Hartmut Peters’ Projects: MIWE – M editerranean Outflow I nternal W ave E xperiment

1. Hartmut Peters’ Projects: • MIWE – Mediterranean Outflow Internal Wave Experiment • NSF (no funding left) • with Jonathan Nash, OSU, Josep Pelegrí, Barcelona, Spain • Development of a Two-Equation Turbulence Model for Mean Shear- and Internal Wave-Driven Mixing • ONR / ONR Global • with Helmut Baumert, IAMARIS, Hamburg, Germany • Common fluid dynamics underpinning: • Stratified flows support both turbulence and internal gravity waves.

2. Internal Waves and Hydraulics in the Med OutflowHartmut Peters Earth and Space Research, Seattle Jonathan Nash and Bill Smyth OSU “MIWE” - The Mediterranean Outflow Internal Waves Experiment PIs: Jonathan Nash (OSU), H.P. (ESR), Josep Pelegrí (Marine Sciences, Barcelona) Funded by NSF and Spanish agencies

4. Instrumentation • Two moorings, at and downstream of sill • Lowered ADCP / CTD in repeated • streamwise and spanwise transects, • tidal variations resolved, • u,v,T,S,r • turbulence from overturning scales. R/V García del Cid

5. Our (original) hypothesis [modified]: Internal wave-driven momentum fluxes are part of the outflow momentum balance. Flip the Equatorial Undercurrent upside-down→ the situations in overflows

6. Mean along-stream fluctuations: APE and e Downstream of sill: - Tenfold increase in available potential energy < N2z2 > - Hundredfold increase in turbulent dissipation rate - APE and e small above overflow

7. Downstream & upstreamvelocity and temperaturespectra Downstream has high-frequency peak with high variance in T and V at ~5-12 cph  N. Upstream has much less horizontal kinetic energy than downstream.

8. Vertical momentum flux We can estimate the contamination (i) of u’ and v’ due to w’ and instrument tilt and, (ii) at least in part, by mooring motion. (i) is demonstrated in the graph by the dashed lines for tilts of 0°-30°. (ii) O(10-20%)… Vertical momentum flux: - O(1 pa) upward – large! – - quantitatively uncertain - qualitatively robust

9. Development of a Two-Equation Turbulence Model for Mean Shear- and Internal Wave-Driven Mixing • -- Nothing to report (yet) – • Theory / modeling • Long-term collaboration, previous publications - series of closure models which build upon each other, few or no adjustable parameters, increasing explicit acknowledgment of internal waves • Adressing the “birth defect” of conventional turbulence closure: Reynolds decomposition into “mean” and turbulence. • Verification through direct 1:1 comparison with oceanic/estuarine turbulence observations

10. Current state: (A) Closure that can reproduce energetuc, shear-driven turbulence for Ri<1/4 well – but fails for weak turbulence at Ri>>1/4 in the pycnocline – where mixing presumably is driven by internal waves.

11. Current state: (B) We have a closure that accounts for the two limits of shear-driven mixing without internal waves and wave-driven mixing with zero mean shear. This model reproduces the wave-turbulence transition of D’Asaro and Lien. Our task: allow mean shear and waves simultaneously.