From f8ad49607749e42af0c676f94833826030b3bca0 Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 3 Oct 2019 09:21:16 -0400
Subject: [PATCH 01/18] Provides Fplane with rotation rate and latitude

---
 src/coriolis.jl | 38 +++++++++++++++++++++++++++++++++-----
 1 file changed, 33 insertions(+), 5 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 64dad24d4e..5cd9e6cd01 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -24,19 +24,47 @@ end
     FPlane([T=Float64;] f)
 
 Returns a parameter object for constant rotation at the angular frequency
-`2f`, and therefore with background vorticity `f`, around a vertical axis.
+`f`, and therefore with background vorticity `2f`, around a vertical axis.
 
-Also called `FPlane`, after the "f-plane" approximation for the local effect of 
+Also called `FPlane`, after the "f-plane" approximation for the local effect of
 Earth's rotation in a planar coordinate system tangent to the Earth's surface.
 """
-function FPlane(T=Float64; f) 
+function FPlane(T=Float64; f)
     return FPlane{T}(f)
 end
 
-@inline fv(i, j, k, grid::RegularCartesianGrid{T}, f, v) where T = 
+"""
+    FPlane([T=Float64;] Ω, lat)
+
+Returns a parameter object for constant rotation at the angular frequency
+`f = 2Ωsin(lat)`, and therefore with background vorticity `f = 4Ωsin(lat)`,
+around a vertical axis.
+
+Also called `FPlane`, after the "f-plane" approximation for the local effect of
+Earth's rotation in a planar coordinate system tangent to the Earth's surface.
+"""
+function FPlane(T=Float64; Ω, lat)
+    return FPlane{T}(2*Ω*sind(lat))
+end
+
+
+# """
+#     βPlane{T} <: AbstractRotation
+#
+# A parameter object for linearly increasing rotation in meridional direction.
+# """
+# struct βPlane{T} <: AbstractRotation
+#     f :: T
+# end
+#
+# function βPlane(T=Float64; f₀, β)
+#     return βPlane{T}(f₀ + β*y)
+# end
+
+@inline fv(i, j, k, grid::RegularCartesianGrid{T}, f, v) where T =
     T(0.5) * f * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
 
-@inline fu(i, j, k, grid::RegularCartesianGrid{T}, f, u) where T = 
+@inline fu(i, j, k, grid::RegularCartesianGrid{T}, f, u) where T =
     T(0.5) * f * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)

From 24fd4e35a99e3ae4d25abeaf035629f86742136e Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 3 Oct 2019 09:33:01 -0400
Subject: [PATCH 02/18] Adds beta-plane

---
 src/coriolis.jl | 33 +++++++++++++++++++++------------
 1 file changed, 21 insertions(+), 12 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 5cd9e6cd01..a4f231d902 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -48,18 +48,19 @@ function FPlane(T=Float64; Ω, lat)
 end
 
 
-# """
-#     βPlane{T} <: AbstractRotation
-#
-# A parameter object for linearly increasing rotation in meridional direction.
-# """
-# struct βPlane{T} <: AbstractRotation
-#     f :: T
-# end
-#
-# function βPlane(T=Float64; f₀, β)
-#     return βPlane{T}(f₀ + β*y)
-# end
+"""
+    βPlane{T} <: AbstractRotation
+
+A parameter object for meridionally increasing rotation (`f = f₀ + βy`).
+"""
+struct βPlane{T} <: AbstractRotation
+    f₀ :: T
+    β  :: T
+end
+
+function βPlane(T=Float64; f₀, β)
+    return βPlane{T}(f₀, β)
+end
 
 @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f, v) where T =
     T(0.5) * f * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
@@ -67,7 +68,15 @@ end
 @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f, u) where T =
     T(0.5) * f * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
+@inline fv(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, v) where T =
+    T(0.5) * (f₀ + β * grid.yC[j]) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
+
+@inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
+    T(0.5) * (f₀ + β * grid.yF[j]) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
+
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)
+@inline x_f_cross_U(i, j, k, grid, rotation::βPlane, U) = -fv(i, j, k, grid, rotation.f, rotation.β, U.v)
+@inline y_f_cross_U(i, j, k, grid, rotation::βPlane, U) =  fu(i, j, k, grid, rotation.f, rotation.β, U.u)
 @inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::FPlane, U) where T = zero(T)
 

From 691635807fa09f8d03cbf3c87a57c9f4896f7024 Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 3 Oct 2019 10:51:45 -0400
Subject: [PATCH 03/18] Fixes docstrings, whitespace, uses inbounds

---
 src/coriolis.jl | 28 +++++++++++++++-------------
 1 file changed, 15 insertions(+), 13 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index a4f231d902..88b9860c97 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -24,7 +24,7 @@ end
     FPlane([T=Float64;] f)
 
 Returns a parameter object for constant rotation at the angular frequency
-`f`, and therefore with background vorticity `2f`, around a vertical axis.
+`f/2`, and therefore with background vorticity `f`, around a vertical axis.
 
