Front. Mar. Sci. Frontiers in Marine Science Front. Mar. Sci. 2296-7745 Frontiers Media S.A. 10.3389/fmars.2024.1388621 Marine Science Correction Corrigendum: A seasonal undercurrent along the northwest coast of Australia Furue Ryo * Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokohama, Japan

Edited and Reviewed by: Zhiyu Liu, Xiamen University, China

*Correspondence: Ryo Furue, ryofurue@gmail.com

05 07 2024 2024 11 1388621 20 02 2024 27 02 2024 Copyright © 2024 Furue 2024 Furue

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 A Corrigendum on A seasonal undercurrent along the northwest coast of Australia by Furue R (2022) Front. Mar. Sci. 8:806659. doi: 10.3389/fmars.2021.806659 eddy-resolving oceanic general circulation model annual cycle North West Shelf eastern boundary coastal trapped waves section-in-acceptance Physical Oceanography

In the published article, there was an error. As described and discussed below, the analytic solutions (A5) and (A7) were incorrect and owing to the error some of the figures were also incorrect. The author apologizes for this error and states that this does not change the scientific conclusions of the article in any way. The original article has been updated.

Correction to equations (A5) and (A7)

Solution (A5) was previously:

ϕ j ( y , t ) = { − G o ( L / π ) [ cos  ( π y / L ) + 1 ]   e ı ( ω t − l j y )   0 < y < L − 2 G o ( L / π )  e ı ( ω t − l j y ) y < 0 ,

The corrected solution appears below:

ϕ j ( y , t ) = { − α G o α 2 − l j 2 [ − ı ( l j / α ) sin α y + cos α y + e − ı l j ( y − L ) ] e ı ω t 0 < y < L − α G o α 2 − l j 2 ( 1 + e ı l j L ) e − ı l j y e ı ω t y < 0 ,

To introduce the new symbol α used in the corrected solution above, the text preceding solution (A5) needs to be modified. It was previously:

τ y ( y , t ) = { G o sin ( π y / L ) e ı ω t     0 ≤ y ≤ L , 0     otherwise .

The corrected text appears below:

τ y ( y , t ) = { G o ( sin α y ) e ı ω t     0 ≤ y ≤ L , 0     otherwise ,

where α ≡ π / L .

As to solution (A7), the relevant text was previously:

and the solution (A5) is modified to

ϕ j ( y , t ) = { − G o ( L / π ) [ cos     ( π y / L ) + 1 ] e ı ( ω t − l j y ) + r ′ y 0 < y < L − 2 G o ( L / π ) e ı ( ω t − l j y ) + r ′ j y y < 0 ,

where r ′ j ≡ r j / c j .

The corrected text appears below:

and the solution is identical to (A5) except that −ılj of (A5) is replaced with −ılj + (rj/cj ) in the present solution.

This change does not affect the rest of the paper because equation number (A7) itself was not referred to anywhere and this was the last equation in the original paper.

 Corrected figures

Since the analytic solutions (A5) and (A7) are corrected as described above, all figures plotting the solutions are also corrected. They are Figures 12 , 13 , A1C , and S7. The corrected figures are all very similar to the original ones and some of them are hardly distinguishable from the original ones.

v from the CTW model (A) along the bottom, (B) at y = −14,000 km, and (C) averaged over x = 190–250 km at an arbitrary time for the annual frequency. The y-range for (C) is the southern-most 1,400 km of (A).

v from the CTW model averaged over x = 190–250 m (A) at y = −14,000 km and (B) at y = −7,000 km; and (C, D) at z = −170 m (A, C) for the annual frequency and (B, D) for the semi-annual frequency. The green line segments indicate speeds of 0.2m/s and 0.4m/s. Note that the latitudinal ranges are different between the annual (A, C) and semi-annual (B, D) frequencies because the beam emerges to the continental slope earlier for the semi-annual frequency. Note also that the range of coloring is narrower (±20 cm/s) here than in Figure 12 because the zonal average weakens the values.

(A) Mean Brunt-Väisälä frequency N(z) based on WOA13 and (B) vertical modes 1, 2, 3, and 100 (red, blue, green, and yellow). The dots on the j = 100 mode indicate the gridpoints for the numerical calculation of Equation (4). (C) Meridional velocity (snapshot at an arbitrary time and at x = 0, eastern boundary) of coastal Kelvin wave on an f plane forced by an annual wind. The velocity field is constructed as a sum of 100 modes [ j = 1–100 in formula (1). The total depth is 5,000 m; only the upper 300 m is shown. The green dashed curve is a WKB ray starting from the southern edge of the forcing region (y > 0). See text for details.

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