between two curves is fab fXgxdx A fab fXgxdx where fX 12x and gx x A fab 12xxdx fab 1xdx These notes only go up to 41 this does not include notes from 42 A section on integrals will be probably released next week Notes for 102814 Surface Circulation There are 6 major gyres in the world NorthSouth Pacific NorthSouth Atlantic Antarctic Current and Indian Ocean Ekman Transport the interaction between wind and current overall current flow is 90 degrees from major zonal wind flow It looks like a spiral staircase heading down from the surface The Coriolus Effect which influences the water to go clockwise in the Northern Hemisphere and opposite in the Southern plays a role in the spiraling The surface current is influenced by the wind the current below it is influenced by the surface current and so on The gyres actually follow the wind patterns in their respective hemispheres Earth s rotation piles water on the west side and forms a mound in the center of the gyre Upwelling occurs at the divergent zone and downweIing in the convergent zone mound Upwelling is really important animal life depends on plant life and the plant life is dependent on nutrients The upwellingdownwelling of the gyres sets up a rotation of water that picks up nutrients from deeper in the ocean and returns them to the surface The currents of the ocean move warm water to the higher latitudes and cold water to the lower latitudes Eastern Boundary Currents broader slowmoving cold water from higher to lower latitudes Western Boundary Currents fastermoving narrower warm water from lower to higher latitudes Thought If the Gulf Stream brings warm water up the Eastern Seaboard why aren t we warmer than Europe It s because we re in the zone of the Westerlies The wind that blows over us comes from the center of the continent Whereas the wind that blows over Europe passes over and picks up some of the warmth of the Gulf Stream Europe or some parts of it have a maritime climate the name for the above effect ENSO Remember that there s a weak current running westeast along the equator in the Pacific This leads to low pressure in the west and slightly higher pressure in east The Southern Oscillation is when the countercurrent becomes stronger while the Trade Winds get weaker Also called El Ni o since it generally begins around Christmas This phenomenon brings more warm water to the coast of South America and part of North America making conditions more stormy La Nina is sometimes used to refer to normal conditions ENSO in fact stands for El Ni o Southern Oscillation Deep Ocean Circulation Thermohaline circulation densitydriven circulation Temperature and salinity are the major factors Mostly it s temperature that is the major factor in density calculations There is one current that comes off the Mediterranean that sinks because of salinity Global Ocean Conveyor the surface currents and deep water currents link up in some places One is up by Greenland and the Canadian Maritime Provinces there s also one at the same latitude on the opposite side of the planet Theres are places where the surface water gets cold enough to sink Waves Groins are structures built perpendicular to shore built to trap sand on its movement down the beach Longshore transport the zigzag movement of sand down a beach wavelength l 4i i l Hough wave base 12 wavelendth direction of waves r g 39 I 39w 39 x r L sandsediment has a tendency to move from headlands into bays evening out the coastline Depositional coasts sedimentmaterial flow toonto the beach Erosional coasts sedimentmaterials flow away from the beach Hard stabilization using armored manmade structures to protect a beach Soft stabilization dumping sandsediment onto a beach to replace what was lost to erosion Breakwaters reduce wave action but may cause sediment to pile up There are both upsides and downsides to doing these things the beach may be preserved in some fashion but a beach elsewhere may be being deprived

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