 Also called `FPlane`, after the "f-plane" approximation for the local effect of
 Earth's rotation in a planar coordinate system tangent to the Earth's surface.
@@ -34,32 +34,32 @@ function FPlane(T=Float64; f)
 end
 
 """
-    FPlane([T=Float64;] Ω, lat)
+    FPlane([T=Float64;] Ω, latitude)
 
 Returns a parameter object for constant rotation at the angular frequency
-`f = 2Ωsin(lat)`, and therefore with background vorticity `f = 4Ωsin(lat)`,
+`Ωsin(latitude), and therefore with background vorticity `f = 2Ωsin(latitude),
 around a vertical axis.
 
 Also called `FPlane`, after the "f-plane" approximation for the local effect of
 Earth's rotation in a planar coordinate system tangent to the Earth's surface.
 """
-function FPlane(T=Float64; Ω, lat)
-    return FPlane{T}(2*Ω*sind(lat))
+function FPlane(T=Float64; Ω, latitude)
+    return FPlane{T}(2*Ω*sind(latitude))
 end
 
 
 """
-    βPlane{T} <: AbstractRotation
+    BetaPlane{T} <: AbstractRotation
 
 A parameter object for meridionally increasing rotation (`f = f₀ + βy`).
 """
-struct βPlane{T} <: AbstractRotation
+struct BetaPlane{T} <: AbstractRotation
     f₀ :: T
     β  :: T
 end
 
-function βPlane(T=Float64; f₀, β)
-    return βPlane{T}(f₀, β)
+function BetaPlane(T=Float64; f₀, β)
+    return BetaPlane{T}(f₀, β)
 end
 
 @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f, v) where T =
@@ -69,14 +69,16 @@ end
     T(0.5) * f * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
 @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, v) where T =
-    T(0.5) * (f₀ + β * grid.yC[j]) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
+     T(0.5) * (f₀ + β * @inbounds(grid.yC[j])) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
 
 @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
-    T(0.5) * (f₀ + β * grid.yF[j]) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
+     T(0.5) * (f₀ + β * @inbounds(grid.yF[j])) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)
-@inline x_f_cross_U(i, j, k, grid, rotation::βPlane, U) = -fv(i, j, k, grid, rotation.f, rotation.β, U.v)
-@inline y_f_cross_U(i, j, k, grid, rotation::βPlane, U) =  fu(i, j, k, grid, rotation.f, rotation.β, U.u)
+
+@inline x_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) = -fv(i, j, k, grid, rotation.f, rotation.β, U.v)
+@inline y_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) =  fu(i, j, k, grid, rotation.f, rotation.β, U.u)
+
 @inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::FPlane, U) where T = zero(T)
 

From 16c784332a093bcd5e856d35fcbbd88a10eda4b9 Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 10 Oct 2019 11:14:41 -0400
Subject: [PATCH 04/18] Additional format for specifying beta plane

---
 src/Oceananigans.jl |  2 +-
 src/coriolis.jl     | 32 +++++++++++++++++++++++++++-----
 2 files changed, 28 insertions(+), 6 deletions(-)

diff --git a/src/Oceananigans.jl b/src/Oceananigans.jl
index cbbc88914f..e8a205508e 100644
--- a/src/Oceananigans.jl
+++ b/src/Oceananigans.jl
@@ -12,7 +12,7 @@ export
     CPU, GPU,
 
     # Constants
-    FPlane,
+    FPlane, BetaPlane,
     second, minute, hour, day,
 
     # Grids
diff --git a/src/coriolis.jl b/src/coriolis.jl
index 88b9860c97..e2f24e499d 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -51,28 +51,50 @@ end
 """
     BetaPlane{T} <: AbstractRotation
 
-A parameter object for meridionally increasing rotation (`f = f₀ + βy`).
+A parameter object for meridionally increasing Coriolis
+parameter (`f = f₀ + βy`).
 """
 struct BetaPlane{T} <: AbstractRotation
     f₀ :: T
     β  :: T
 end
 
+"""
+    BetaPlane([T=Float64;] f₀, β)
+
+A parameter object for meridionally increasing Coriolis
+parameter (`f = f₀ + βy`).
+"""
 function BetaPlane(T=Float64; f₀, β)
     return BetaPlane{T}(f₀, β)
 end
 
