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Vorticity dynamics in Admiralty Inlet

Vorticity dynamics in Admiralty Inlet

Poster presented at the Gordon Research Conference on Ocean Circulation in 2013.

Kristen Thyng

June 09, 2013
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  1. Vorticity Dynamics in
    Admiralty Inlet
    Kristen Thyngα, James J. Rileyβ and Mitsuhiro Kawaseγ
    αOceanography, Texas A&M University
    βDepartment of Mechanical Engineering, γSchool of Oceanography,
    University of Washington
    [email protected]
    Vorticity Background
    • Measure of the local rotation rate of a fluid element
    • ω = ∇ × v, v = (u, v, w)
    • Mainly vertical vorticity considered here: ω = ∂v
    ∂x
    − ∂u
    ∂y
    • 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 and
    causes flow separation (Signell and Geyer, 1991)
    • in 3D: Evidence of tilted baroclinic vortices, sloping due to gen-
    eration 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 Ad-
    miralty Head?
    The vertical vorticity equation based on simplified governing equa-
    tions for ROMS is
    Rate-of-change
    ∂ωz
    a
    ∂t
    =
    Tilting/stretching
    ωa · ∇ w −
    Advection
    ∇ · (vωz
    a) +
    Reynolds stress generation
    ∇ × (∇ · τ
    R
    ) · ˆ
    nz
    +
    Numerical viscosity generation
    ∇ × (∇ · τ
    N
    ) · ˆ
    nz
    stretching tilting
    • Vortex tubes can be stretched or contracted to conserve angu-
    lar momentum – increasing or decreasing the magnitude of the
    vorticity, stretching = ωzwz
    x
    z
    ω
    ωx
    ωz
    Vertical to
    horizontal vorticity
    ω
    ωx
    ωz
    Horizontal to
    vertical vorticity
    • Vorticity can change orientation by tilting, exchanging vorticity be-
    tween horizontal and vertical components, tilting = ωxwx + ωywy
    Numerical Model
    Admiralty
    Head
    Point
    Wilson
    Marrowstone
    Island
    Bush
    Point
    Pilot Site
    Nodule
    Point
    Admiralty
    Bay
    Port
    Townsend
    Surface salinity of regional model (Sutherland et al., 2011),
    (http://faculty.washington.edu/pmacc/MoSSea) and bathymetry of
    nested model of Admiralty Inlet.
    • Run in ROMS: hydrostatic, 3D, parallelized (Shchepetkin and
    McWilliams, 2005)
    • Horizontal resolution of 65 meters, 20 vertical layers
    • 2.6 million computational cells, k- turbulence closure scheme
    • Realistic boundary and initial conditions from regional model
    • M2 tide is about 25% low for both free surface and velocity
    Vortex
    area
    Admiralty
    Head
    Ebb tide
    • Google Earth satellite image and simulation snapshot show the
    model includes headland-generated eddies near Admiralty Head.
    • Model captures features of vortex as seen in ver-
    tical cross-section from shipboard ADCP. (Data from
    http://depts.washington.edu/nnmrec/)
    Gordon Research Conference: Coastal Ocean Circulation, June 9 14 at University of New England, Biddeford, Maine

    View Slide

  2. Results
    Volume-integrated vertical vorticity equation can be used to understand dominant terms in an area (Dong et al., 2007).
    Rate-of-change of total volume vorticity
    d
    dt
    ωz
    adV =
    Tilting throughout volume
    ωx∂w
    ∂x
    + ωy∂w
    ∂y
    dV +
    Stretching throughout volume
    ωz
    a
    ∂w
    ∂z
    dV

