diff --git a/GeophysicalFlows.jl/GeophysicalFlows_decaying2Dturbulence.jl b/GeophysicalFlows.jl/GeophysicalFlows_decaying2Dturbulence.jl
index e5ce9ad..bde33a5 100644
--- a/GeophysicalFlows.jl/GeophysicalFlows_decaying2Dturbulence.jl
+++ b/GeophysicalFlows.jl/GeophysicalFlows_decaying2Dturbulence.jl
@@ -1,70 +1,64 @@
-using FourierFlows, Printf, Random, FFTW
-
-using Random: seed!
+using FourierFlows, Printf
 
 import GeophysicalFlows.TwoDNavierStokes
-import GeophysicalFlows.TwoDNavierStokes: energy, enstrophy
-import GeophysicalFlows: peakedisotropicspectrum
+
+using Random: seed!
+using Statistics: mean
 
 dev = CPU()     # Device (CPU/GPU)
 
 # Parameters
-  n = 256
-  L = 2π
- nν = 2
-  ν = 0.0
- dt = 1e-3
-nstepsjit = 10 # call stepforward for nstepsjit to force compilation
+ n = 256
+ L = 2π
+ ν = 1e-4
+nν = 1
+dt = 1e-3
+nsteps_jit = 10 # call stepforward for nsteps_jit to force compilation
 nsteps = 5000
- nothingfunction(args...) = nothing
-
-
-gr = TwoDGrid(dev, n, L, n, L; nthreads=1)
-pr = TwoDNavierStokes.Params(ν, nν)
-vs = TwoDNavierStokes.Vars(dev, gr)
-eq = TwoDNavierStokes.Equation(pr, gr)
-
-prob = FourierFlows.Problem(eq, "FilteredAB3", dt, gr, vs, pr, dev)
-filter = FourierFlows.makefilter(prob.eqn)
+stepper = "AB3"
+floattype = Float64
 
-# some aliases
-sol, cl, vs, gr = prob.sol, prob.clock, prob.vars, prob.grid
+grid2D = TwoDGrid(dev, n, L, n, L; nthreads=1, T=floattype)
+params = TwoDNavierStokes.Params(ν, nν)
+vars = TwoDNavierStokes.Vars(dev, grid2D)
+equation = TwoDNavierStokes.Equation(params, grid2D)
 
-x, y = gridpoints(gr)
+prob = FourierFlows.Problem(equation, stepper, dt, grid2D, vars, params, dev)
 
-# Initial condition closely following pyqg barotropic example
-# that reproduces the results of the paper by McWilliams (1984)
+# Random initial condition
 seed!(1234)
-k0, E0 = 6, 0.5
-zetai  = peakedisotropicspectrum(gr, k0, E0, mask=filter)
-TwoDNavierStokes.set_zeta!(prob, zetai)
+zeta_initial = randn(floattype, (n, n))
+zeta_initial = zeta_initial .- mean(zeta_initial) # make sure initial condition has zero mean
+TwoDNavierStokes.set_zeta!(prob, zeta_initial)
 
-for j=1:nstepsjit  #just-in-time compilation
+for j=1:nsteps_jit  #just-in-time compilation
   stepforward!(prob)
 end
 
-TwoDNavierStokes.set_zeta!(prob, zetai)
+TwoDNavierStokes.set_zeta!(prob, zeta_initial)
 
 startwalltime = time()
-while cl.step < nsteps
+while prob.clock.step < nsteps
   stepforward!(prob)
+  dealias!(prob.sol, prob.grid)
 end
 
 println(round((time()-startwalltime)/(nsteps-1)*1000, digits=3), " ms per time-step")
 