+"""
+    BetaPlane([T=Float64;] Ω, latitude, R)
+
+Returns a parameter object for meridionally increasing rotation at the
+angular frequency `Ωsin(latitude), and therefore with Coriolis parameter
+ `f₀ = 2Ωsin(latitude), around a vertical axis.
+The Coriolis parameter increases meridionally as `f = f₀ + βy`, where
+`β = 2Ωcos(latitude)/R`.
+"""
+function BetaPlane(T=Float64; Ω, latitude, R)
+    f₀ = 2*Ω*sind(latitude)
+    β = 2*Ω*cosd(latitude)/R
+    return BetaPlane{T}(f₀, β)
+end
+
 @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f, v) where T =
     T(0.5) * f * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
 
 @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f, u) where T =
     T(0.5) * f * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
-@inline fv(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, v) where T =
-     T(0.5) * (f₀ + β * @inbounds(grid.yC[j])) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
+@inbounds @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, v) where T =
+     T(0.5) * (f₀ + β * grid.yC[j]) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
 
-@inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
-     T(0.5) * (f₀ + β * @inbounds(grid.yF[j])) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
+@inbounbds @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
+     T(0.5) * (f₀ + β * grid.yF[j]) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)

From 29cc97da6a8067a3c2eb0cee8dfd0eecf618165b Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 10 Oct 2019 11:25:07 -0400
Subject: [PATCH 05/18] Fixes a typo

---
 src/coriolis.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index beb18115af..2392efe1c7 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -93,7 +93,7 @@ end
 @inbounds @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, v) where T =
      T(0.5) * (f₀ + β * grid.yC[j]) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
 
-@inbounbds @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
+@inbounds @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
      T(0.5) * (f₀ + β * grid.yF[j]) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)

From a9489c3d815c37ab275a36efbbeefd678b6cbc6e Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 10 Oct 2019 11:34:35 -0400
Subject: [PATCH 06/18] Now rotation calls f0 instead of f for BetaPlane

---
 src/coriolis.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 2392efe1c7..236b10afc7 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -99,8 +99,8 @@ end
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)
 
-@inline x_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) = -fv(i, j, k, grid, rotation.f, rotation.β, U.v)
-@inline y_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) =  fu(i, j, k, grid, rotation.f, rotation.β, U.u)
+@inline x_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) = -fv(i, j, k, grid, rotation.f₀, rotation.β, U.v)
+@inline y_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) =  fu(i, j, k, grid, rotation.f₀, rotation.β, U.u)
 
 @inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::FPlane, U) where T = zero(T)
 

From d56d755a69f9880cc7f9a09dc59c5b1442a9c75c Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 10 Oct 2019 11:57:22 -0400
Subject: [PATCH 07/18] zfcrossu for betaplane

---
 src/coriolis.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 236b10afc7..4df4e14af2 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -29,7 +29,7 @@ Returns a parameter object for constant rotation at the angular frequency
 Also called `FPlane`, after the "f-plane" approximation for the local effect of
 Earth's rotation in a planar coordinate system tangent to the Earth's surface.
 """
-function FPlane(T::DataType=Float64; f) 
+function FPlane(T::DataType=Float64; f)
     return FPlane{T}(f)
 end
 
@@ -98,9 +98,9 @@ end
 
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)
+@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::FPlane, U) where T = zero(T)
+
 
 @inline x_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) = -fv(i, j, k, grid, rotation.f₀, rotation.β, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) =  fu(i, j, k, grid, rotation.f₀, rotation.β, U.u)
-
-@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::FPlane, U) where T = zero(T)
-
+@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::BetaPlane, U) where T = zero(T)

From 9cb54b1e07f3f2be72ff0b881508455bd9801820 Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Thu, 10 Oct 2019 12:03:58 -0400
Subject: [PATCH 08/18] z_f_cross_U for betaplane

---
 src/coriolis.jl | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 4df4e14af2..cbad4f6684 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -98,9 +98,8 @@ end
 
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)
-@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::FPlane, U) where T = zero(T)
-
 
 @inline x_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) = -fv(i, j, k, grid, rotation.f₀, rotation.β, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) =  fu(i, j, k, grid, rotation.f₀, rotation.β, U.u)
-@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::BetaPlane, U) where T = zero(T)
+
+@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::Union{FPlane, BetaPlane}, U) where T = zero(T)

From 59ee18a923718841a5b1acb82cafffb66a10f2a9 Mon Sep 17 00:00:00 2001
From: Gregory Wagner <wagner.greg@gmail.com>
Date: Mon, 21 Oct 2019 07:11:59 -0400
Subject: [PATCH 09/18] Adds BetaPlane as possible coriolis option

