Turbulent Mixing During an Admiralty Inlet Bottom Water Intrusion

1. Turbulent Mixing During an Admiralty Inlet Bottom Water Intrusion Philip Orton Hats off to the A-Team: Sally, Erin, Karin and Christie! Profs extraordinaire: Rocky and Parker!

2. Motivation - Why Study Mixing/ Dissipation Echo Sounder Backscatter, 120 kHz, 04-Aug-2006, 11:28h sorted profile raw profile sigma-t (kg m-3) • Power/ importance • Difficulty for modeling

3. Plan-of-Attack H0: Mixing during our study was spatially uniform test: Compute buoyancy flux at many locations in along- and across-channel surveys • Methods - dissipation/mixing estimation • Along- and across-channel comparisons • Consistency check: Observed dissipation vs Expected? • Dynamical explanation for weak mixing

4. Field Program 300kHz ADCP Seabird 19 CTD Echo Sounder Full transect Two half-transects Cross-channel survey Bush Point 8W 8

5. Fine-Structure Instability Turbulence Analysis Matlab mixing toolbox for CTD fine-structure and Lowered-ADCP A “Thorpe scale” analysis of ~138 CTD density profiles The Thorpe scale (LT) is the rms re-sorting distance of all points in an overturning “patch”. sorted profile raw profile Method gives comparable results to microstructure instrumentation (e.g. Klymak and Gregg, JPO 34:1135, 2004).

6. Mixing & Dissipation from Thorpe Scales Assume: (a) LO = LT, (b) LO is length-scale for TKE, (c) N is time-scale for dissipation. Dissipation of turbulent kinetic energy: Station 16, 8/4 15:17h, slack after greater flood where a ≈ 1 (Klymak and Gregg; Peters and Johns, 2004) eddy diffusivity: buoyancy frequency, N = [(g/r)(dr/dz)]0.5, is computed over overturn patch heights. We assume a mixing efficiency, G ≈ 0.22, reasonable for stratified conditions (discussion in Macdonald and Geyer, JGR 109: C05004, 2004).

7. Richardson Number, Ri = N2/Shear2 Ricrit= 0.25 Transect #1 FLOOD! Transect #2 weak ebb Transect #3 weak flood

8. Buoyancy Flux, B = N2Kr Transect #1 FLOOD! Transect #2 weak ebb Transect #3 weak flood

9. Along-Channel Variability? W/kg

10. Across-Channel Variability? W/kg

11. Consistency Check: Tidal Dissipation • Dissipation mean (away from bed) over entire study was 6.4 x 10-4 W/m3 • Hudson has mid-water column values of 10-2 (spring) to 10-3 W/m3 (neap; Peters, 1999) • NOAA study (Lavelle et al., 1988) showed total tidal dissipation averages ~500 MW • I estimate the total dissipation during our study as eoverturns + eloglayer = 12 + 112 = 124 MW • assumed log layer dissipation (e ~ U*3) • quad drag law: CD = 0.002 for velocity at 5-10m height • This is reasonable, as our tidal range was ~3/4 the mean, U ~ range, e ~ U3, and (3/4)3 = 0.4

12. Why Weak Mixing in Most Places? horizontal Richardson (Stacey) number, Rix ebb EBB Results suggest low mixing because tidal straining is overcoming mixing

13. Summary • Was mixing during our study spatially uniform? • Cross-channel variability: results were inconclusive • Along-channel variability: No -- mixing was elevated by a factor of O(10) in at least one hotspot • Tidal dissipation estimates were consistent with a prior study, downscaled for below avg. tidal range • Tidal straining can explain the low mixing that occurred in most of the estuary • Excellent conditions for a bottom water intrusion!

17. Overturn Analysis: Quality Control To avoid mistaking noise for overturns, each “resorting region” must pass various tests: 1) the rms Dr (st,sort - st,raw) in a patch must be greater than the instrument noise (r = 0.002 kg m-3) 2) the T-S space tests of Galbraith and Kelley (J-Tech, 13:688, 1996) a) near-linearity in the T-r relationship b) near-linearity in the S-r relationship 3) rms run-length of overturn patch must be longer than 7 points total

18. Ambient Conditions • Tides - end of a ~5 day period of weaker than normal tidal currents • Semidiurnal tidal range near annual low • Diurnal tidal range on the rise, but below average • Winds light • Riverflow into Puget Sound - [likely had an above average summertime flow]