 # using PyPlot
+# x, y = gridpoints(prob.grid)
 # TwoDNavierStokes.updatevars!(prob)
 # figure(figsize=(10, 4))
 # subplot(121)
-# pcolormesh(x, y, zetai)
+# pcolormesh(x, y, zeta_initial)
 # xlabel("x")
 # ylabel("y")
 # title("vorticity @ t=0")
 # axis("square")
 # subplot(122)
-# pcolormesh(x, y, vs.zeta)
+# pcolormesh(x, y, prob.vars.zeta)
 # axis("square")
 # xlabel("x")
 # ylabel("y")
-# title("vorticity @ t="*string(round(cl.t, digits=2)))
+# title("vorticity @ t="*string(round(prob.clock.t, digits=2)))
 # savefig("GeophysicalFlows_n"*string(n)*".png", dpi=400)
diff --git a/GeophysicalFlows.jl/GeophysicalFlows_n256.png b/GeophysicalFlows.jl/GeophysicalFlows_n256.png
index 601d532..573eb6e 100644
Binary files a/GeophysicalFlows.jl/GeophysicalFlows_n256.png and b/GeophysicalFlows.jl/GeophysicalFlows_n256.png differ
diff --git a/GeophysicalFlows.jl/Manifest.toml b/GeophysicalFlows.jl/Manifest.toml
index 9c2e7ff..19d728f 100644
--- a/GeophysicalFlows.jl/Manifest.toml
+++ b/GeophysicalFlows.jl/Manifest.toml
@@ -8,9 +8,9 @@ version = "0.5.0"
 
 [[Adapt]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "82dab828020b872fa9efd3abec1152b075bc7cbf"
+git-tree-sha1 = "fd04049c7dd78cfef0b06cdc1f0f181467655712"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "1.0.0"
+version = "1.1.0"
 
 [[AxisAlgorithms]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
@@ -21,164 +21,170 @@ version = "1.0.0"
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
-[[BinDeps]]
-deps = ["Libdl", "Pkg", "SHA", "URIParser", "Unicode"]
-git-tree-sha1 = "66158ad56b4bf6cc8413b37d0b7bc52402682764"
-uuid = "9e28174c-4ba2-5203-b857-d8d62c4213ee"
-version = "1.0.0"
-
 [[BinaryProvider]]
-deps = ["Libdl", "SHA"]
-git-tree-sha1 = "5b08ed6036d9d3f0ee6369410b830f8873d4024c"
+deps = ["Libdl", "Logging", "SHA"]
+git-tree-sha1 = "ecdec412a9abc8db54c0efc5548c64dfce072058"
 uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
-version = "0.5.8"
+version = "0.5.10"
 
 [[CEnum]]
-git-tree-sha1 = "62847acab40e6855a9b5905ccb99c2b5cf6b3ebb"
+git-tree-sha1 = "1b77a77c3b28e0b3f413f7567c9bb8dd9bdccd14"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
-version = "0.2.0"
+version = "0.3.0"
 
 [[CUDAapi]]
 deps = ["Libdl", "Logging"]
-git-tree-sha1 = "56a813440ac98a1aa64672ab460a1512552211a7"
+git-tree-sha1 = "831b825d10104bd29e28f6da93312a976830717b"
 uuid = "3895d2a7-ec45-59b8-82bb-cfc6a382f9b3"
-version = "2.1.0"
+version = "4.0.0"
 
 [[CUDAdrv]]
 deps = ["CEnum", "CUDAapi", "Printf"]
-git-tree-sha1 = "1fce616fa0806c67c133eb1d2f68f0f1a7504665"
+git-tree-sha1 = "f56bbf18c86bcff7a961a32a4947a5abb2963a29"
 uuid = "c5f51814-7f29-56b8-a69c-e4d8f6be1fde"
-version = "5.0.1"
+version = "6.3.0"
 