---
 src/coriolis.jl | 60 +++++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 58 insertions(+), 2 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index d4e4f1a891..6d946ee250 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -1,3 +1,5 @@
+using .TurbulenceClosures: ▶xy_cfa, ▶xy_fca
+
 #####
 ##### Functions for non-rotating models
 #####
@@ -39,7 +41,61 @@ end
 @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f, u) where T = 
     T(0.5) * f * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
-@inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
-@inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)
+@inbounds @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, v) where T =
+
+@inbounds @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
+     T(0.5) * (f₀ + β * grid.yF[j]) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
+
+@inline x_f_cross_U(i, j, k, grid, coriolis::FPlane, U) = -fv(i, j, k, grid, coriolis.f, U.v)
+@inline y_f_cross_U(i, j, k, grid, coriolis::FPlane, U) =  fu(i, j, k, grid, coriolis.f, U.u)
 @inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::FPlane, U) where T = zero(T)
 
+#####
+##### The Beta Plane
+#####
+
+"""
+    BetaPlane{T} <: AbstractRotation
+
+A parameter object for meridionally increasing Coriolis
+parameter (`f = f₀ + βy`).
+"""
+struct BetaPlane{T} <: AbstractRotation
+    f₀ :: T
+     β :: T
+end
+
+"""
+    BetaPlane([T=Float64;] f₀=nothing, β=nothing, 
+                           rotation_rate=nothing, latitude=nothing, radius=nothing)
+
+A parameter object for meridionally increasing Coriolis parameter (`f = f₀ + βy`).
+
+The user may specify both `f₀` and `β`, or the three parameters
+`rotation_rate`, `latitude`, and `radius` that specify the rotation rate and radius 
+of a planet, and the central latitude at which the `β`-plane approximation is to be made.
+"""
+function BetaPlane(T=Float64; f₀=nothing, β=nothing, 
+                              rotation_rate=nothing, latitude=nothing, radius=nothing)
+
+    f_and_β = f₀ != nothing && β != nothing
+    planet_parameters = rotation_rate != nothing && latitude != nothing && radius != nothing
+
+    (f_and_β || planet_parameters) && !(f_and_β && planet_parameters) || throw(ArgumentError(
+        "Either keywords f₀ and β must be specified, *or* all of rotation_rate, latitude, and radius."))
+
+    if planet_parameters
+        f₀ = 2rotation_rate * sind(latitude)
+         β = 2rotation_rate * cosd(latitude) / radius
+     end
+
+    return BetaPlane{T}(f₀, β)
+end
+
+@inline x_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =
+    @inbounds (coriolis.f₀ + coriolis.β * grid.yC[j]) * ▶xy_fca(i, j, k, grid, v)
+
+@inline y_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =
+    @inbounds (coriolis.f₀ + coriolis.β * grid.yF[j]) * ▶xy_cfa(i, j, k, grid, v) 
+
+@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::BetaPlane, U) where T = zero(T)

From 966ec68409a07563a000212388a48febe3fce6bc Mon Sep 17 00:00:00 2001
From: Gregory Wagner <wagner.greg@gmail.com>
Date: Mon, 21 Oct 2019 07:12:52 -0400
Subject: [PATCH 10/18] Adds tests for instantiating beta plane and exports
 from top level

---
 src/Oceananigans.jl   |  2 +-
 test/test_coriolis.jl | 17 +++++++++++++++--
 2 files changed, 16 insertions(+), 3 deletions(-)

diff --git a/src/Oceananigans.jl b/src/Oceananigans.jl
index 66b36566ae..437a07d42b 100644
--- a/src/Oceananigans.jl
+++ b/src/Oceananigans.jl
@@ -12,7 +12,7 @@ export
     CPU, GPU,
 
     # Constants
-    FPlane,
+    FPlane, BetaPlane,
     second, minute, hour, day,
 
     # Grids
diff --git a/test/test_coriolis.jl b/test/test_coriolis.jl
index 0317fb2e56..8612ba08a3 100644
--- a/test/test_coriolis.jl
+++ b/test/test_coriolis.jl
@@ -1,14 +1,27 @@
-function instantiate_coriolis(T)
+function instantiate_fplane(T)
     coriolis = FPlane(T, f=π)
     return coriolis.f == T(π)
 end
 
+function instantiate_betaplane_1(T)
+    coriolis = BetaPlane(T, f₀=π, β=2π)
+    return coriolis.f₀ == T(π)
+end
+
+function instantiate_betaplane_2(T)
+    coriolis = BetaPlane(T, latitude=70, radius=2π, rotation_rate=3π)
+    return coriolis.f₀ == T(6π * sind(70))
+end
+
+
 @testset "Coriolis" begin
     println("Testing Coriolis...")
 
