module Bickley

# The Bickley jet
Ψ(y, L) = - tanh(y) + 2y / L
U(y, L) = sech(y)^2 + 2 / L

# A sinusoidal tracer
C(y, L) = sin(2π * y / L)

# Slightly off-center vortical perturbations
ψ̃(x, y, ℓ, k) = exp(-(y + ℓ/10)^2 / 2ℓ^2) * cos(k * x) * cos(k * y)

# Vortical velocity fields (ũ, ṽ) = (-∂_y, +∂_x) ψ̃
ũ(x, y, ℓ, k) = + ψ̃(x, y, ℓ, k) * (k * tan(k * y) + y / ℓ^2) 
ṽ(x, y, ℓ, k) = - ψ̃(x, y, ℓ, k) * k * tan(k * x) 

end # module