 [[CUDAnative]]
-deps = ["Adapt", "CEnum", "CUDAapi", "CUDAdrv", "DataStructures", "InteractiveUtils", "LLVM", "Libdl", "Printf", "TimerOutputs"]
-git-tree-sha1 = "ba0725f487fb4a6c63efad7890a659659b6a6754"
+deps = ["Adapt", "BinaryProvider", "CEnum", "CUDAapi", "CUDAdrv", "ExprTools", "GPUCompiler", "LLVM", "Libdl", "Pkg", "Printf"]
+git-tree-sha1 = "ac86db2b05fdfec96b011e25a504ffe7476e8a68"
 uuid = "be33ccc6-a3ff-5ff2-a52e-74243cff1e17"
-version = "2.8.1"
+version = "3.1.0"
+
+[[CodeTracking]]
+deps = ["InteractiveUtils", "UUIDs"]
+git-tree-sha1 = "cab4da992adc0a64f63fa30d2db2fd8bec40cab4"
+uuid = "da1fd8a2-8d9e-5ec2-8556-3022fb5608a2"
+version = "0.5.11"
 
 [[CodecZlib]]
-deps = ["BinaryProvider", "Libdl", "TranscodingStreams"]
-git-tree-sha1 = "05916673a2627dd91b4969ff8ba6941bc85a960e"
+deps = ["TranscodingStreams", "Zlib_jll"]
+git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da"
 uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
-version = "0.6.0"
+version = "0.7.0"
 
 [[ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
-git-tree-sha1 = "b41d0f666d46ba128c6a0fc632d6e33fbfc03604"
+git-tree-sha1 = "c73d9cfc2a9d8433dc77f5bff4bddf46b1d78c20"
 uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
-version = "0.9.0"
+version = "0.10.3"
 
 [[Colors]]
-deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Printf", "Reexport"]
-git-tree-sha1 = "288e7a907bd993d50f5664e8e4fcddb9a3107039"
+deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Reexport"]
+git-tree-sha1 = "db9c215e2d92379d341e40dd1d5be893af2bfeb2"
 uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
-version = "0.11.1"
+version = "0.12.1"
 
-[[Compat]]
-deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "ed2c4abadf84c53d9e58510b5fc48912c2336fbb"
-uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "2.2.0"
+[[CompilerSupportLibraries_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "7c4f882c41faa72118841185afc58a2eb00ef612"
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "0.3.3+0"
 
 [[Conda]]
 deps = ["JSON", "VersionParsing"]
-git-tree-sha1 = "9a11d428dcdc425072af4aea19ab1e8c3e01c032"
+git-tree-sha1 = "7a58bb32ce5d85f8bf7559aa7c2842f9aecf52fc"
 uuid = "8f4d0f93-b110-5947-807f-2305c1781a2d"
-version = "1.3.0"
+version = "1.4.1"
 
-[[Coverage]]
-deps = ["CoverageTools", "HTTP", "JSON", "LibGit2", "MbedTLS"]
-git-tree-sha1 = "540c90d34374c82bbb12c4e06df1ef246a81ace2"
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-
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-uuid = "c36e975a-824b-4404-a568-ef97ca766997"
-version = "1.0.0"
+[[Cthulhu]]
+deps = ["CodeTracking", "InteractiveUtils", "REPL", "UUIDs", "Unicode"]
+git-tree-sha1 = "f3643e78353199d3097821e806348bd83f364155"
+uuid = "f68482b8-f384-11e8-15f7-abe071a5a75f"
+version = "1.1.1"
 
 [[CuArrays]]
-deps = ["AbstractFFTs", "Adapt", "CEnum", "CUDAapi", "CUDAdrv", "CUDAnative", "DataStructures", "GPUArrays", "Libdl", "LinearAlgebra", "MacroTools", "NNlib", "Printf", "Random", "Requires", "SparseArrays", "TimerOutputs"]
-git-tree-sha1 = "51fbe053dea29ed2513e02d38380007310cf4c4b"
+deps = ["AbstractFFTs", "Adapt", "CEnum", "CUDAapi", "CUDAdrv", "CUDAnative", "DataStructures", "GPUArrays", "Libdl", "LinearAlgebra", "MacroTools", "NNlib", "Pkg", "Printf", "Random", "Reexport", "Requires", "SparseArrays", "Statistics", "TimerOutputs"]
+git-tree-sha1 = "870a4ac61e99c36f42d15e496fd290c841541d90"
 uuid = "3a865a2d-5b23-5a0f-bc46-62713ec82fae"
-version = "1.6.0"
+version = "2.2.0"
 
