Vorticity Dynamics in Admiralty Inlet, Puget Sound

Transcription

1 in Admiralty Inlet, Puget Sound Texas A&M University June 9, 2013 Collaborators: Jim Riley and Mitsuhiro Kawase (UW)

2 Vorticity Impacts M C C A B E E T A L of drifter tracks from all 9 days od tide, and serves to highlight n the lee of the headland. South Africa the reduced momentum locities and accelerations were fferencing of the position data, d with a 10-min Hanning winive-induced noise. Because the mately follow horizontal water ns give the horizontal material vertical advective terms. Conmponents of Eq. (1), the only these accelerations are the Coess divergence (e.g., resulting re gradient (both internal and hneider et al. (1985) used an t data to show that the windch April 1983 at TTP was cone water column. They reported of 8 m s 1 with low-passly less than 5 m s 1, similar to Tacoma International Airport Because winds were relatively of our experiment and the - to 25-m depths, we assume ffects were small. radient forcing should also be es were shallow relative to the. A mean density profile from ng the experiment had a nearkg m 3 and a deep value of more highly stratified water during the March 2001 experi- 2004), where bottom-to-surface only 0.3 kg m 3. We might er baroclinic response at TTP indings of that study. To more ternal pressure gradient forcing erical model (discussed in sec- 2004) used the same model for urements of wave drag at TTP odel indicated relatively little ressure at 20-m depth in comht deformations (std only onesurface std), with internal presno clear organization. Internal ever, significant at 50-m depth at 100-m depth in the model. d in section 3d) were used to ective terms and indicated that elatively small at 20-m depth, FIG. 3. Panels of drifter tracks centered at three different times relative to the time of maximum flood t max. Lunar-hour-long tracks (1 lunar hour 12.42/12 h) are colored black, while shorter tracks are colored gray. Flood currents are directed from left to right, as indicated by the gray arrows. Times (from top to bottom) are (a) 2 lunar hours before maximum flood, (b) maximum flood, and (c) 2 lunar hours after maximum flood. Each panel represents a composite of data from 9 different days, with filled circles indicating the most recent drifter position. Bathymetry contours (gray) are every 50 m. From McCabe, MacCready, and Pawlak 2006 Eddy Jesse Allen/NASA. Terra - MODIS

3 Impacts on Tidal Current Turbines Pilot Site Admiralty Head Point Wilson Port Townsend Admiralty Bay Marrowstone Island Nodule Point Bush Point

4 Vorticity Measure of the local rotation rate of a fluid element ω = v, v = (u, v, w) Mainly vertical vorticity considered here: ω z = v x u y

5 Tidal, headland, vorticity background Unsteadiness increases boundary vorticity generation (Black and Gay 1987, Signell and Geyer 1991) In advection-dominated regime, vorticity injects into main flow from boundary where pressure gradient at wall changes sign and causes flow separation (Signell and Geyer 1991) Evidence of tilted baroclinic vortices, sloping due to generation off sloping ridge but maintained by tilting of isopycnals (Canals et al 2009) Horizontal density gradients can strongly influence behavior of eddies (Farmer et al 2002) What are the dominant effects in vorticity dynamics near Admiralty Head?

6 Vertical vorticity governing equation in ROMS Rate-of-change {}}{ ω z a t Reynolds stress generation Tilting/stretching ({}}{ = ωa ) Advection {}}{ [{}} ] { w (vωa) z + ( τ R ) ˆn z + Numerical viscosity generation [{}} ] { ( τ N ) ˆn z

7 Vorticity Attributes stretching contracting Vortex tubes can be stretched or contracted to conserve angular momentum increasing or decreasing the magnitude of the vorticity

8 Vorticity Attributes ω z ω Vertical to horizontal vorticity ω z ω ω x Horizontal to vertical vorticity z x ω x Vorticity can change orientation by tilting, exchanging vorticity between horizontal and vertical components

9 Realistic Model Domain Point Wilson Port Townsend Pilot Site Admiralty Head Admiralty Bay Marrowstone Island Nodule Point Bush Point Surface salinity of regional model D. Sutherland, J. Phys. Ocean, 2011 Bathymetry of nested model of Admiralty Inlet.

10 Realistic Model Domain Run in ROMS: hydrostatic, 3D, parallelized Horizontal resolution of 65 meters 20 vertical layers 2.6 million computational cells k-ɛ turbulence closure scheme Realistic boundary and initial conditions from regional model Quadratic bottom friction, no-slip sidewalls Point Wilson Port Townsend Pilot Site Admiralty Head Marrowstone Island Admiralty Bay Nodule Point Bush Point Bathymetry of nested model of Admiralty Inlet.

