1. ISLAND WAKES GENERATED BY AN ELLIPTICAL TIDAL FLOW Philippe Estrade Jason Middleton University of New South Wales

2. Outline ➢ introduction ➢ model set-up ➢ some 2D results ➢ some 3D results ➢ concluding remarks

3. Introduction Wake flows often govern near shore environmental processes (sediments, nutrients, pollutants,...) Wakes generated by constant upstream flows are well documented however oceanic flows are unsteady and non-uniform (topography, tidal currents, forcing variability,...) Transient wake generated by unidirectional tidal flow have been addressed for headland (Signell & Geyer, 1991) & inner shelf island (Rattray island) but not for mid & outer shelf island for which the tidal flow is not polarized Impact of an elliptical tidal current on island wake structure ? ROMS has been used in idealized configurations to address this question...

4. Dynamical context : “isolated outer shelf island in shallow water” (e.g. Great Barrier Reef) : homogeneous fluid flowing around a topographic obstacle both in 2D & 3D 3D : 2D : also barotropic mode in 3D

5. Dynamical preconditioning : Topography : (circular island with or without surrounding bathymetry) + additional eddy viscosity within sponge layers (600 m wide - up to 10 m ² /s at open boundaries) 3D : cyl gauss

6. Forcing and boundary conditions : all boundaries are open with : 2D & 3D : FS_CHAPMAN & M2_FLATHER ( η,u,v specified analytically) 3D : M3_RADIATION & T_RADIATION (u,v,w,T not specified) η v u given by basic [2D – flat bottom – linear – inviscid] theory : solution can be written as a linear combination of inertia gravity waves (igw) : where are input parameters for each tidal component of interest wave number(s) given by the dispersion relation : η u η v η u η v

7. Elliptical tidal forcing : Study limited to 1 component : meridional (k x =0, k=k y ) & semi-diurnal wave (period T=12h) ==> 2 cases : Progressive wave :Standing wave single wave (k)incident (k) + reflected wave (-k) similar elliptical forcing can be found with adequate choice of y sw & t sw η 0 (m)latitude (°N) e10.515 e20.45530 e30.26560 flood/ebb in phasevs out of phase high/low

8. a “control” run : 2D / flat bottom (no island) / e1grid : 200*300 ; res=50 m ; dt=1s “error” < 5% except :when t/T ~ n+1/4 or n+3/4( η & v ~ 0 ) when t/T ~ n or n +1/2( u ~ 0 ) the numerical solution propagates almost like the linear igw (used to force the model at the 4 open boundaries) despite non-linearity (advection, bottom friction)

9. 12 experiments : Spin-up : (insignificant difference between 2D/3D & cyl/gauss) grid : 2Dcyle1400*450 / /e2450*550 3Dgausse3600*600 2D & 3D :horizontal resolution 50 mbarotropic mode 1 s 3D : baroclinic mode 48 s20 σ levels initial conditions : from rest

10. some 2D results (vorticity & circulation) : thin ellipse (e1 & e2) : transient 2 eddies structures during flood & ebb phases & dissipation in between (stronger activity with varying bottom topography) large ellipse : vorticity filaments continuously progressing (weak sensitivity to topography)

11. about the free surface elevation (2d/gauss/e1) : : η-η pw : residual : Larger negative “anomalies” in the flow separation regions leads to residual depression along minor axis despite residual flow convergence

12. residual circulation and vorticity (2D & 3D) : the tidal current rotation favors the development of the eddy rotating in the same direction and weakens the development of the second eddy no qualitative difference in η, u, v between 2D & 3D modelling (for this particular range of parameters !)

13. some 3D results (vertical velocity) : z = -H/2 Upwellings are : stronger with a varying topography weaker with larger ellipse Which mechanisms drive these vertical motions ?

14. Secondary circulation & vertical motions : Alaee et al (2004) :flow curvature can generate significant vertical motions by convergence/divergence of the secondary circulation (u’,v’) t/T=5.1 3D/gauss/e1 vertically integrating the continuity equation from the bottom (or from the surface) to depth z and then replacing (u,v) by (u’,v’) + (u,v) gives w = w p + w s :

15. Example vertical velocity decomposition : t/T = 5.1 z = -3/4.H Vertical motions mainly stem from : flow curvature (i.e convergence/divergence of the secondary circulation) for a cylindrical island Combination of w p & w s for a varying topography

16. Residual vertical velocities : z = -3/4.H 3D/gauss/e1 & e2 : wide & strong residual upwelling along the major axis consistent feature ?

17. Concluding remarks : ➢ further sensitivity studies needed to identify wake regimes vs relevant dimensionless numbers (h0/[Cd.R], V0/[ω.R], ω/f, others ?) ➢ similar tidal forcing method can be applied for headland or innershelf island wake studies (Kelvin waves propagating along a closed boundary) but limited to idealized configurations as well (flat bottom near open boundaries) ➢ study motivated by transient wake observations around LEI (Lady Elliot Island – Great Barrier Reef) ➢ current studies : adding missing LEI ingredients (stratification, buoyancy flux, wetting & drying, wind, neap/spring M2 & S2,...) and applying GST tools ➢ heading for realistic modelling of LEI...