Homework Questions March 2016

1) Turbulence can occur when shear (? V) in a current reaches critical (high) values. This is particularly important in the upper thermocline.

Turbulent mixing occurs when the shear overcomes the vertical stability of the water column as measured by the Brunt-Viasala frequency

N² = - g/ρ dρ/dz [1/s²].

Turbulence occurs when the non-dimensional Richardson number

Ri = N²/ (dV/dz)² < 1.

a) If N ~ f ~ 10 ^-4 [1/s] what shear is necessary to create turbulent mixing?

b) What does this do to the phytoplankton thin layers discussed in Durham et al. 2009 Science , 323, 20 Feb, 2009 (also see Perspective in same issue)?

c) What does the horizontal gradient in the thermocline depth have to do with this?

2) A bottom mounted acoustic Doppler current profiler (ADCP) deployed on a reef measures mean velocities at two depths above the deployment depth. The lower one at z = 1 m measures a mean flow of 0.046 m/s and the upper one at z = 2 m measures a flow of 0.148 m/s. Using the log-law formulation calculate u* and zo. Also calculated the vertical diffusivity, Kz.

3) Two ports along a coast line are 300 km apart. One port has high tides 30 minutes later than the other. How deep is the effective depth for the tidal propagation. If we are on the western side of an ocean in the northern hemisphere which port is farther north?

4) A community of mussels lives one meter (1 m) below mean sea level. If the region has a two meter (2 m) semidiurnal tide, how many hours per day are the mussels exposed?

If blue heron can consume 2 mussels per hour but require exposed mussels and a croaker can consume one mussel per hour but requires 0.5 m of water to swim, which is the greater predator?

5) Consider a tidal estuary with a surface area of 100 X 20 Km = 2,000 km² and an average depth of 2 m. If the tidal range is 0.2 m driven by a dominate M2 tide and the riverine input is Qr = 100 m³/s calculate the following:

a) The mean residence time for fresh water in the estuary.

b) Expected tidal flushing time.

c) Average estuarine salinity if the offshore salinity is So=33.

Discuss the issues involved with pollutants entering the estuary via the river versus those directly input to the estuary.

6) Upwelling on the California coast is typically estimated to amount to approximately a Sverdrup (T= 1 X 10^6 m^3/s) along a coast of L ~ 2000 km. Convert this to mass transport (kg/s) using an appropriate estimate of density and then calculate the wind stress needed to produce this flux using the Ekman transport equation. (Note this problem involves a careful attention to units. The answer should be in Nt/m²).

7) The Columbia River plume extends in the expected direction in the low flow regime, but in summer puts freshwater on the Oregon coast. Explain this phenomenon.

8) Choose another river in the world and produce an analysis of their estuaries and the coastal circulations they are involved with.

9) Discuss the influence of tidal friction and the history of the earth-moon system on  either the sedimentary history or biology of the oceans.

10) Consider the Winyah Bay estuary in South Carolina. The Bay is feed by the Pee Dee River system with a drainage area of 33 X 10³ km² and two smaller rivers that combined with Winyah Bay (65 km² in area). The two smaller rivers drain an area of 5,000 km².

Now if the Pee Dee system has been gauged to have a minimum flow in Aug.-Nov. of 200 m³/s and a maximum flow during the rainy season (Dec.-Mar.) of 1500 m³/s for an average of 600 m³/s, what is the expected total freshwater flux? (Hint: At this point you know nothing about the surface fluxes over the area, i.e. E or P.)

Now if the annual average temperature in South Carolina is T = 18º C and the precipitation based on a rain gauge network is P = 130 cm/yr calculate the freshwater influx to the Bay using the ?f/P equation given in the lecture. How does this compare with the estimate obtained above? Why might a difference be expected?
If the average depth of the Bay is 2 m, what is the expected residence time for freshwater in the estuary? Given a semi-diurnal tidal range of one meter what flushing time does the tidal prism balance give? Discuss the possible reasons for any difference.