    Advection through walls
    o
    ωz
    a(v · ˆ
    n)d dz +
    Reynolds viscous flux along open walls
    o
    KMuzz · d dz +
    Boundary generation
    ωbg
    0 1 2 3 4 5 6 7
    2.0
    1.5
    1.0
    0.5
    0.0
    0.5
    1.0
    1.5
    2.0
    free surface (m) speed (m/s)
    0 1 2 3 4 5 6 7
    Hours into flood tide
    1000
    500
    0
    500
    1000
    Vorticity terms m3 s−2
    gen tilting stretching rate-of-change advection
    • Terms from the volume-integrated vertical vorticity equation for a
    box around Admiralty Head show that boundary generation, tilt-
    ing, and stretching are the most important terms (advection is
    clearly important but mostly occurs within the analysis box).
    Snapshots through flood tide show progress of generation.
    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 seems to be
    controlled by a combination of headland shape/channel geom-
    etry, lee horizontal density gradient, and vertical velocity, as in
    Farmer et al.
    • Different causes of vertical velocity may be important at different
    times in cycle (i.e., upsloping vs. upwelling vertical velocity)
    • Transects near headland show tilting/stretching due to vertical ve-
    locity
    • Upsloping (caused by bathymetry) may initially be more impor-
    tant, then upwelling vertical velocity is stronger
    • Density gradient may affect behaviors
    56 D. Farmer et al. / Dynamics of Atmospheres and Oceans 36 (2002) 43–58
    Fig. 9. Sketch showing tidal flow of density ρ1 past a headland with separation. A vertical shear layer or vortex sheet
    is formed (A) separating this flow from water of density ρ2 behind the headland. Instabilities evolve into vertically
    oriented rotating columns of fluid. The vortices move downstream, but begin to tilt and stretch due to horizontal
    density gradients across the front. The tilting converts horizontal to vertical motions; advective instabilities occur
    as heavy water is transported above light water and vice versa leading to intense mixing (B).
    large flood tides in this region, this single feature might account for as much as 14% of
    the total mixing. These estimates are necessarily approximate, but give an indication of the
    contribution to mixing. It should be mentioned here that this front is by no means unique
    in the Haro Strait/Juan de Fuca region, so that a significant fraction of the total mixing is
    likely to occur in this way.
    An idealized representation of the proposed evolution of the flow is sketched in Fig. 9,
    illustrating initial separation of the boundary layer at A, followed by tilting and stretching
    of the shear layer at B. Bubbles are entrained at the surface in whirlpools and from breaking
    waves in convergence zones, subsequently descending to great depths in the active zone.
    Further downstream (C in Fig. 3) the shear layer becomes broader, vortical motions decay,
    the surface expression weakens and in the absence of other factors relevant here, such as
    irregular topography and the changing tidal forcing, further development would be expected
    to assume the form of a steady coastal front (Bowden, 1983) in which friction balances the
    horizontal pressure gradient.
    For the reasons outlined earlier, the detailed response of the separated flow is sensitive to
    the density structure on either side of the shear zone. Additional measurements near Turn
    Point front were acquired in September 2000. In this case, denser water occurred on the
    eastern side of the front, but only at intermediate depths. Moreover, a sharply defined fresh
    layer remained on the surface to the east of the front. As before, the front was initially
    vertical in the neighborhood of the sharply curved portion, but further downstream there
    was evidence of interleaving of the different water masses. In this configuration, the hori-
    zontal interface bounding the fresh layer was only 20 m deep and the large vertical motions
    prevalent in the 1996 observations shown in Fig. 6 were not observed.
    4. Conclusions
    Boundary layer separation is a common phenomenon wherever strong tidal currents occur
    in the presence of irregular coastlines. If differential mixing or different origins of the two
    Farmer et al. (2002)
    fresher
    denser
    Ebb tide brings
    fresher water
    northward
    Flood tide
    brings denser
    water south
    front
    References
    Black, K. P. and Gay, S. L. (1987). Eddy formation in unsteady flows. Journal of Geophysical Research, 92(C9):9514–9522.
    Canals, M., Pawlak, G., and MacCready, P. (2009). Tilted baroclinic tidal vortices. Journal of Physical Oceanography, 39:333–350.
    Dong, C., McWilliams, J. C., and Shchepetkin, A. F. (2007). Island wakes in deep water. Journal of Physical Oceanography, 37(4):962–981.
    Farmer, D., Pawlowicz, R., and Jiang, R. (2002). Tilting separation flows: a mechanism for intense vertical mixing in the coastal ocean.
    Dynamics of Atmospheres and Oceans, 36(1):43–58.
    Shchepetkin, A. F. and McWilliams, J. C. (2005). The Regional Ocean Modeling System (ROMS): A split-explicit, free-surface, topography-
    following coordinates ocean model. Ocean Modelling, 9(4):347–404.
    Signell, R. P. and Geyer, W. R. (1991). Transient eddy formation around headlands. Journal of Geophysical Research, 96(C2):2561–2575.
    Sutherland, D. A., MacCready, P., Banas, N. S., and Smedstad, L. F. (2011). A model study of the Salish Sea estuarine circulation. Journal
    of Physical Oceanography, 41(6):1125–1143.
    Gordon Research Conference: Coastal Ocean Circulation, June 9 14 at University of New England, Biddeford, Maine

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