B) What Is Phase Speed of the Waves on Each Day?

Name______

Turkey Homework Due Nov 29th

1)  The cook aboard the UNOLS vessel the R/V Knorr decided to brine a turkey in ocean water by hanging the bird off the side of the ship over night outside the galley’s porthole that is 4m above the water line. The chef followed a recipe published in Cooks Illustrated that called for brining the turkey for 24 hours prior to cooking. Having only 4 meters of rope the chef had to wait until the waves were big enough to cause the boat to heave, pitch and role sufficiently such that for ½ the time the turkey was immersed in sea water. Subsequently the Cook decided to brine the turkey for 2 days since it was only immersed half the time. Also on the menu were deviled eggs. During the brining process the cook prepared the eggs. When he started brining the turkey he found that to cook the perfect hard boiled egg, which takes 5 minutes, all he had to do was count the passage of 20 waves. However at the end of the brining process, 2 days later, he found that the eggs, despite still using the 20 –wave method, were perfectly soft boiled—or the classic 3 minute egg.

a)  Why are the eggs at the end of the brining process undercooked (i.e. way did the 20 wave method not work) ?

b)  What is phase speed of the waves on each day?

c)  What is the group velocity of the waves on each day?

d)  How far away is the storm that produced these waves?

2)  A two layer fluid has an upper and lower layer each 10m deep with the lower layer with a density contrast of 12 kg/m3 (which, by the way, is equivalent to the lower layer containing one 25 lb turkey in each cubic meter). Currents in this region are in geostrophically balanced and driven by a sea-level slope that varies by 10 cm over 50 km. The current associated with this geostropic flow produces turbulence energy that is equal to Cd u3 /H where u is the current speed, H, the water column depth and Cd ,the coefficient for bottom stress and equal to 2x10-3. Eventually the turbulence generated by the currents homogenize the water column. Assume that 10 percent of the turbulence goes into mixing the water column and 90 percent into dissipation.

a)  What is the change of potential energy from the two layer system from the initial stratified case to the well mixed case.

b)  How long does the turbulence take to mix this two layer system (i.e. the time rate of change of potential energy equal the shear production times 0.1. The 0.1 factor represents the fact that only 10% of the turbulent production goes into mixing