Advanced Ocean Modelling: Using Open-Source Software

3.21 Tilted Coordinate Systems 79Fig. 3.46 Exercise 12. Evolution of temperature and salinity contrasts between the layers (arrow)expressed in equivalent density units. The open circle denotes the initial value. The arrow headpoints to the final value after 24 hrs of simulation3.20.4 Additional Exercises for the ReaderRepeat Exercises 11 and 12 with a two-layer configuration corresponding to aTurner angle in a range of (plus or minus) 60 ◦ –75 ◦ . Explore how the Turner angleevolves over time. The reader is also encouraged to consider a fluid of three superimposedlayers that are density compensated but display contrasts of temperatureand salinity.3.21 Tilted Coordinate Systems3.21.1 The Governing EquationsThe Cartesian coordinate system can be tilted by a certain angle γ (Fig. 3.47)for studies of the dynamics of stratified flows on a sea floor of constant bottominclination. Since this rotation rotates the entire model domain, inclusion of a freesea surface is not possible anymore, and the rigid-lid approximation (see Sect. 3.7)must be employed. With this approach, the rotated vertical axis z r differs from thelocal vertical and, hence, from the orientation of the gravity force. Accordingly,some fraction of the reduced-gravity force appears along rotated x r surfaces and the