The baroclinity of a fluid with density ρ(x, y, z) is given by 1 ρ 2 (∇ρ × ∇p). It measures the misalignment between level surfaces of the density and pressure fields. Show that if λ(x, y, z) = f(ρ(x, y, z), p(x, y, z)) for some function f, then 1 ρ 3 ∇λ · (∇ρ × ∇p) = 0.