/
solid_body_rotation.jl
2501 lines (2053 loc) · 88.2 KB
/
solid_body_rotation.jl
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### A Pluto.jl notebook ###
# v0.19.40
using Markdown
using InteractiveUtils
# ╔═╡ 0fea38f6-2c9e-43c6-bfc1-267ff220a0cc
begin
using IndividualDisplacements, DataFrames, MeshArrays, PlutoUI
using CairoMakie
"done with loading packages"
end
# ╔═╡ abdcae13-40fe-495a-bf6c-dba5549c558a
TableOfContents()
# ╔═╡ 5c7e4e72-3f69-11ec-258b-6bcfdc7b1d65
md"""# Simple Three Dimensional Flow Field
Simulate the trajectory of an individual point, first in a perfectly circular flow (a.k.a. solid body rotation). Then add a convergent term to obtain a spiraling trajectory, and a constant vertical velocity for the third dimension. These simple flow configurations can be thought of as idealized models e.g. ocean meso-scale eddies.
For additional documentation e.g. see :
[1](https://JuliaClimate.github.io/IndividualDisplacements.jl/dev/),
[2](https://JuliaClimate.github.io/MeshArrays.jl/dev/),
[3](https://docs.juliadiffeq.org/latest/solvers/ode_solve.html),
[4](https://en.wikipedia.org/wiki/Displacement_(vector))
### Exercise examples:
- make the sinking velocity decrease with time (hint: it increases in the original notebook)
- change the number of times the particle goes around the origin
- flow field parameters (e.g. intensity and sign of the convergent term)
"""
# ╔═╡ aadd082a-3ed9-41b7-ba5e-7c5f77d59508
md"""## 1. Problem Configuration
### 1.1 Gridded Flow Fields
Set up an idealized flow field which consists of
[rigid body rotation](https://en.wikipedia.org/wiki/Rigid_body),
plus a convergent term, plus a sinking term.
"""
# ╔═╡ 2200503c-605c-4dfd-878f-ffea2431f7ba
begin
(np,nz)=(24,16) #gridded domain size (horizontal and vertical)
u,v,w=IndividualDisplacements.vortex_flow_field(np=np,nz=nz) #staggered velocity arrays
𝐹=FlowFields(u,u,v,v,0*w,1*w,[0,19.95*2*pi]); #FlowFields data structure
"Done with defining the flow fields."
end
# ╔═╡ bde49eaf-3747-4edf-b712-3ee6f08ffe20
md"""### 1.2 Initialize Individuals
Here just one individual is initialized at [np*1/3,np*1/3,nz*1/3] in the three-dimensional space of the flow fields."""
# ╔═╡ c60a48e0-6f51-44b0-bd6e-332e04d2d332
begin
(x,y,z)=(np*1/3,np*1/3,nz*1/3)
𝐼=Individuals(𝐹,x,y,z)
end
# ╔═╡ 45762eb1-7404-4524-8d1d-788a70f8f5ef
md"""### 1.3 A Closer Look
The above `Individuals` constructor wraps up 𝐹, the initial position, and other needed components within 𝐼. **At this point, you can either jump to section 2 or read through the next code cell**
to learn more about how the details as needed e.g. if you wanted to overide default options
that were selected for you by the section 1.2 constructor.
"""
# ╔═╡ b70d76d1-09f3-462a-b550-8fa51cb90c2c
begin
# Initial position is
📌=[x,y,z]
# and the data structure ([DataFrame](http://juliadata.github.io/DataFrames.jl/stable/))
# to record properties along the individual's path accordingly.
🔴 = DataFrame(ID=Int[], x=Float64[], y=Float64[], z=Float64[], t=Float64[])
# It is the postprocessing function's responsibility to provide the record. It is thus
# important that this intermediary (`postproc`) be consistent with the solver setup (`sol`)
# and the expected record format (`🔴`).
function postproc(sol,𝐹::FlowFields;id=missing,𝑇=missing)
df=postprocess_xy(sol,𝐹,id=id,𝑇=𝑇)
#add third coordinate
z=sol[3,:]
df.z=z[:]
return df
end
# The velocity function `🚄` relies only on flow fields obtained from
# `𝐹` (which is defined above) to interpolate velocity at the specified
# space-time position (e.g. those of individuals).
🚄 = dxdt!
# Now that every thing needed to carry out the computation is in place,
# we wrap up the problem configuration in a struct (`Individuals`) which
# links to the initial positions, flow fields, etc. all that will be
# necessary to compute trajectories over time (`∫!(𝐼,𝑇)`).
#assemble as a NamedTuple:
I=(position=📌,record=🔴,velocity=🚄,
postprocessing=postproc,parameters=𝐹)
#construct Individuals from NamedTuple:
𝐽=Individuals(I)
end
# ╔═╡ 8cc54cc2-5284-40b1-9a30-0ad6f725053f
md"""## 2 Trajectory Simulations
The `∫!` function call below returns the final positions & updates `𝐼.📌` accordingly. It also records properties observed along the trajectory in `𝐼.🔴`.
Simple methods to visualize the individual trajectory (plot or movie) are provided at the end.
### 2.1 Compute Trajectory
"""
# ╔═╡ 503c8702-df0b-4495-8245-4ba6608431e3
begin
𝑇=(0.0,𝐼.𝑃.𝑇[2])
∫!(𝐼,𝑇)
end
# ╔═╡ 32a8b0ee-e61d-495b-ba53-56a6c6126950
md"""### 2.2 Visualize Trajectory"""
# ╔═╡ dd62433c-2274-4c6f-9e27-34bc2c620df1
begin
nt=length(𝐼.🔴.x)
time = Observable(nt)
xx=@lift( [𝐼.🔴.x[1:$time];fill(NaN,nt-$time)] )
yy=@lift( [𝐼.🔴.y[1:$time];fill(NaN,nt-$time)] )
zz=@lift( [𝐼.🔴.z[1:$time];fill(NaN,nt-$time)] )
set_theme!(theme_light())
f=Figure(resolution = (900, 600))
a = Axis3(f[1, 1],xlabel="x",ylabel="y",zlabel="z",
title="Solid body rotation / Spiral example")
lines!(a,xx,yy,zz,linewidth=1.0,color=:black)
scatter!(a,[𝐼.🔴.x[1]],[𝐼.🔴.y[1]],[𝐼.🔴.z[1]],color=:red)
scatter!(a,[𝐼.🔴.x[nt]],[𝐼.🔴.y[nt]],[𝐼.🔴.z[nt]],color=:green)
f
end
# ╔═╡ 250d011e-57db-4d80-b16e-dbc28fec9fba
begin
#plt=myplot(nt)
#scatter!(plt,[📌[1]],[📌[2]],[📌[3]])
#scatter!(plt,[𝐼.🔴.x[end]],[𝐼.🔴.y[end]],[𝐼.🔴.z[end]])
#scatter!(plt,[𝐼.🔴.x[1]],[𝐼.🔴.y[1]],[𝐼.🔴.z[1]])
end
# ╔═╡ a0bf6d10-5d42-481b-8720-dadd3f727e8b
md"""### 2.3 Animation example"""
# ╔═╡ 2b8ee43d-1225-4475-91c9-161cf612bfb2
begin
if false
p=Int(ceil(nt/50))
tt=1:p:nt
tt=tt.+(nt-maximum(tt))
fil=joinpath(tempdir(),"solid_body_rotation.mp4")
record(f,fil, tt; framerate = 20) do t
time[] = t
end
LocalResource(fil)
else
"""try code in this cell to generate animation"""
end
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
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