The self-similar stratified inner-shelf response to transient rip-current-induced mixing. (19th March 2021) - Grimes, Derek J.; Feddersen, Falk
Abstract: Abstract : The stratified inner-shelf response to surf-zone-generated transient rip currents (TRC) is examined using idealized simulations with uniform initial thermal stratification $\mathrm {d}{T_0}/\mathrm {d}{z}$, with initial temperature T 0 and vertical coordinate z, or initial squared buoyancy frequency $N_0^2$, varying from unstratified to highly stratified ( $0.75^\circ \text {C}\ \text {m}^{-1}$ ). The TRC-induced depth-integrated cross-shore eddy kinetic energy flux is independent of $\mathrm {d}{T_0}/\mathrm {d}{z}$ and decays to near zero within $4L_{SZ}$ (surf-zone width $L_{SZ}=100$ m). Cross-shore inhomogeneous TRC mixing causes shoreward broadening isotherms, driving a near-field inner-shelf overturning circulation and a far-field geostrophic along-shore velocity that strengthen with $\mathrm {d}{T_0}/\mathrm {d}{z}$ . TRC mixing mostly (90 %) increases background potential energy (BPE) and also available (APE, 10 %) potential energy, driving inner-shelf mean circulation. The specific BPE zero-crossing depth $d_{s}$ collapses the near-field $3$ -layer cross-shore velocity, using an intrusive gravity current scaling $(d_{s} N_0)$ . The approximately steady exchange flow exports low-stratification fluid ( $N/N_0\approx 1/2$ ) at a depth $z/d_{s}\approx -1$, re-supplying the TRC region with stratified fluid from above/below, similar to localized mixing laboratory experiments. Offshore of $\approx 5L_{SZ}$, a self-similar far-field intrusion with characteristic isotherm slope $d_{s}/L_{R}$ (Rossby deformation radius $L_{R}\sim d_{s} f/N_0$ ) is in approximate geostrophic balance with the non-dimensional along-shore velocity. Inner-shelf near-field and far-field horizontal length scales vary as $x/d_{s}$ and $x/L_{R}$, respectively. The length scale $d_{s}$ is related to the work performed by TRC mixing using an idealized well-mixed wedge geometry. Idealized analytical scalings are qualitatively consistent with modelled BPE and APE distributions. Thus, the self-similar stratified inner-shelf response to TRC-driven mixing depends on key dimensional parameters $N_0$ and $d_{s}$ .