changes variable names in TwoDTurb from U, V --> u, v

examples/twodturb_randomdecay.jl

@@ -49,7 +49,7 @@ while cl.step < ntot
 end
 
 # Plot the radial energy spectrum
-E = @. 0.5*(vs.U^2 + vs.V^2) # energy density
+E = @. 0.5*(vs.u^2 + vs.v^2) # energy density
 Eh = rfft(E)
 kr, Ehr = FourierFlows.radialspectrum(Eh, gr, refinement=1)
 

examples/twodturb_stochasticforcing.jl

@@ -57,7 +57,7 @@ function makeplot(prob, diags)
 
   t = round(mu*cl.t, digits=2)
   sca(axs[1]); cla()
-  pcolormesh(x, y, prob.vars.q)
+  pcolormesh(x, y, v.q)
   xlabel(L"$x$")
   ylabel(L"$y$")
   title("\$\\nabla^2\\psi(x,y,\\mu t= $t )\$")
@@ -74,15 +74,15 @@ function makeplot(prob, diags)
 
   # If the Ito interpretation was used for the work
   # then we need to add the drift term
-  # total = W[ii2]+σ - D[ii] - R[ii]      # Ito
+  # total = W[ii2]+ε - D[ii] - R[ii]      # Ito
   total = W[ii2] - D[ii] - R[ii]        # Stratonovich
   residual = dEdt - total
 
   # If the Ito interpretation was used for the work
-  # then we need to add the drift term: I[ii2] + σ
+  # then we need to add the drift term: I[ii2] + ε
   plot(mu*E.t[ii], W[ii2], label=L"work ($W$)")   # Ito
   # plot(mu*E.t[ii], W[ii2] , label=L"work ($W$)")      # Stratonovich
-  plot(mu*E.t[ii], σ .+ 0*E.t[ii], "--", label=L"ensemble mean  work ($\langle W\rangle $)")
+  plot(mu*E.t[ii], ε .+ 0*E.t[ii], "--", label=L"ensemble mean  work ($\langle W\rangle $)")
   # plot(mu*E.t[ii], -D[ii], label="dissipation (\$D\$)")
   plot(mu*E.t[ii], -R[ii], label=L"drag ($D=2\mu E$)")
   plot(mu*E.t[ii], 0*E.t[ii], "k:", linewidth=0.5)
@@ -116,14 +116,14 @@ for i = 1:ns
   TwoDTurb.updatevars!(prob)
   # saveoutput(out)
 
-  cfl = cl.dt*maximum([maximum(v.U)/g.dx, maximum(v.V)/g.dy])
+  cfl = cl.dt*maximum([maximum(v.u)/g.dx, maximum(v.v)/g.dy])
   res = makeplot(prob, diags)
   pause(0.01)
 
   @printf("step: %04d, t: %.1f, cfl: %.3f, time: %.2f s\n", cl.step, cl.t,
         cfl, (time()-startwalltime)/60)
 
-  # savename = @sprintf("%s_%09d.png", joinpath(plotpath, plotname), prob.step)
+  # savename = @sprintf("%s_%09d.png", joinpath(plotpath, plotname), cl.step)
   # savefig(savename, dpi=240)
 end
 

src/twodturb.jl

@@ -23,7 +23,7 @@ using FourierFlows: getfieldspecs, structvarsexpr, parsevalsum, parsevalsum2
 
 abstract type TwoDTurbVars <: AbstractVars end
 
-const physicalvars = [:q, :U, :V]
+const physicalvars = [:q, :u, :v]
 const transformvars = [ Symbol(var, :h) for var in physicalvars ]
 const forcedvars = [:Fh]
 const stochforcedvars = [:prevsol]
@@ -120,9 +120,9 @@ eval(structvarsexpr(:StochasticForcedVars, stochforcedvarspecs; parent=:TwoDTurb
 Returns the vars for unforced two-dimensional turbulence with grid g.
 """
 function Vars(g; T=typeof(g.Lx))
-  @createarrays T (g.nx, g.ny) q U V
-  @createarrays Complex{T} (g.nkr, g.nl) sol qh Uh Vh
-  Vars(q, U, V, qh, Uh, Vh)
+  @createarrays T (g.nx, g.ny) q u v
+  @createarrays Complex{T} (g.nkr, g.nl) sol qh uh vh
+  Vars(q, u, v, qh, uh, vh)
 end
 
 """
@@ -159,21 +159,21 @@ end
 Calculates the advection term.
 """
 function calcN_advection!(N, sol, t, cl, v, p, g)
-  @. v.Uh =  im * g.l  * g.invKrsq * sol
-  @. v.Vh = -im * g.kr * g.invKrsq * sol
+  @. v.uh =  im * g.l  * g.invKrsq * sol
+  @. v.vh = -im * g.kr * g.invKrsq * sol
   @. v.qh = sol
 