 [[DataStructures]]
 deps = ["InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "b7720de347734f4716d1815b00ce5664ed6bbfd4"
+git-tree-sha1 = "af6d9c86e191c917c2276fbede1137e8ea20157f"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.17.9"
+version = "0.17.17"
 
 [[Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
-[[DelimitedFiles]]
-deps = ["Mmap"]
-uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
-
 [[Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
+[[ExprTools]]
+git-tree-sha1 = "6f0517056812fd6aa3af23d4b70d5325a2ae4e95"
+uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
+version = "0.1.1"
+
 [[FFTW]]
-deps = ["AbstractFFTs", "BinaryProvider", "Conda", "Libdl", "LinearAlgebra", "Reexport"]
-git-tree-sha1 = "4cfd3d43819228b9e73ab46600d0af0aa5cedceb"
+deps = ["AbstractFFTs", "FFTW_jll", "IntelOpenMP_jll", "Libdl", "LinearAlgebra", "MKL_jll", "Reexport"]
+git-tree-sha1 = "14536c95939aadcee44014728a459d2fe3ca9acf"
 uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
-version = "1.1.0"
+version = "1.2.2"
+
+[[FFTW_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "6c975cd606128d45d1df432fb812d6eb10fee00b"
+uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
+version = "3.3.9+5"
 
 [[FileIO]]
 deps = ["Pkg"]
-git-tree-sha1 = "74585bf1f7ed7259e166011e89f49363d7fa89a6"
+git-tree-sha1 = "202335fd24c2776493e198d6c66a6d910400a895"
 uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
-version = "1.2.1"
+version = "1.3.0"
+
+[[FixedPointNumbers]]
+git-tree-sha1 = "3ba9ea634d4c8b289d590403b4a06f8e227a6238"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.0"
 
 [[FourierFlows]]
-deps = ["CUDAapi", "Coverage", "CuArrays", "FFTW", "Interpolations", "JLD2", "LinearAlgebra", "Printf", "Random", "Reexport", "Requires", "Statistics"]
-git-tree-sha1 = "153b295514c016e30b300b9e65b0615061976166"
+deps = ["CUDAapi", "CuArrays", "FFTW", "Interpolations", "JLD2", "LinearAlgebra", "Random", "Reexport", "Requires", "Statistics"]
+git-tree-sha1 = "af1d7dd410e51ee8b58a8542208abf670180aab5"
 uuid = "2aec4490-903f-5c70-9b11-9bed06a700e1"
-version = "0.3.2"
+version = "0.4.5"
 
 [[GPUArrays]]
 deps = ["AbstractFFTs", "Adapt", "LinearAlgebra", "Printf", "Random", "Serialization"]
-git-tree-sha1 = "e756da6cee76a5f1436a05827fa8fdf3badc577f"
+git-tree-sha1 = "d887693eb1bd5e1fd573262a978745481895ec7d"
 uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
-version = "2.0.1"
+version = "3.4.1"
+
+[[GPUCompiler]]
+deps = ["Cthulhu", "DataStructures", "InteractiveUtils", "LLVM", "Libdl", "TimerOutputs"]
+git-tree-sha1 = "5275aa268ecd09640b32560e1eae90c78816e4d1"
+uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
+version = "0.2.0"
 
