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