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

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

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...

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

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

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

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) e e e flood/ebb in phasevs out of phase high/low

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)

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

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)

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

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 !)

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 ?

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 :

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

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

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...