 [[GeophysicalFlows]]
 deps = ["CuArrays", "FFTW", "FourierFlows", "JLD2", "LinearAlgebra", "Random", "Reexport", "SpecialFunctions", "Statistics"]
-git-tree-sha1 = "c7b2d8e2fac9a023d7dd12c9551f6a607d208aae"
+git-tree-sha1 = "af97c086df798baaea1488923b7b46a47a284b39"
 uuid = "44ee3b1c-bc02-53fa-8355-8e347616e15e"
-version = "0.3.1"
-
-[[HTTP]]
-deps = ["Base64", "Dates", "IniFile", "MbedTLS", "Sockets"]
-git-tree-sha1 = "5c49dab19938b119fe204fd7d7e8e174f4e9c68b"
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-
-[[IniFile]]
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-uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
 version = "0.5.0"
 
+[[IntelOpenMP_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "fb8e1c7a5594ba56f9011310790e03b5384998d6"
+uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
+version = "2018.0.3+0"
+
 [[InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[Interpolations]]
 deps = ["AxisAlgorithms", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
-git-tree-sha1 = "96b16bb44b1037f42a50e3fa9ba38dd78c9c1a3e"
+git-tree-sha1 = "2b7d4e9be8b74f03115e64cf36ed2f48ae83d946"
 uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
-version = "0.12.7"
+version = "0.12.10"
 
 [[JLD2]]
 deps = ["CodecZlib", "DataStructures", "FileIO", "Mmap", "Pkg", "Printf", "UUIDs"]
-git-tree-sha1 = "5deae9f0745ef505ed155a0029629cf08502ccab"
+git-tree-sha1 = "e03e697cf84c275ece9cbefd1eabaf49bf5e7254"
 uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
-version = "0.1.11"
+version = "0.1.13"
 
 [[JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
@@ -188,11 +194,17 @@ version = "0.21.0"
 
 [[LLVM]]
 deps = ["CEnum", "Libdl", "Printf", "Unicode"]
-git-tree-sha1 = "1d08d7e4250f452f6cb20e4574daaebfdbee0ff7"
+git-tree-sha1 = "dd3f584c3dbefe39b2a8fbafa1a3b77e31e21255"
 uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
-version = "1.3.3"
+version = "1.5.1"
+
+[[LaTeXStrings]]
+git-tree-sha1 = "de44b395389b84fd681394d4e8d39ef14e3a2ea8"
+uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
+version = "1.1.0"
 
 [[LibGit2]]
+deps = ["Printf"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 
 [[Libdl]]
@@ -205,56 +217,73 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
+[[MKL_jll]]
+deps = ["IntelOpenMP_jll", "Libdl", "Pkg"]
+git-tree-sha1 = "0ce9a7fa68c70cf83c49d05d2c04d91b47404b08"
+uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
+version = "2020.1.216+0"
+
 [[MacroTools]]
-deps = ["DataStructures", "Markdown", "Random"]
-git-tree-sha1 = "e2fc7a55bb2224e203bbd8b59f72b91323233458"
+deps = ["Markdown", "Random"]
+git-tree-sha1 = "f7d2e3f654af75f01ec49be82c231c382214223a"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
-version = "0.5.3"
+version = "0.5.5"
 
 [[Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
-[[MbedTLS]]
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-
 [[Mmap]]
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 deps = ["BinaryProvider", "Libdl", "LinearAlgebra", "Requires", "Statistics"]
-git-tree-sha1 = "755c0bab3912ff782167e1b4b774b833f8a0e550"
+git-tree-sha1 = "d9f196d911f55aeaff11b11f681b135980783824"
 uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
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 [[OffsetArrays]]
-git-tree-sha1 = "fcfb0d1acd89dd37bbfce2873c8401713a855f80"
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 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
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+version = "1.0.4"
+
+[[OpenSpecFun_jll]]
+deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
+git-tree-sha1 = "d51c416559217d974a1113522d5919235ae67a87"
+uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
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 [[OrderedCollections]]
-deps = ["Random", "Serialization", "Test"]
-git-tree-sha1 = "c4c13474d23c60d20a67b217f1d7f22a40edf8f1"
+git-tree-sha1 = "12ce190210d278e12644bcadf5b21cbdcf225cd3"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
-version = "1.1.0"
+version = "1.2.0"
 
