SIO 210 Problem Set 3 November 10, 2014 Due Nov. 24, 2014 Answer key 1. 10 total 6 points (a) The following kinds of wave motion were mentioned in class A. light 3 x 10 9 m/sec B. sound in air (340 m/sec) C. sound in water (1500 m/sec) D. seismic waves (few km/sec) E. deep water ocean surface gravity waves (4 m/sec for 10 m wavelength) F. shallow water ocean surface gravity waves (220 m/sec in 5 km water) G. capillary ocean surface waves (few cm/sec to few tens of cm/sec) Order these waves by propagation speed, putting the fastest first, the next fastest second... etc., the slowest last. Express your answer by writing the letters that label the different waves in the requested order. A, D, C, B, F, E, G 2 points (b) With respect to the list of the previous question (#10), the kind(s) of ocean waves that are energized both in tsunamis and in ocean tides are (answer by writing appropriate letter label(s) from list of different waves in previous question). F 2 points (c) With respect to the list of the previous questions, the kind(s) of ocean waves that are energized by winds over the ocean are (answer by writing appropriate letter label(s) from list of different waves in previous question). _E, F, G 2. 10 points (2 points each) This is a list of astronomical events associated with tides: A. times of half moon B. time of full moon C. time of new moon D. time of lunar perigee E. times when moon is in earth's equatorial plane F. times when moon is farthest out of earth's equatorial plane G. times when the sun is in the earth's equatorial plane H. times when sun is farthest out of earth's equatorial plane Answer the following questions using letters A through H : (a) Which one of the above events occurs at the equinoxes, that is, the times of year when day and night are the same length? G (b) Which one of the above events occurs at the solstices, when the sun is as far north or south in the sky as it will be during the year? H
(c) Flooding once per day at La Jolla Shores at e.g. the Marine Room due to strong winter storms is particularly common in early January. Which one event on the list A through H is this close to in time? H (d) Spring tides are most pronounced around the time(s) of which astronomical events on the list A through H? (one or more events) B, C (e) The daily inequality is most pronounced around the time(s) of which astronomical events on the list A through H? (one or more events) F, H 3. 16 total Potential vorticity. Assume a column of water in the Northern Hemisphere has no relative vorticity, and has a height H = 500m (for instance, water column above the thermocline). Assume that it conserves potential vorticity. (a) 4 points Write down the expression for potential vorticity for this column and explain what could change as it moves northward. (Don t get carried away thinking about the deeper layer!) Q = (f + ζ)/h As it moves northward, f increases. If Q is conserved, then either the height H would increase, or the relative vorticity would decrease. (b) 10 points If the water column moves (northward) without generating any relative vorticity, calculate how much its height would change. This needed more information! Assume it moves 5 northward for want of a better idea. Suppose it starts at a latitude of 10 N (since I already calculated f for 10 N for problem 5). Q o = (f 10 /500 m) = (0.25 x10-4 sec -1 )/500 m Move to 15 N. Here f 15 = 0.26* 1.46 x10-4 /sec = (0.31 x10-4 sec -1 ) (f 10 /H 10 ) = (f 15 /H 15 ) so H 15 = (f 15 / f 10 )H 10 = [(0.31 x10-4 sec -1 )/( 0.25 x10-4 sec -1 )](500 m) = 620 m (c) 2 points If the water column moves (northward) without changing height, what direction will it spin? ζ will be negative, so spin would be clockwise 4. 20 total There are 5 subtropical gyres in the world ocean. The following questions are in regards to their western boundary currents. (a) 2 points Which subtropical western boundary current would extend much farther poleward if its western boundary extended farther poleward? (one) Agulhas (b) 2 points Which subtropical western boundary currents separate cleanly from their western boundaries, and never reattach again? (two) Brazil Current and Agulhas Current (c) 2 points Which western boundary currents reattach to a second western boundary
after they have been free from the western boundary for some distance? (two) three my mistake!! Gulf Stream, East Australian Current, and the East Madagascar Current/Agulhas (d) 5 points Pick one of the Southern Hemisphere western boundary currents. Sketch qualitatively the sea surface height distribution from west to east across the western boundary current, and then across the full width of the subtropical gyre. Indicate approximately how wide the western boundary current is, and how wide the gyre is, in kilometers (order of magnitude). I ve drawn a completely generic one. Students might be taking the Niiler et al. sea surface height maps and trying to sketch all of the various features, which is OK. Most important is to have a WBC with highest SSH about 100 km to east of boundary, and then falling gently to eastern boundary, order 5000 to 10000 km to the east. (e) 4 points Continue the sketch from (d). Indicate using arrows, arrowheads and/or arrowtails which direction the surface current flows. Added to drawing most important to get a southward WBC and northward interior flow. Useful to also show relative strength of meridional velocity through small circles in interior and large circle(s) in WBC. (f) 5 points Assuming that the western boundary current is strongest at the sea surface, sketch a few isopycnals beneath the sea surface, making sure that you have the correct slopes of the isopycnals relative to the sea surface height. Vertical scale doesn t matter - if they draw it on the figure, it is of course much larger than the 1 m of sea surface height.
