Wave intensity within a floating ice sheet of arbitrary plan form in the marginal ice zone

We derive theoretical results that show that the wave intensity in a floating ice sheet within the marginal ice zone (MIZ) can be related to the wave intensity in the surrounding open water by the ratio of wavenumbers in the ice-covered and open-water regions, independent of ice plan form geometry. Under the assumption of isotropic incident waves, we first derive a short-wavelength asymptotic (SWA) result valid for ice wavelength lamda Superscript upper I Baseline equals 2 pi divided by k Superscript upper I λ I = 2 π / k I $\lambda ^I=2\pi /k^I$ that is small compared with the ice sheet dimension script l ℓ $\ell$ . The SWA result shows that intensity is reduced in the ice sheet compared with open water due to total reflection over a range of incident angles. We then derive a more general result using the ice sheet Green function. Away from ice edges, the Green function for an ice sheet of arbitrary plan form can be locally approximated by that of an ice sheet of infinite extent. With this approximation, we obtain a more general result which recovers the SWA prediction for k Superscript upper I Baseline script l much greater than 1 k I ℓ ≫ 1 $k^I\ell \gg 1$ but is also valid when the flexural-gravity length scale script l Subscript upper D ℓ D $\ell _D$ is small compared with script l ℓ $\ell$ , regardless of k Superscript upper I Baseline script l k I ℓ $k^I\ell$ . We elucidate the range of validity of these theoretical results using direct computations of the deflection of an ice sheet in an isotropic, narrow-banded wave field. We find that the wave intensity in the bulk of the ice sheet matches the theoretical predictions when script l greater than or equivalent to 3 lamda Superscript upper I ℓ ≳ 3 λ I $\ell \gtrsim 3\lambda ^I$ ;