66
3 Basics of Nonhydrostatic Modelling
3.16.3 Task Description
For illustration of the convective entrainment process, we repeat Exercise 8 with
addition of both Eulerian tracer concentration and non-buoyant Lagrangian floats.
To this end, an advection-diffusion equation for tracer concentration C is added to
the code reading:
∂C
∂t
+ Adv(C) = Diff(C)
where the same eddy diffusivities are used as in the density conservation equation.
Concentrations are initialised with values of unity in a 25-m thick near-bottom layer
and zero values elsewhere. In conjunction with this, 3,000 Lagrangian floats are
initially distributed at random locations within 25 m from the sea floor. Changes of
float locations (x
∗ , z
∗ ) are calculated from simple displacement equations:
dx
∗
dt
= u and
dz
∗
dt
= w
where (u, w) is the velocity predicted by model in vicinity of the float. Instead of
accurate interpolation of velocity to the precise location of a float, it is sufficient for
the purpose of this exercise to use the velocity in the grid cell surrounding a float
as a proxy. Hereby, velocity components are interpolated to pressure grid points
and the grid cell containing a float is defined within ±0.5Δx distance horizontally
and ±0.5Δz distance vertically with respect to this grid point. Special treatment is
required to avoid stranding of floats in dry grid cells. Section 5.8 describes a more
accurate method.
The total simulation time is 6 hrs with data outputs at every 2.5 min of the simulation. The time step is set to Δt = 1 s using the rigid-lid approximation. Note
that the model gives similar results with inclusion of a free surface. This, however,
requires a shorter time step of Δt = 0.1 s, leading to a tenfold increase of the total
simulation time.
3.16.4 Results
It takes about 2 hrs of applied surface buoyancy flux until convective plumes
reach into the bottom layer to entrain near-bottom water into the convection layer
(Fig. 3.34). Again, we can see that the product of convection is an almost perfectly
mixed water column. As expected, Lagrangian floats are also entrained into the convection layer (Fig. 3.35). We can imagine that these floats represent small sediment
particles being mixed into the water column.
3 Basics of Nonhydrostatic Modelling
3.16.3 Task Description
For illustration of the convective entrainment process, we repeat Exercise 8 with
addition of both Eulerian tracer concentration and non-buoyant Lagrangian floats.
To this end, an advection-diffusion equation for tracer concentration C is added to
the code reading:
∂C
∂t
+ Adv(C) = Diff(C)
where the same eddy diffusivities are used as in the density conservation equation.
Concentrations are initialised with values of unity in a 25-m thick near-bottom layer
and zero values elsewhere. In conjunction with this, 3,000 Lagrangian floats are
initially distributed at random locations within 25 m from the sea floor. Changes of
float locations (x
∗ , z
∗ ) are calculated from simple displacement equations:
dx
∗
dt
= u and
dz
∗
dt
= w
where (u, w) is the velocity predicted by model in vicinity of the float. Instead of
accurate interpolation of velocity to the precise location of a float, it is sufficient for
the purpose of this exercise to use the velocity in the grid cell surrounding a float
as a proxy. Hereby, velocity components are interpolated to pressure grid points
and the grid cell containing a float is defined within ±0.5Δx distance horizontally
and ±0.5Δz distance vertically with respect to this grid point. Special treatment is
required to avoid stranding of floats in dry grid cells. Section 5.8 describes a more
accurate method.
The total simulation time is 6 hrs with data outputs at every 2.5 min of the simulation. The time step is set to Δt = 1 s using the rigid-lid approximation. Note
that the model gives similar results with inclusion of a free surface. This, however,
requires a shorter time step of Δt = 0.1 s, leading to a tenfold increase of the total
simulation time.
3.16.4 Results
It takes about 2 hrs of applied surface buoyancy flux until convective plumes
reach into the bottom layer to entrain near-bottom water into the convection layer
(Fig. 3.34). Again, we can see that the product of convection is an almost perfectly
mixed water column. As expected, Lagrangian floats are also entrained into the convection layer (Fig. 3.35). We can imagine that these floats represent small sediment
particles being mixed into the water column.