74
3 Basics of Nonhydrostatic Modelling
Fig. 3.41 Dynamical regimes for different gradient ratios and Turner angles
3.19 Exercise 11: Double-Diffusive Instability
3.19.1 Aim
The aim of this exercise is to explore the double-diffusive instability mechanism
with application of the nonhydrostatic ocean-slice model.
3.19.2 Task Description
We consider a model domain, 200 m in length and 20 m deep, resolved by equidistant grid spacings of Δx = Δz = 1 m. Lateral boundaries are cyclic. Advectiondiffusion equations for temperature and salinity together with a linearised equation
of state are added to the model code. Diffusivity of heat is set to a uniform value of
10
−4 m
2
/s and diffusivity of salt is chosen as 10
−6 m
2
/s. These values, exceeding
true values by a factor of 1,000, are deliberately chosen to speed up the simulation.
Rather than full values, we use temperature anomalies T
and salinity anomalies
S
with reference to constant background values as field variables. Accordingly, the
linearised equation of state can be written as:
ρ
= ρ − ρ o = ρ o (β S
− αT
)
(3.77)
3 Basics of Nonhydrostatic Modelling
Fig. 3.41 Dynamical regimes for different gradient ratios and Turner angles
3.19 Exercise 11: Double-Diffusive Instability
3.19.1 Aim
The aim of this exercise is to explore the double-diffusive instability mechanism
with application of the nonhydrostatic ocean-slice model.
3.19.2 Task Description
We consider a model domain, 200 m in length and 20 m deep, resolved by equidistant grid spacings of Δx = Δz = 1 m. Lateral boundaries are cyclic. Advectiondiffusion equations for temperature and salinity together with a linearised equation
of state are added to the model code. Diffusivity of heat is set to a uniform value of
10
−4 m
2
/s and diffusivity of salt is chosen as 10
−6 m
2
/s. These values, exceeding
true values by a factor of 1,000, are deliberately chosen to speed up the simulation.
Rather than full values, we use temperature anomalies T
and salinity anomalies
S
with reference to constant background values as field variables. Accordingly, the
linearised equation of state can be written as:
ρ
= ρ − ρ o = ρ o (β S
− αT
)
(3.77)