-  ldiv!(v.U, g.rfftplan, v.Uh)
-  ldiv!(v.V, g.rfftplan, v.Vh)
+  ldiv!(v.u, g.rfftplan, v.uh)
+  ldiv!(v.v, g.rfftplan, v.vh)
   ldiv!(v.q, g.rfftplan, v.qh)
 
-  @. v.U *= v.q # U*q
-  @. v.V *= v.q # V*q
+  @. v.u *= v.q # U*q
+  @. v.v *= v.q # V*q
 
-  mul!(v.Uh, g.rfftplan, v.U) # \hat{U*q}
-  mul!(v.Vh, g.rfftplan, v.V) # \hat{U*q}
+  mul!(v.uh, g.rfftplan, v.u) # \hat{U*q}
+  mul!(v.vh, g.rfftplan, v.v) # \hat{U*q}
 
-  @. N = -im*g.kr*v.Uh - im*g.l*v.Vh
+  @. N = -im*g.kr*v.uh - im*g.l*v.vh
   nothing
 end
 
@@ -213,11 +213,11 @@ Update the vars in v on the grid g with the solution in sol.
 function updatevars!(prob)
   v, g, sol = prob.vars, prob.grid, prob.sol
   v.qh .= sol
-  @. v.Uh =  im * g.l  * g.invKrsq * sol
-  @. v.Vh = -im * g.kr * g.invKrsq * sol
+  @. v.uh =  im * g.l  * g.invKrsq * sol
+  @. v.vh = -im * g.kr * g.invKrsq * sol
   ldiv!(v.q, g.rfftplan, deepcopy(v.qh))
-  ldiv!(v.U, g.rfftplan, deepcopy(v.Uh))
-  ldiv!(v.V, g.rfftplan, deepcopy(v.Vh))
+  ldiv!(v.u, g.rfftplan, deepcopy(v.uh))
+  ldiv!(v.v, g.rfftplan, deepcopy(v.vh))
   nothing
 end
 
@@ -243,8 +243,8 @@ solution `sol`.
 """
 @inline function energy(prob)
   sol, v, g = prob.sol, prob.vars, prob.grid
-  @. v.Uh = g.invKrsq * abs2(sol)
-  1/(2*g.Lx*g.Ly)*parsevalsum(v.Uh, g)
+  @. v.uh = g.invKrsq * abs2(sol)
+  1/(2*g.Lx*g.Ly)*parsevalsum(v.uh, g)
 end
 
 """
@@ -265,9 +265,9 @@ Returns the domain-averaged dissipation rate. nnu must be >= 1.
 """
 @inline function dissipation(prob)
   sol, v, p, g = prob.sol, prob.vars, prob.params, prob.grid
-  @. v.Uh = g.Krsq^(p.nnu-1) * abs2(sol)
-  v.Uh[1, 1] = 0
-  p.nu/(g.Lx*g.Ly)*parsevalsum(v.Uh, g)
+  @. v.uh = g.Krsq^(p.nnu-1) * abs2(sol)
+  v.uh[1, 1] = 0
+  p.nu/(g.Lx*g.Ly)*parsevalsum(v.uh, g)
 end
 
 """
@@ -277,14 +277,14 @@ end
 Returns the domain-averaged rate of work of energy by the forcing Fh.
 """
 @inline function work(sol, v::ForcedVars, g)
-  @. v.Uh = g.invKrsq * sol * conj(v.Fh)
-  1/(g.Lx*g.Ly)*parsevalsum(v.Uh, g)
+  @. v.uh = g.invKrsq * sol * conj(v.Fh)
+  1/(g.Lx*g.Ly)*parsevalsum(v.uh, g)
 end
 
 @inline function work(sol, v::StochasticForcedVars, g)
-  @. v.Uh = g.invKrsq * (v.prevsol + sol)/2.0 * conj(v.Fh) # Stratonovich
-  # @. v.Uh = g.invKrsq * v.prevsol * conj(v.Fh)           # Ito
-  1/(g.Lx*g.Ly)*parsevalsum(v.Uh, g)
+  @. v.uh = g.invKrsq * (v.prevsol + sol)/2.0 * conj(v.Fh) # Stratonovich
+  # @. v.uh = g.invKrsq * v.prevsol * conj(v.Fh)           # Ito
+  1/(g.Lx*g.Ly)*parsevalsum(v.uh, g)
 end
 
