The Self-Similar Stratified Inner-Shelf Response To Transient Rip-Current-Induced Mixing

The stratified inner-shelf response to surf-zone-generated transient rip currents (TRC) is examined using idealized simulations with uniform initial thermal stratification dT(0)/dz, 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 degrees C m(-1)). The TRC-induced depth-integrated cross-shore eddy kinetic energy flux is independent of dT(0)/dz 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 dT(0)/dz. 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 approximate to 1/2) at a depth z/d(s) approximate to -1, re-supplying the TRC region with stratified fluid from above/below, similar to localized mixing laboratory experiments. Offshore of approximate to 5L(SZ), a self-similar far-field intrusion with characteristic isotherm slope d(s)/L-R (Rossby deformation radius L-R similar to 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).