 [[Parsers]]
 deps = ["Dates", "Test"]
-git-tree-sha1 = "0139ba59ce9bc680e2925aec5b7db79065d60556"
+git-tree-sha1 = "eb3e09940c0d7ae01b01d9291ebad7b081c844d3"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "0.3.10"
+version = "1.0.5"
 
 [[Pkg]]
-deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Test", "UUIDs"]
+deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
 [[Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
+[[PyCall]]
+deps = ["Conda", "Dates", "Libdl", "LinearAlgebra", "MacroTools", "Serialization", "VersionParsing"]
+git-tree-sha1 = "3a3fdb9000d35958c9ba2323ca7c4958901f115d"
+uuid = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
+version = "1.91.4"
+
+[[PyPlot]]
+deps = ["Colors", "LaTeXStrings", "PyCall", "Sockets", "Test", "VersionParsing"]
+git-tree-sha1 = "67dde2482fe1a72ef62ed93f8c239f947638e5a2"
+uuid = "d330b81b-6aea-500a-939a-2ce795aea3ee"
+version = "2.9.0"
+
 [[REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -264,10 +293,9 @@ deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [[Ratios]]
-deps = ["Compat"]
-git-tree-sha1 = "cdbbe0f350581296f3a2e3e7a91b214121934407"
+git-tree-sha1 = "37d210f612d70f3f7d57d488cb3b6eff56ad4e41"
 uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
-version = "0.3.1"
+version = "0.4.0"
 
 [[Reexport]]
 deps = ["Pkg"]
@@ -277,9 +305,9 @@ version = "0.2.0"
 
 [[Requires]]
 deps = ["UUIDs"]
-git-tree-sha1 = "999513b7dea8ac17359ed50ae8ea089e4464e35e"
+git-tree-sha1 = "d37400976e98018ee840e0ca4f9d20baa231dc6b"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.0.0"
+version = "1.0.1"
 
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@@ -299,16 +327,16 @@ deps = ["LinearAlgebra", "Random"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[SpecialFunctions]]
-deps = ["BinDeps", "BinaryProvider", "Libdl"]
-git-tree-sha1 = "3bdd374b6fd78faf0119b8c5d538788dbf910c6e"
+deps = ["OpenSpecFun_jll"]
+git-tree-sha1 = "d8d8b8a9f4119829410ecd706da4cc8594a1e020"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "0.8.0"
+version = "0.10.3"
 
 [[StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
-git-tree-sha1 = "5a3bcb6233adabde68ebc97be66e95dcb787424c"
+git-tree-sha1 = "5c06c0aeb81bef54aed4b3f446847905eb6cbda0"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "0.12.1"
+version = "0.12.3"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
@@ -320,9 +348,9 @@ uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [[TimerOutputs]]
 deps = ["Printf"]
-git-tree-sha1 = "311765af81bbb48d7bad01fb016d9c328c6ede03"
+git-tree-sha1 = "f458ca23ff80e46a630922c555d838303e4b9603"
 uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
-version = "0.5.3"
+version = "0.5.6"
 
 [[TranscodingStreams]]
 deps = ["Random", "Test"]
@@ -330,12 +358,6 @@ git-tree-sha1 = "7c53c35547de1c5b9d46a4797cf6d8253807108c"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
 version = "0.9.5"
 
-[[URIParser]]
-deps = ["Test", "Unicode"]
-git-tree-sha1 = "6ddf8244220dfda2f17539fa8c9de20d6c575b69"
-uuid = "30578b45-9adc-5946-b283-645ec420af67"
-version = "0.4.0"
-
 [[UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
@@ -350,6 +372,12 @@ version = "1.2.0"
 
