# Erratum to: Gravity currents in two-layer stratified media

Abstract: This brief communication corrects a minor error in the presentation of the model results described in §2 of Tan et al. [1] (referred to hereafter as T.al.). Previously, we predicted that the solution of Eqs. 2.10 and 2.11 becomes unphysical for g′ 12/g′ 02 ≥ 3/4 irrespective of h′1. Upon closer inspection, we observe that model breakdown occurs at g′ 12/g′ 02 = 3/4 when h′1 0.50 but extends beyond this value when h′1 0.50. This is illustrated in Fig. 2a which shows the surface plot of Fr vs. g′ 12/g′ 02 and h′1 and is identical to Fig. 3a of T. al. with the exception of the aforementioned correction. In like fashion, Figs. 1, 2, 3 and 4 are, respectively, the corrected versions of Figs. 2, 3, 4 and 5 from T. al. (Note, that the geometric variables h′1, h1, h′2 and h2 used here have been non-dimensionalized by H , the channel depth.) As these new figures make clear, the region of parameter space where the model is valid and, by extension, where the gravity current is predicted to be supercritical, is larger than described in the original manuscript. Notwithstanding this correction, the principal conclusions of T. al. remain unchanged. In addition to calculating head loss along streamlines as we do with Eqs. 2.14 and 2.15 of T. al., one can also evaluate the global dissipation by determining the change of D = ∫ u(p + 1 2ρu + ρgz) dz from far upstream to far downstream. The expression for D, written in non-dimensional form reads

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### "Erratum to: Gravity currents in two..." refers background in this paper

...Broken lines for large h′1 and g′ 12/g′ 02 indicate model breakdown [2]....

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### Additional excerpts

...The expression for D, written in non-dimensional form reads D = Fr [ g′ 12 g′ 02 (h′2h1 − h′1h′2) + g′ 01 g′ 02 h′1h0 + h′2h0 − 1 2 Fr2 ( h′3 1 h(2)1 + h ′3 2 h(2)2 )] (1) The online version of the original article can be found under doi:10....

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