Retraction Note: A Complete Formula of Ocean Surface Absolute Geostrophic Current

Editor's Note: this Article has been retracted; the Retraction Note is available at https://doi.org/10.1038/s41598-021-86517-3.

The influence of a geostrophic current on the internal tide generation

<p>We investigate the influence of a barotropic geostrophic current on<br>internal tide (IT) generation over a shelf slope.<br>The current $V_g(x)$ is modeled as an idealized Gaussian function centered at<br>$x_0$ with width $x_r$ and maximum velocity $V_{max}$.<br>The bathymetry is modelled as a linear slope with smoothed corners.<br>We calculate the total barotropic-to-baroclinic energy conversion $C =<br>\int \overbar{C} \,dx = \int \int \rho' g W \,dx\, dz$. <br>$\overbar{C}(x,t)$ can be either positive or negative. Positive (negative) conversion means energy is<br>converted from barotropic to baroclinic (baroclinic to barotropic)<br>waves. <br>The main conclusions are: 1) $V_g(x)$ changes the effective<br>frequency $f_{eff}$. This has a direct impact on the slope of the IT<br>characteristics and the slope criticality, which affects the total<br>conversion rate;<br>2) Since $(V_g)_x$ is not a constant value, $f_{eff}$ varies along the<br>slope. This has a significant effect on the IT beam generation<br>location and its propagation path. If the current is strong enough so<br>that $f_{eff}$ is greater than the barotropic tidal frequency $\sigma_T$, a blocking<br>region is formed where the conversion vanishes and IT propagation is blocked;<br>3) Changes of sign in $\bar{C}(x,t)$ correspond to the locations where<br>IT beams reflect from the boundaries. As a result, the total conversion rate $C$ is<br>also strongly affected by the IT beam pattern.<br>In conclusion, the total conversion rate $C$ is affected by a<br>combination of three factors: slope criticality, size and location of the blocking<br>region and the IT beam patterm, all of which can be varied by changing<br>the strength, width and location of the geostrophic current $V_g(x)$.</p>

Estimation of geostrophic current in the Red Sea based on sea level anomalies derived from extended satellite altimetry data

Geostrophic current data near the coast of the Red Sea have large gaps. Hence, the sea level anomaly (SLA) data from Jason-2 have been reprocessed and extended towards the coast of the Red Sea and merged with AVISO data at the offshore region. This processing has been applied to build a gridded dataset to achieve the best results for the SLA and geostrophic current. The results obtained from the new extended data at the coast are more consistent with the observed data (conductivity–temperature–depth, CTD) and hence geostrophic current calculation. The patterns of SLA distribution and geostrophic currents are divided into two seasons: winter (October–May) and summer (June–September). The geostrophic currents in summer are flowing southward over the Red Sea except for narrow northward flow along the east coast. In winter, currents flow to the north for the entire Red Sea except for a small southward flow near the central eastern and western coast. This flow is modified by the presence of cyclonic and anticyclonic eddies, which are more concentrated in the central and northern Red Sea. The results show anticyclonic eddies (AEs) on the eastern side of the Red Sea and cyclonic eddies (CEs) on the western side during winter. In summer, cyclonic eddies are more dominant for the entire Red Sea. The result shows a change in some eddies from anticyclonic during winter to cyclonic during summer in the north between 26.3 and 27.5∘ N. Furthermore, the life span of cyclonic eddies is longer than that of anticyclonic eddies.