5. 44 total The mean winds in the Pacific are shown in the attached plot. (a) 4 points Indicate where the trade winds are. (LABEL on figure.) Indicate where the westerlies are. (LABEL on figure.) on figure (b) 4 points In North Pacific subtropical gyre region, sketch the direction of mean Ekman transport relative to the trade winds and westerlies. (DRAW on figure.) blue arrows on figure (only did strictly north south because of lack of control on powerpoint arrows; students might draw them properly perpendicular to the wind stress) (c) 4 points Is the Ekman transport convergent or divergent between 10 N and 40 N? Does this imply Ekman pumping (downwelling) or Ekman suction (upwelling) between 10 and 40 N? convergent. Ekman downwelling. (d) 10 points If the wind stress (magnitude) is 0.1 N/m 2 at 10 N, calculate the Ekman transport at a given point ( transport in m 2 /sec). Do the same for a wind stress of 0.1 N/m 2 at 40 N. f o = 1.46 x10-4 /sec x sin(latitude). At 10 N, f = 0.17 x f o = 0.25 x10-4 /sec At 40 N, f =0.64 x f o = 0.92x10-4 /sec V(10 N) = τ/ρf = 0.1 N/m 2 /[(1025 kg/m 3 )( 0.25 x10-4 /sec)]=3.93 m 2 /sec V(40 N) = -τ/ρf = -0.1 N/m 2 /[(1025 kg/m 3 )( 0.92x10-4 /sec)]=-1.06 m 2 /sec (e) 6 points If the Pacific is 13,000 km wide at 10 N and the Ekman transport is the same as your value calculated in (d), what is the total Ekman transport across the width of the ocean at 10 N? (in m 3 /sec). Calculate the total Ekman transport at 40 N, assuming the width of the ocean is 8500 km there. Calculate total southward transport across 40 N and total northward transport across 10 N. V tot (10 N) = (13,000 x 10 3 m)( 3.93 m 2 /sec) = 51 x10 6 m 3 /sec = 51 Sv V tot (40 N) = -(8500 x 10 3 m)( 1.06 m 2 /sec) = -9 x10 6 m 3 /sec = -9 Sv (f) 6 points Estimate the average vertical velocity at the base of the Ekman layer, over the whole area between 10 N and 40 N. (Assume that it s uniform, and make a rough estimate of the ocean area between 10 and 40 N, using the simplest possible geometry.) Net convergence is 60 Sv. Area: meridional distance = 30 x 111 km/ = 3330 km Zonal distance mean = 10,750 km Area = (3330 km)(10,750 km) = 3.58 x 10 13 m 2
W = convergent transport/area = 60x106 m3/sec / (3.58 x 1013m2) = 1.7x10-6m/sec (g) 4 points Is the Sverdrup transport northwards or southwards between 10 N and 40 N based on the preceding, and using the same very simple averaging assumptions as in (f)? Sketch this also on the map. Southwards. Red arrows on map. (h) 4 points Is the western boundary current northward or southwards between 10 N and 40 N, based on your answer to (g)? Sketch this on the map. Northwards. Green arrow on map. (i) 2 points What is the name of the western boundary current that you just sketched? Kuroshio