6.3 Exercise 15: Coastal Kelvin Waves
121
η(x, y, t) = η o exp (−y/R) sin (kx − ωt)
(6.4)
u(x, y, t) =
g
H
η o exp (−y/R) sin (kx − ωt)
(6.5)
where k = 2π/λ (λ is wavelength), ω = 2π/T (T is wave period), and R is the
Rossby radius of deformation, define by:
R =
√ g H
| f |
(6.6)
It can also be shown that these waves travel with a phase speed of long surface
gravity waves of c =
√ g H along the coast with the coast on their right in the
northern hemisphere and on their left in the southern hemisphere. Their amplitude
is maximum at the coast and decreases exponentially away from the coast on a
lengthscale of the deformation radius.
6.3 Exercise 15: Coastal Kelvin Waves
6.3.1 Aim
The aim of this exercise is to simulate the structure and dynamics of coastal Kelvin
waves.
6.3.2 Task Description
Consider a rectangular model domain with a length of 400 km, a width of 100 km,
and a depth of 10 m. Lateral grid spacing is set to Δx = Δy = 2 km. The time step
is set to Δt = 10 s. All boundaries are treated as coasts. An unrealistically high value
of the Coriolis parameter of f = +5×10
−4
s
−1
is chosen to reduce the deformation
radius to R ≈ 20 km and to keep the total simulation time within a reasonable limit.
The associated inertial period is 3.5 h. The smart reader will jump on the table and
claim that the minimum inertial period on Earth is 12 hours. This is true, but with a
model we can do a little bit of science fiction can’t we?
A wave paddle is located near the lower left corner of the model domain oscillating the sea level with an amplitude of 1 m and a period of 2 hours. This period is
not far away from the fictiona inertial period, so that an influenc by the Coriolis
force can be anticipated. The task is to simulate the resultant wave fiel over half a
day (or 3.4 inertial periods) with outputs of sea-level elevation and velocity field at
every 10 mins.
The f rst-order Shapiro filte with a smoothing parameter of = 0.05 should be
applied. For simplicity, wind-stress forcing, bottom friction and lateral momentum
121
η(x, y, t) = η o exp (−y/R) sin (kx − ωt)
(6.4)
u(x, y, t) =
g
H
η o exp (−y/R) sin (kx − ωt)
(6.5)
where k = 2π/λ (λ is wavelength), ω = 2π/T (T is wave period), and R is the
Rossby radius of deformation, define by:
R =
√ g H
| f |
(6.6)
It can also be shown that these waves travel with a phase speed of long surface
gravity waves of c =
√ g H along the coast with the coast on their right in the
northern hemisphere and on their left in the southern hemisphere. Their amplitude
is maximum at the coast and decreases exponentially away from the coast on a
lengthscale of the deformation radius.
6.3 Exercise 15: Coastal Kelvin Waves
6.3.1 Aim
The aim of this exercise is to simulate the structure and dynamics of coastal Kelvin
waves.
6.3.2 Task Description
Consider a rectangular model domain with a length of 400 km, a width of 100 km,
and a depth of 10 m. Lateral grid spacing is set to Δx = Δy = 2 km. The time step
is set to Δt = 10 s. All boundaries are treated as coasts. An unrealistically high value
of the Coriolis parameter of f = +5×10
−4
s
−1
is chosen to reduce the deformation
radius to R ≈ 20 km and to keep the total simulation time within a reasonable limit.
The associated inertial period is 3.5 h. The smart reader will jump on the table and
claim that the minimum inertial period on Earth is 12 hours. This is true, but with a
model we can do a little bit of science fiction can’t we?
A wave paddle is located near the lower left corner of the model domain oscillating the sea level with an amplitude of 1 m and a period of 2 hours. This period is
not far away from the fictiona inertial period, so that an influenc by the Coriolis
force can be anticipated. The task is to simulate the resultant wave fiel over half a
day (or 3.4 inertial periods) with outputs of sea-level elevation and velocity field at
every 10 mins.
The f rst-order Shapiro filte with a smoothing parameter of = 0.05 should be
applied. For simplicity, wind-stress forcing, bottom friction and lateral momentum