     @testset "Coriolis" begin
         for T in float_types
-            @test instantiate_coriolis(T)
+            @test instantiate_fplane(T)
+            @test instantiate_betaplane_1(T)
+            @test instantiate_betaplane_2(T)
         end
     end
 end

From 5d8b480181e5da0efe05919d6d9d29c52789416a Mon Sep 17 00:00:00 2001
From: Gregory Wagner <wagner.greg@gmail.com>
Date: Mon, 21 Oct 2019 07:28:04 -0400
Subject: [PATCH 11/18] Adds test for argument error on instatntiation of
 betaplane

---
 test/test_coriolis.jl | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/test/test_coriolis.jl b/test/test_coriolis.jl
index 8612ba08a3..64a0165a92 100644
--- a/test/test_coriolis.jl
+++ b/test/test_coriolis.jl
@@ -13,7 +13,6 @@ function instantiate_betaplane_2(T)
     return coriolis.f₀ == T(6π * sind(70))
 end
 
-
 @testset "Coriolis" begin
     println("Testing Coriolis...")
 
@@ -22,6 +21,11 @@ end
             @test instantiate_fplane(T)
             @test instantiate_betaplane_1(T)
             @test instantiate_betaplane_2(T)
+            # Non-exhaustively test that BetaPlane throws an ArgumentError
+            @test_throws ArgumentError BetaPlane(T, f₀=1)
+            @test_throws ArgumentError BetaPlane(T, β=1)
+            @test_throws ArgumentError BetaPlane(T, latitude=70)
+            @test_throws ArgumentError BetaPlane(T, f₀=1e-4, β=1e-11, latitude=70)
         end
     end
 end

From 23e44f9fb75bc5edce1529c0b2775ce027700f56 Mon Sep 17 00:00:00 2001
From: Gregory Wagner <wagner.greg@gmail.com>
Date: Mon, 21 Oct 2019 07:28:19 -0400
Subject: [PATCH 12/18] Fixes bugs in coriolis force and beta plane arguments

---
 src/coriolis.jl | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 6d946ee250..f1bdc437a8 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -81,8 +81,10 @@ function BetaPlane(T=Float64; f₀=nothing, β=nothing,
     f_and_β = f₀ != nothing && β != nothing
     planet_parameters = rotation_rate != nothing && latitude != nothing && radius != nothing
 
-    (f_and_β || planet_parameters) && !(f_and_β && planet_parameters) || throw(ArgumentError(
-        "Either keywords f₀ and β must be specified, *or* all of rotation_rate, latitude, and radius."))
+    (f_and_β && all(Tuple(p === nothing for p in (rotation_rate, latitude, radius)))) || 
+    (planet_parameters && all(Tuple(p === nothing for p in (f₀, β)))) ||
+        throw(ArgumentError("Either both keywords f₀ and β must be specified, 
+                            *or* all of rotation_rate, latitude, and radius."))
 
     if planet_parameters
         f₀ = 2rotation_rate * sind(latitude)
@@ -93,9 +95,9 @@ function BetaPlane(T=Float64; f₀=nothing, β=nothing,
 end
 
 @inline x_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =
-    @inbounds (coriolis.f₀ + coriolis.β * grid.yC[j]) * ▶xy_fca(i, j, k, grid, v)
+    @inbounds (coriolis.f₀ + coriolis.β * grid.yC[j]) * ▶xy_fca(i, j, k, grid, U.v)
 
 @inline y_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =
-    @inbounds (coriolis.f₀ + coriolis.β * grid.yF[j]) * ▶xy_cfa(i, j, k, grid, v) 
+    @inbounds (coriolis.f₀ + coriolis.β * grid.yF[j]) * ▶xy_cfa(i, j, k, grid, U.v) 
 
 @inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::BetaPlane, U) where T = zero(T)

From 383e103a19e3f25806b8310d2cf271db33158d9c Mon Sep 17 00:00:00 2001
From: Gregory Wagner <wagner.greg@gmail.com>
Date: Mon, 21 Oct 2019 07:28:36 -0400
Subject: [PATCH 13/18] Adds test for time-stepping with beta plane coriolis

---
 test/test_time_stepping.jl | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/test/test_time_stepping.jl b/test/test_time_stepping.jl
index 05c284a1e2..5cfffb1098 100644
--- a/test/test_time_stepping.jl
+++ b/test/test_time_stepping.jl
@@ -5,6 +5,17 @@ function time_stepping_works(arch, FT, Closure)
     return true # test that no errors/crashes happen when time stepping.
 end
 