 [[WoodburyMatrices]]
 deps = ["LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "bbb9f7fd6fbdd9582e77c0b698312c543de5eb71"
+git-tree-sha1 = "28ffe06d28b1ba8fdb2f36ec7bb079fac81bac0d"
 uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
-version = "0.5.0"
+version = "0.5.2"
+
+[[Zlib_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "a2e0d558f6031002e380a90613b199e37a8565bf"
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+version = "1.2.11+10"
diff --git a/matlab/AB3timestep.m b/matlab/AB3timestep.m
index 178bd35..e992a66 100644
--- a/matlab/AB3timestep.m
+++ b/matlab/AB3timestep.m
@@ -1,7 +1,6 @@
 function [qhnew, RHSp, RHSpp] = AB3timestep(qh, RHSp, RHSpp, dt)
-    global filter
     RHS = RHS_eq(qh);   
-    qhnew = filter.*(qh + (23*RHS - 16*RHSp + 5*RHSpp)*dt/12);
+    qhnew = qh + (23*RHS - 16*RHSp + 5*RHSpp)*dt/12;
     RHSpp = RHSp;
     RHSp  = RHS;
 end
\ No newline at end of file
diff --git a/matlab/ForwardEulertimestep.m b/matlab/ForwardEulertimestep.m
index d9c19fc..f902497 100644
--- a/matlab/ForwardEulertimestep.m
+++ b/matlab/ForwardEulertimestep.m
@@ -1,5 +1,4 @@
 function [qhnew] = ForwardEulertimestep(qh, dt)
-    global filter
     RHS = RHS_eq(qh);    
-    qhnew = filter.*(qh + RHS*dt);
+    qhnew = qh + RHS*dt;
 end
\ No newline at end of file
diff --git a/matlab/RK4timestep.m b/matlab/RK4timestep.m
index aa5b2bd..78262c0 100644
--- a/matlab/RK4timestep.m
+++ b/matlab/RK4timestep.m
@@ -4,5 +4,5 @@
     k2 = RHS_eq(qh+k1*dt/2);
     k3 = RHS_eq(qh+k2*dt/2);
     k4 = RHS_eq(qh+k3*dt);
-    qhnew = filter.*(qh + (k1 + 2*k2 + 2*k3 + k4)*dt/6);
+    qhnew = qh + (k1 + 2*k2 + 2*k3 + k4)*dt/6;
 end
\ No newline at end of file
diff --git a/matlab/matlab_decaying2Dturbulence.m b/matlab/matlab_decaying2Dturbulence.m
index 481f3e9..c451ab4 100644
--- a/matlab/matlab_decaying2Dturbulence.m
+++ b/matlab/matlab_decaying2Dturbulence.m
@@ -1,9 +1,9 @@
 clear all;
 
-global invKsq K L Ksq nu nnu filter
+global invKsq K L Ksq nu nnu
 
 maxNumCompThreads(1);
-GPU = 0; % set =1 to run on GPU
+GPU = 0; % set equal to 1 to run on GPU
 
 nx = 256;
 ny = nx;
@@ -11,8 +11,8 @@
 Lx = 2*pi;
 Ly = Lx;
 
-nu = 0.0;
-nnu = 2;
+nu = 1e-4;
+nnu = 1;
 
 dt = 1e-3;
 nsteps = 5000;
@@ -35,24 +35,10 @@
 invKsq = 1 ./ Ksq;
 invKsq(Ksq==0)=0;
 
