Lecture: April 26 (Monday), 14:00 Prof. Dr. Gerrit Lohmann
Tutorial: April 26 (Monday), ca. 15:30 Justus Contzen, Lars Ackermann
Time required for Sheet 3: 8 h
AtmosphericDynamics Chapter01 Part02 The Material Derivative (22 min)
AtmosphericDynamics Chapter01 Part04 Thermodynamics (16 min)
This is based on Chapter 1 “The Equations of Atmospheric Dynamics”" from Holton and Hakim (2013)
Reading/learning might take 60 min.
It is emphasized that the rotating frame equation of motion has some inherent awkwardness, namely the Coriolis force and the loss of Galilean invariance. However, the gain in simplicity when analyzing the motions of the atmosphere and ocean more than compensates. The reasons are several, but primarily that the inertial frame velocity consists of the solid body rotation plus the relative velocity v on the Earth, V = Ω a cos(latitude) + v, with the former being very much larger than the latter. a is earth’s radius, 6350 km, and thus Ω a ≈ O(500) m/s near the equator. This very large velocity is accelerated centripetally, and is balanced by a centripetal force associated with the ellipsoidal shape of the Earth.
The inertial frame equations have to account for all of this explicitly and yet our interest is almost always the small relative motions of the atmosphere and ocean, since it is the relative motion that transports heat and mass over the Earth. In that important regard, the velocity associated with the solid body rotation of the Earth, atmosphere and ocean is invisible, no matter how large it is. As well, when we observe the winds and ocean currents we almost always do so from a reference frame that is fixed to the Earth. Given that our goal is to solve for or observe the relative velocity, then the rotating frame equations are generally much simpler and more appropriate than are the inertial frame equations.
Content in the script: Atmosphere and Ocean Dynamics, Scaling of the dynamical equations, Geostrophy
Water tank experiments: Taylor column. A Taylor column is a fluid dynamics phenomenon that occurs as a result of the Coriolis effect. It was named after Geoffrey Ingram Taylor. Rotating fluids that are perturbed by a solid body tend to form columns parallel to the axis of rotation called Taylor columns. At levels below the top of the obstacle, the flow must of course go around it. But the Taylor-Proudman theorem says that the flow must be the same at all levels in the fluid: so, at all heights, the flow must be deflected as if the bump on the boundary extended all the way through the fluid!
Reading/learning (the sections with a star are voluntary). It might take 60 min.
Some short videos:
Laboratory experiments showing the formation of a Taylor column, go to 2:50, other material:
This is based on Chapter 2 “The Equations of Atmospheric Dynamics”" from Holton and Hakim (2013)
Reading/learning might take 60 min.