+function time_stepping_works_with_beta_plane(arch, FT)
+    model = Model(
+                    float_type = FT,
+                  architecture = arch,
+                          grid = RegularCartesianGrid(FT, (16, 16, 16), (1, 2, 3)),
+                      coriolis = BetaPlane(FT, f₀=1e-4, β=1e-11)
+                 )
+    time_step!(model, 1, 1)
+    return true # test that no errors/crashes happen when time stepping.
+end
+
 function run_first_AB2_time_step_tests(arch, FT)
     add_ones(args...) = 1.0
     model = BasicModel(N=(16, 16, 16), L=(1, 2, 3), architecture=arch, float_type=FT,
@@ -151,6 +162,10 @@ Closures = (ConstantIsotropicDiffusivity, ConstantAnisotropicDiffusivity,
         @test time_stepping_works(arch, FT, Closure)
     end
 
+    for arch in archs, FT in float_types
+        @test time_stepping_works_with_beta_plane(arch, FT)
+    end
+
     @testset "2nd-order Adams-Bashforth" begin
         println("  Testing 2nd-order Adams-Bashforth...")
         for arch in archs, FT in float_types

From de5764b9810dfd1a178cb3c4f04286891890092b Mon Sep 17 00:00:00 2001
From: Gregory Wagner <wagner.greg@gmail.com>
Date: Mon, 21 Oct 2019 07:30:28 -0400
Subject: [PATCH 14/18] Another bug fix in beta plane coriolis implementation

---
 src/coriolis.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index f1bdc437a8..cb0471921f 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -95,9 +95,9 @@ function BetaPlane(T=Float64; f₀=nothing, β=nothing,
 end
 
 @inline x_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =
-    @inbounds (coriolis.f₀ + coriolis.β * grid.yC[j]) * ▶xy_fca(i, j, k, grid, U.v)
+    @inbounds - (coriolis.f₀ + coriolis.β * grid.yC[j]) * ▶xy_fca(i, j, k, grid, U.v)
 
 @inline y_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =
-    @inbounds (coriolis.f₀ + coriolis.β * grid.yF[j]) * ▶xy_cfa(i, j, k, grid, U.v) 
+    @inbounds   (coriolis.f₀ + coriolis.β * grid.yF[j]) * ▶xy_cfa(i, j, k, grid, U.u) 
 
 @inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::BetaPlane, U) where T = zero(T)

From efa43fcdaa122435f5203002d7a0e52afc18c48c Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Mon, 21 Oct 2019 13:21:14 -0400
Subject: [PATCH 15/18] Few minor changes

---
 src/coriolis.jl | 64 ++++++++++++++++++++++++-------------------------
 1 file changed, 32 insertions(+), 32 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index cbad4f6684..b0ad28df9e 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -2,9 +2,9 @@
 ##### Functions for non-rotating models
 #####
 
-@inline x_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::Nothing, U) where T = zero(T)
-@inline y_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::Nothing, U) where T = zero(T)
-@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::Nothing, U) where T = zero(T)
+@inline x_f_cross_U(i, j, k, grid::AbstractGrid{FT}, ::Nothing, U) where FT = zero(FT)
+@inline y_f_cross_U(i, j, k, grid::AbstractGrid{FT}, ::Nothing, U) where FT = zero(FT)
+@inline z_f_cross_U(i, j, k, grid::AbstractGrid{FT}, ::Nothing, U) where FT = zero(FT)
 
 #####
 ##### The 'FPlane' approximation. This is equivalent to a model with a constant
@@ -12,16 +12,16 @@
 #####
 
 """
-    FPlane{T} <: AbstractRotation
+    FPlane{FT} <: AbstractRotation
 
 A parameter object for constant rotation around a vertical axis.
 """
-struct FPlane{T} <: AbstractRotation
-    f :: T
+struct FPlane{FT} <: AbstractRotation
+    f :: FT
 end
 
 """
-    FPlane([T=Float64;] f)
+    FPlane([FT=Float64;] f)
 
 Returns a parameter object for constant rotation at the angular frequency
 `f/2`, and therefore with background vorticity `f`, around a vertical axis.
@@ -29,12 +29,12 @@ Returns a parameter object for constant rotation at the angular frequency
 Also called `FPlane`, after the "f-plane" approximation for the local effect of
 Earth's rotation in a planar coordinate system tangent to the Earth's surface.
 """
-function FPlane(T::DataType=Float64; f)
-    return FPlane{T}(f)
+function FPlane(FT=Float64; f)
+    return FPlane{FT}(f)
 end
 
 """
-    FPlane([T=Float64;] Ω, latitude)
+    FPlane([FT=Float64;] Ω, latitude)
 