-% creat a filter in wavenumber space;
-% a is chosen so that the energy at the largest nondim
-% wavenumber K*dx be zero whithin machine double precision
-s=4;
-Kmax = ny/2; Kmax_s=Kmax*dy;
-kcut = 2/3*Kmax;kcut_s=kcut*dy;
-a = -log(1e-15)/(Kmax_s-kcut_s)^s * dy^s;
-Kmag=sqrt(Ksq);
-
-filter = ones(ny, nx).*abs(Kmag<=ny/3) + exp(-a*(Kmag-kcut).^s).*abs(Kmag>ny/3);
-
-psih0 = (Ksq.*(1 + (Kmag/6).^4)).^(-1/2) .* (randn(ny, nx) + 1i*randn(ny, nx));
-psih0(1, 1)=0;
-psih0 = fft2(real(ifft2(psih0)));
-Etemp = sum(0.5*Ksq(:).*abs(psih0(:)).^2/(nx*ny)^2);
-psih0 = psih0*sqrt(0.5/Etemp);
-qh0 = -Ksq.*psih0.*filter;
-qh = qh0;
+% Random initial condition
+q0 = randn(ny, nx);
+q0 = q0 - mean(q0);  % make sure initial condition has zero mean
+qh = fft2(q0);
 
 if GPU==1
     qh = gpuArray(qh); K = gpuArray(K); L = gpuArray(L); Ksq = gpuArray(Ksq);
@@ -85,7 +71,7 @@
 % figure()
 % set(gcf,'units','inches','position',[3, 3, 10, 4])
 % subplot(1,2,1)
-% pcolor2(X, Y, real(ifft2(qh0)))
+% pcolor2(X, Y, q0)
 % set(gca, 'fontsize', 12, 'Box', 'on', 'layer', 'top')
 % xticks(-3:3); yticks(-3:3);
 % xlabel('$x$', 'fontsize', 16, 'Interpreter', 'latex')
@@ -101,4 +87,4 @@
 % title(['vorticity @ $t=' num2str(T(end)) '$'], 'fontsize', 16, 'Interpreter', 'latex')
 % axis square;
 % set(gcf,'PaperPositionMode','auto')
-% print('matlab_n256.png', '-dpng', '-r400'); 
\ No newline at end of file
+% print(['matlab_n' num2str(nx) '.png'], '-dpng', '-r400');
\ No newline at end of file
diff --git a/matlab/matlab_n256.png b/matlab/matlab_n256.png
index 88db4cd..1e12755 100644
Binary files a/matlab/matlab_n256.png and b/matlab/matlab_n256.png differ
diff --git a/pyqg/pyqg_decaying2Dturbulence.py b/pyqg/pyqg_decaying2Dturbulence.py
index 578a2e8..9814bf6 100644
--- a/pyqg/pyqg_decaying2Dturbulence.py
+++ b/pyqg/pyqg_decaying2Dturbulence.py
@@ -13,26 +13,11 @@
         beta=0., H=1., rek=0., rd=None, dt=dt,
         twrite=np.inf, taveint=np.inf, ntd=1)
 
-# McWilliams 84 IC condition
-fk = m.wv != 0
-ckappa = np.zeros_like(m.wv2)
-ckappa[fk] = np.sqrt( m.wv2[fk]*(1. + (m.wv2[fk]/36.)**2) )**-1
-
-nhx, nhy = m.wv2.shape
-
-Pi_hat = np.random.randn(nhx, nhy)*ckappa +1j*np.random.randn(nhx,nhy)*ckappa
-
-Pi = m.ifft( Pi_hat[np.newaxis] )
-Pi = Pi - Pi.mean()
-Pi_hat = m.fft( Pi )
-KEaux = spec_var( m, m.filtr*m.wv*Pi_hat )
-
-pih = ( Pi_hat * np.sqrt(0.5/KEaux) )
-qih = -m.wv2*pih
-qi = m.ifft(qih)
+# Random initial condition
+qi = np.random.randn(m.nz, m.nx, m.ny)
+qi = qi - qi.mean()
 m.set_q(qi)
 
-
 t = time.time()
 # run the model
 m.run()
diff --git a/pyqg/pyqg_n256.png b/pyqg/pyqg_n256.png
index ba4b228..75370c1 100644
Binary files a/pyqg/pyqg_n256.png and b/pyqg/pyqg_n256.png differ