 @inline work(prob) = work(prob.sol, prob.vars, prob.grid)
@@ -296,9 +296,9 @@ Returns the extraction of domain-averaged energy by drag/hypodrag mu.
 """
 @inline function drag(prob)
   sol, v, p, g = prob.sol, prob.vars, prob.params, prob.grid
-  @. v.Uh = g.Krsq^(p.nmu-1) * abs2(sol)
-  v.Uh[1, 1] = 0
-  p.mu/(g.Lx*g.Ly)*parsevalsum(v.Uh, g)
+  @. v.uh = g.Krsq^(p.nmu-1) * abs2(sol)
+  v.uh[1, 1] = 0
+  p.mu/(g.Lx*g.Ly)*parsevalsum(v.uh, g)
 end
 
 end # module

test/runtests.jl

@@ -24,8 +24,8 @@ const rtol_niwqg = 1e-13 # tolerance for niwqg forcing tests
 const rtol_twodturb = 1e-13 # tolerance for niwqg forcing tests
 
 "Get the CFL number, assuming a uniform grid with `dx=dy`."
-cfl(U, V, dt, dx) = maximum([maximum(abs.(U)), maximum(abs.(V))]*dt/dx)
-cfl(prob) = cfl(prob.vars.U, prob.vars.V, prob.clock.dt, prob.grid.dx)
+cfl(u, v, dt, dx) = maximum([maximum(abs.(u)), maximum(abs.(v))]*dt/dx)
+cfl(prob) = cfl(prob.vars.u, prob.vars.v, prob.clock.dt, prob.grid.dx)
 
 "Returns the energy in vertically Fourier mode 1 in the Boussinesq equations."
 e1_fourier(u, v, p, m, N) = @. abs2(u) + abs2(v) + m^2*abs2(p)/N^2

test/test_twodturb.jl

@@ -30,7 +30,7 @@ function test_twodturb_stochasticforcingbudgets(; n=256, dt=0.01, L=2π, nu=1e-7
 
   # Forcing
   kf, dkf = 12.0, 2.0
-  σ = 0.1
+  ε = 0.1
 
   gr  = TwoDGrid(n, L)
   x, y = gridpoints(gr)
@@ -42,8 +42,8 @@ function test_twodturb_stochasticforcingbudgets(; n=256, dt=0.01, L=2π, nu=1e-7
   @. force2k[gr.Krsq .< 2.0^2 ] = 0
   @. force2k[gr.Krsq .> 20.0^2 ] = 0
   @. force2k[Kr .< 2π/L] = 0
-  σ0 = parsevalsum(force2k.*gr.invKrsq/2.0, gr)/(gr.Lx*gr.Ly)
-  force2k .= σ/σ0 * force2k
+  ε0 = parsevalsum(force2k.*gr.invKrsq/2.0, gr)/(gr.Lx*gr.Ly)
+  force2k .= ε/ε0 * force2k
 
   Random.seed!(1234)
 
@@ -70,7 +70,6 @@ function test_twodturb_stochasticforcingbudgets(; n=256, dt=0.01, L=2π, nu=1e-7
   stepforward!(prob, diags, round(Int, nt))
   TwoDTurb.updatevars!(prob)
 
-  cfl = cl.dt*maximum([maximum(v.V)/g.dx, maximum(v.U)/g.dy])
   E, D, W, R = diags
   t = round(mu*cl.t, digits=2)
 
@@ -82,15 +81,15 @@ function test_twodturb_stochasticforcingbudgets(; n=256, dt=0.01, L=2π, nu=1e-7
   # dEdt = W - D - R?
   # If the Ito interpretation was used for the work
   # then we need to add the drift term
-  # total = W[ii2]+σ - D[ii] - R[ii]      # Ito
+  # total = W[ii2]+ε - D[ii] - R[ii]      # Ito
   total = W[ii2] - D[ii] - R[ii]        # Stratonovich
 
   residual = dEdt - total
   isapprox(mean(abs.(residual)), 0, atol=1e-4)
 end
 
 
-function test_twodturb_deterministicforcingbudgets(; n=256, dt=0.01, L=2π, nu=1e-7, nnu=2, mu=1e-1, nmu=0, message=false)
+function test_twodturb_deterministicforcingbudgets(; n=256, dt=0.01, L=2π, nu=1e-7, nnu=2, mu=1e-1, nmu=0)
   n, L  = 256, 2π
   nu, nnu = 1e-7, 2
   mu, nmu = 1e-1, 0
@@ -126,7 +125,6 @@ function test_twodturb_deterministicforcingbudgets(; n=256, dt=0.01, L=2π, nu=1
   stepforward!(prob, diags, round(Int, nt))
   TwoDTurb.updatevars!(prob)
 
-  cfl = cl.dt*maximum([maximum(v.V)/g.dx, maximum(v.U)/g.dy])
   E, D, W, R = diags
   t = round(mu*cl.t, digits=2)
 
@@ -140,10 +138,6 @@ function test_twodturb_deterministicforcingbudgets(; n=256, dt=0.01, L=2π, nu=1
 
   residual = dEdt - total
 
-  if message
-    println("step: %04d, t: %.1f, cfl: %.3f, time: %.2f s\n", cl.step, cl.t, cfl, tc)
-  end
-
   isapprox(mean(abs.(residual)), 0, atol=1e-8)
 end