 Returns a parameter object for constant rotation at the angular frequency
 `Ωsin(latitude), and therefore with background vorticity `f = 2Ωsin(latitude),
@@ -43,58 +43,58 @@ around a vertical axis.
 Also called `FPlane`, after the "f-plane" approximation for the local effect of
 Earth's rotation in a planar coordinate system tangent to the Earth's surface.
 """
-function FPlane(T=Float64; Ω, latitude)
-    return FPlane{T}(2*Ω*sind(latitude))
+function FPlane(FT=Float64; Ω, latitude)
+    return FPlane{FT}(2*Ω*sind(latitude))
 end
 
 
 """
-    BetaPlane{T} <: AbstractRotation
+    BetaPlane{FT} <: AbstractRotation
 
 A parameter object for meridionally increasing Coriolis
 parameter (`f = f₀ + βy`).
 """
-struct BetaPlane{T} <: AbstractRotation
-    f₀ :: T
-    β  :: T
+struct BetaPlane{FT} <: AbstractRotation
+    f₀ :: FT
+    β  :: FT
 end
 
 """
-    BetaPlane([T=Float64;] f₀, β)
+    BetaPlane([FT=Float64;] f₀, β)
 
 A parameter object for meridionally increasing Coriolis
 parameter (`f = f₀ + βy`).
 """
-function BetaPlane(T=Float64; f₀, β)
-    return BetaPlane{T}(f₀, β)
+function BetaPlane(FT=Float64; f₀, β)
+    return BetaPlane{FT}(f₀, β)
 end
 
 """
-    BetaPlane([T=Float64;] Ω, latitude, R)
+    BetaPlane([FT=Float64;] Ω, latitude, R)
 
 Returns a parameter object for meridionally increasing rotation at the
 angular frequency `Ωsin(latitude), and therefore with Coriolis parameter
  `f₀ = 2Ωsin(latitude), around a vertical axis.
 The Coriolis parameter increases meridionally as `f = f₀ + βy`, where
-`β = 2Ωcos(latitude)/R`.
+`β = 2Ωcos(latitude)/R`, and `R` is the radius of the planet.
 """
-function BetaPlane(T=Float64; Ω, latitude, R)
+function BetaPlane(FT=Float64; Ω, latitude, R)
     f₀ = 2*Ω*sind(latitude)
     β = 2*Ω*cosd(latitude)/R
-    return BetaPlane{T}(f₀, β)
+    return BetaPlane{FT}(f₀, β)
 end
 
-@inline fv(i, j, k, grid::RegularCartesianGrid{T}, f, v) where T =
-    T(0.5) * f * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
+@inline fv(i, j, k, grid::RegularCartesianGrid{FT}, f, v) where FT =
+    FT(0.5) * f * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
 
-@inline fu(i, j, k, grid::RegularCartesianGrid{T}, f, u) where T =
-    T(0.5) * f * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
+@inline fu(i, j, k, grid::RegularCartesianGrid{FT}, f, u) where FT =
+    FT(0.5) * f * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
-@inbounds @inline fv(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, v) where T =
-     T(0.5) * (f₀ + β * grid.yC[j]) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
+@inbounds @inline fv(i, j, k, grid::RegularCartesianGrid{FT}, f₀, β, v) where FT =
+     FT(0.5) * (f₀ + β * grid.yC[j]) * (avgy_f2c(grid, v, i-1,  j, k) + avgy_f2c(grid, v, i, j, k))
 
-@inbounds @inline fu(i, j, k, grid::RegularCartesianGrid{T}, f₀, β, u) where T =
-     T(0.5) * (f₀ + β * grid.yF[j]) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
+@inbounds @inline fu(i, j, k, grid::RegularCartesianGrid{FT}, f₀, β, u) where FT =
+     FT(0.5) * (f₀ + β * grid.yF[j]) * (avgx_f2c(grid, u, i,  j-1, k) + avgx_f2c(grid, u, i, j, k))
 
 @inline x_f_cross_U(i, j, k, grid, rotation::FPlane, U) = -fv(i, j, k, grid, rotation.f, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::FPlane, U) =  fu(i, j, k, grid, rotation.f, U.u)
@@ -102,4 +102,4 @@ end
 @inline x_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) = -fv(i, j, k, grid, rotation.f₀, rotation.β, U.v)
 @inline y_f_cross_U(i, j, k, grid, rotation::BetaPlane, U) =  fu(i, j, k, grid, rotation.f₀, rotation.β, U.u)
 
-@inline z_f_cross_U(i, j, k, grid::AbstractGrid{T}, ::Union{FPlane, BetaPlane}, U) where T = zero(T)
+@inline z_f_cross_U(i, j, k, grid::AbstractGrid{FT}, ::Union{FPlane, BetaPlane}, U) where FT = zero(FT)

From 282db77b1298615b88e9efbc7c694efc354c4f06 Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Wed, 23 Oct 2019 12:09:20 -0400
Subject: [PATCH 16/18] Fixes tests

