Advanced Ocean Modelling: Using Open-Source Software

46 3 Basics of Nonhydrostatic ModellingFigure 3.19 displays the vertical structure of horizontal and vertical velocity componentsof the first three internal wave modes. The mode number n gives the numberof maxima of the vertical velocity profile and the number of nodes (zero crossings)of the horizontal speed profile. Phase speeds associated with individual wave modesare given by:c = λ T =± N(3.55)√(2π/λ) 2 + (nπ/h) 2Fig. 3.19 Vertical structure of (a) vertical and (b) horizontal velocity components for the first threenormal modes of internal waves with N = constant. Adapted from Pond and Pickard (1983)3.9 Exercise 5: Internal Waves3.9.1 AimThe aim of this exercise is to simulate the dynamics of internal waves in a finitedepthocean of continuous density stratification on the basis of Eqs. (3.38).3.9.2 Task DescriptionConsider a model domain of 500 m in length and 100 m in depth, resolved by gridspacings of Δx = 5 m and Δz = 2 m. Both lateral boundaries are closed. To makethe dynamics slightly more complex, the author decided to add a shallower region