11 Free Surface data model 09/03/06 09/10/06 09/17/06 09/24/06 Free surface is low when M 2 tide is important Data from NOAA tide gauge station

12 Surface Vortex Google Earth Satellite Surface vorticity snapshot from simulation

13 Vortex in Depth: OTS Data Data from

14 Volume-integrated vorticity eqn terms for Admiralty Inlet Pilot Site Admiralty Head Point Wilson Port Townsend Admiralty Bay Marrowstone Island Nodule Point Bush Point d dt ( ωadv z = ω x w x ωa(v z ˆn)dS + o ) w + ωy dv + ω z w a y z dv K M u zz lds + ω bg o Dong, McWilliams, and Shchepetkin, 2007

15 Volume-integrated vorticity eqn terms for Admiralty Inlet free surface (m) 2 3 speed (m/s) Vorticity terms m 3 s d dt ( ωadv z = gen 1 tilting 2 stretching rate-of-change advection Hours into flood tide ω x w x ωa(v z ˆn)dS + o Dong, McWilliams, and Shchepetkin, 2007 ) w + ωy dv + ω z w a y z dv K M u zz lds + ω bg o

16 Vortex generation, shedding, and advection

17 Vortex generation, shedding, and advection

18 Vortex generation, shedding, and advection

19 Vortex generation, shedding, and advection

20 Vortex generation, shedding, and advection

21 Vortex generation, shedding, and advection

22 Volume-integrated vorticity eqn terms for Admiralty Inlet free surface (m) 2 3 speed (m/s) Vorticity terms m 3 s d dt ( ωadv z = gen 1 tilting 2 stretching rate-of-change advection Hours into flood tide ω x w x ωa(v z ˆn)dS + o ) w + ωy dv + ω z w a y z dv K M u zz lds + ω bg o

23 Vorticity stretching and tilting

24 Vorticity stretching and tilting

25 Vorticity stretching and tilting

26 Density behavior denser fresher

27 Density behavior Ebb tide brings fresher water northward

28 Density behavior Flood tide brings denser water south

29 Density behavior front

30 Vorticity stretching and tilting D. Farmer et al. / Dynamics of Atmospheres and Oceans 36 (2002) etch showing tidal flow of density ρ 1 past a headland with separation. A vertical shear layer or vo (A) separating Farmer, Pawlowicz, this flow and Jiang, from2002 water of density ρ 2 behind the headland. Instabilities evolve into otating columns of fluid. The vortices move downstream, but begin to tilt and stretch due to h adients across the front. The tilting converts horizontal to vertical motions; advective instabilit

31 Conclusions Volume-integrated analysis enables identification of dominant mechanisms in vertical vorticity Rate of vorticity generation due to boundary can be quantified Tilting and stretching of vorticity off headland tip may be related to a combination of headland shape/channel geometry, lee horizontal density gradient, and vertical velocity, as in Farmer et al.

32 Questions What is the main cause of the strong downwelling signal? What interplay between fields is seen on other flood tides, given the wide range of tidal and density behavior? What about on ebb tide? Density may not be as strongly horizontally stratified there. Upwelling vs. upsloping vertical velocity? Can the mixing be quantified?

33 Funding This work was done as part of the Northwest National Renewable Energy Center at the University of Washington Partial funding for this project was provided by the US Department of Energy. Additional support came from the PACCAR Professorship.

34 Front behavior is seen in satellite image Front at transition from flood to ebb tide Admiralty Head Front starting ebb tide Vorticity from flood tide Google Earth Marrowstone Island Satellite Snapshot from simulation

35 Upsloping vs. upwelling vertical velocity z x After Deleersnijder 1989

36 Upsloping vs. upwelling vertical velocity + w - w z x After Deleersnijder 1989

37 Vertical velocity due to convergence/divergence with bottom friction L. White, E. Wolanski / Estuarine, Coastal and Shelf Science 77 (2008) 457e (a) Top view Side view Diverging flow Surface water depletion replaced by upwelled water (b) Converging flow Downwelling of accumulated water near the surface (c) Onshore flow Downwelling of accumulated water near the surface + tilting of sea surface (adverse pressure gradient) (d) Eddy or island s tip Separation point Curved flow Balance breakdown near the bottom between pressure gradient and centrifugal acceleration followed by inward flow and upwelling Pressure Centrifugal gradient acceleration Fig. 6. Summary of mechanisms generating vertical motions in shallow-water flows interacting with topography. All vertical motions owe their existence to the prevalence of bottom friction. Both eddy and tip upwelling arise in curved flows (see panel D).

38 Signell and Geyer parameters Headland aspect ratio: α = b/a = 2km/1.5km = 4/3 Advection/friction: Re f d H C D a = 22 Advection/local acceleration: K C U 0 σa = 89

39 Depth (m) Depth (m) Depth (m) Depth (m) More flood transect Horizontal gradient stronger near surface due to sharp headland tip Vertical shear stronger near seabed Horizontal convergence leads to negative vertical velocity Bending of +ω and -ω due to varying horizontal gradient of w ω in 3D, follows shear profile Stretching and contracting of -ω due to varying vertical gradient of w Some horizontal baroclinic generation due to ρ gradient

40 Depth (m) Depth (m) Depth (m) Depth (m) Ebb transect Horizontal and vertical shear regions Horizontal convergence leads to negative vertical velocity -ω in 3D +ω z due to recirculation flow -ω z advected downstream from headland tip +ω in 3D Tilting aside from main flow Bending of -ω and + ω due to varying horizontal gradient of w Some other ω h due to shear and ρ gradient ω h due to shear midcolumn and at seabed along main flow and recirculation Stretching and contracting of -ω due to varying vertical gradient of w Some horizontal baroclinic generation Density gradient away from main vorticity

41 Horizontal momentum equations u t + v u fv = p x + ( ρ 0 z v t + v v + fu = p y ρ 0 + z ) u K M z ( ) v K M z