---
 src/coriolis.jl            | 2 +-
 test/test_time_stepping.jl | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 48621bbdcd..0d20139b23 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -35,7 +35,7 @@ Earth's rotation in a planar coordinate system tangent to the Earth's surface.
 """
 function FPlane(FT=Float64; f=nothing, rotation_rate=nothing, latitude=nothing)
 
-    if f==nothing && rotation_rate != nothing && latitude != nothing
+    if f == nothing && rotation_rate != nothing && latitude != nothing
         return FPlane{FT}(2rotation_rate*sind(latitude))
     elseif f != nothing && rotation_rate == nothing && latitude == nothing
         return FPlane{FT}(f)
diff --git a/test/test_time_stepping.jl b/test/test_time_stepping.jl
index e5be62c9c3..906c9031ec 100644
--- a/test/test_time_stepping.jl
+++ b/test/test_time_stepping.jl
@@ -9,7 +9,7 @@ function time_stepping_works_with_beta_plane(arch, FT)
     model = Model(
                     float_type = FT,
                   architecture = arch,
-                          grid = RegularCartesianGrid(FT, (16, 16, 16), (1, 2, 3)),
+                          grid = RegularCartesianGrid(FT, size=(16, 16, 16), length=(1, 2, 3)),
                       coriolis = BetaPlane(FT, f₀=1e-4, β=1e-11)
                  )
     time_step!(model, 1, 1)

From d84656aa04849ee2d1b87f0c7ab9650ffc88965e Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Wed, 23 Oct 2019 13:48:40 -0400
Subject: [PATCH 17/18] Adds more tests

---
 test/test_coriolis.jl | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/test/test_coriolis.jl b/test/test_coriolis.jl
index b4b35a3cc3..9c52138873 100644
--- a/test/test_coriolis.jl
+++ b/test/test_coriolis.jl
@@ -4,8 +4,8 @@ function instantiate_fplane_1(T)
 end
 
 function instantiate_fplane_2(T)
-    coriolis = FPlane(T, rotation_rate=7.29e-5, latitude=45)
-    return coriolis.f == T(2rotation_rate*sind(latitude))
+    coriolis = FPlane(T, rotation_rate=2, latitude=30)
+    return coriolis.f == T(2)
 end
 
 function instantiate_betaplane_1(T)
@@ -24,9 +24,12 @@ end
     @testset "Coriolis" begin
         for T in float_types
             @test instantiate_fplane_1(T)
+            @test instantiate_fplane_2(T)
             @test instantiate_betaplane_1(T)
             @test instantiate_betaplane_2(T)
             # Test that FPlane throws an ArgumentError
+            @test_throws ArgumentError FPlane(T, rotation_rate=7e-5)
+            @test_throws ArgumentError FPlane(T, latitude=40)
             @test_throws ArgumentError FPlane(T, f=1, rotation_rate=7e-5)
             @test_throws ArgumentError FPlane(T, f=1, latitude=40)
             @test_throws ArgumentError FPlane(T, f=1, rotation_rate=7e-5, latitude=40)

From eecb2976edb2517e8392cb6e8705c0b5f55f0819 Mon Sep 17 00:00:00 2001
From: suyashbire1 <suyash309@gmail.com>
Date: Wed, 23 Oct 2019 13:49:47 -0400
Subject: [PATCH 18/18] Eliminates whitespace

---
 src/coriolis.jl | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/src/coriolis.jl b/src/coriolis.jl
index 0d20139b23..c14aa88b1c 100644
--- a/src/coriolis.jl
+++ b/src/coriolis.jl
@@ -47,10 +47,9 @@ function FPlane(FT=Float64; f=nothing, rotation_rate=nothing, latitude=nothing)
 end
 
 @inline x_f_cross_U(i, j, k, grid, coriolis::FPlane, U) = - coriolis.f * ▶xy_fca(i, j, k, grid, U.v)
-
 @inline y_f_cross_U(i, j, k, grid, coriolis::FPlane, U) =   coriolis.f * ▶xy_cfa(i, j, k, grid, U.u)
-
 @inline z_f_cross_U(i, j, k, grid::AbstractGrid{FT}, coriolis::FPlane, U) where FT = zero(FT)
+
 #####
 ##### The Beta Plane
 #####
@@ -95,8 +94,6 @@ function BetaPlane(T=Float64; f₀=nothing, β=nothing,
     return BetaPlane{T}(f₀, β)
 end
 
-
-
 @inline x_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =
     @inbounds - (coriolis.f₀ + coriolis.β * grid.yC[j]) * ▶xy_fca(i, j, k, grid, U.v)
 @inline y_f_cross_U(i, j, k, grid, coriolis::BetaPlane, U) =