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!

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

Plan-of-Attack Methods - dissipation/mixing estimation Along- and across-channel comparisons Consistency check: Observed dissipation vs Expected? Dynamical explanation for weak mixing H 0 : Mixing during our study was spatially uniform test: Compute buoyancy flux at many locations in along- and across-channel surveys

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

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

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

Richardson Number, Ri = N 2 /Shear 2 Ri crit = 0.25 Transect #1 FLOOD! Transect #2 weak ebb Transect #3 weak flood

Buoyancy Flux, B = N 2 K  Transect #1 FLOOD! Transect #2 weak ebb Transect #3 weak flood

Along-Channel Variability? W/kg

Across-Channel Variability? W/kg

Consistency Check: Tidal Dissipation Dissipation mean (away from bed) over entire study was 6.4 x W/m 3 Hudson has mid-water column values of (spring) to W/m 3 (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  overturns +  loglayer = = 124 MW –assumed log layer dissipation (  ~ U * 3 ) –quad drag law: C D = for velocity at 5-10m height This is reasonable, as our tidal range was ~3/4 the mean, U ~ range,  ~ U 3, and (3/4) 3 = 0.4

Why Weak Mixing in Most Places? Results suggest low mixing because tidal straining is overcoming mixing horizontal Richardson (Stacey) number, Ri x ebbEBB

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!

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

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]