 Dilute frazil polynya similarity solution

ID: dilute-frazil-polynya-similarity-solution

In a uniformly wind-forced polynya with normalized heat loss

f

, let

H = L + c_{p} m C_{\infty}

K = f / H

J = 3 S / (4 ρ)

and

r = ρ - ρ_{s}

. The dilute equilibrium model gives

b u^{2} = J x

ϕ b u = K x

and

r g ϕ b b^{'} = S /4

. Hence

u = (r g K x / ρ)^{1/3}

b = J x / u^{2}

and

ϕ = (K / J) u

. This similarity solution is valid only while the frazil ice volume fraction is small and no exported crystal flux has been neglected improperly.

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