Bibliography - Sonya Legg

1. Klymak, J, M C Buijsman, Sonya Legg, and R Pinkel, in press: Parameterizing surface and internal tide scattering and breaking on supercritical topography: the one- and two-ridge cases. Journal of Physical Oceanography. doi:10.1175/JPO-D-12-061.1. 1/13.
   [ Abstract ]

   A parameterization is presented for turbulence dissipation due to internal tides generated at and impinging upon topography steep enough to be “supercritical” with respect to the tide. The parameterization requires knowledge of the topography, stratification, and the remote forcing, either barotropic or baroclinic. Internal modes that are arrested at the crest of the topography are assumed to dissipate, and faster modes assumed to propagate away. The energy flux into each mode is predicted using a knife-edge topography that allows linear numerical solutions. The parameterization is tested using high-resolution two-dimensional numerical models of barotropic and internal tides impinging on an isolated ridge, and for the generation problem on a two-ridge system. The recipe is seen to work well compared to numerical simulations of isolated ridges, so long as the ridge has a slope steeper than twice the critical steepness. For less steeply sloped ridges, near-critical generation becomes more dominant. For the two-ridge case, the recipe works well when compared to numerical model runs with very thin ridges. However, as the ridges are widened, even by a small amount, the recipe does poorly in an unspecified manner, because the linear response at high modes becomes compromised as it interacts with the slopes.

2. Melet, Angelique, Robert W Hallberg, Sonya Legg, and K Polzin, March 2013: Sensitivity of the Ocean State to the Vertical Distribution of Internal-Tide Driven Mixing. Journal of Physical Oceanography, 43(3), doi:10.1175/JPO-D-12-055.1.
   [ Abstract ]

   The ocean interior stratification and meridional overturning circulation are largely sustained by diapycnal mixing. The breaking of internal tides is a major source of diapycnal mixing. Many recent climate models parameterize internal-tide breaking using the scheme of St Laurent et al. (2002). While this parameterization dynamically accounts for internal-tide generation, the vertical distribution of the resultant mixing is ad hoc, prescribing energy dissipation to decay exponentially above the ocean bottom with a fixed length scale. Recently, Polzin (2009) formulated a dynamically based parameterization, in which the vertical profile of dissipation decays algebraically with a varying decay scale, accounting for variable stratification using WKB stretching. We compare two simulations using the St Laurent and Polzin formulations in the CM2G ocean-ice-atmosphere coupled model, with the same formulation for internal-tide energy input. Focusing mainly on the Pacific Ocean, where the deep low-frequency variability is relatively small, we show that the ocean state shows modest but robust and significant sensitivity to the vertical profile of internal-tide driven mixing. Therefore, not only the energy input to the internal tides matters, but also where in the vertical it is dissipated.

3. Buijsman, M C., Sonya Legg, and J Klymak, August 2012: Double Ridge Internal Tide Interference and its Effect on Dissipation in Luzon Strait. Journal of Physical Oceanography, 42(8), doi:10.1175/JPO-D-11-0210.1.
   [ Abstract ]

   Luzon Strait between Taiwan and the Phillipines features two parallel north-south oriented ridges. The barotropic tides that propagate over these ridges cause strong internal waves and dissipation. The energy dissipation mechanisms and the role of the baroclinic wave fields in this dissipation are investigated using numerical simulations with the MITgcm. The model is integrated over two-dimensional configurations along a zonal transect at 20.6�N for a maximum duration of a spring-neap cycle. Nearly all dissipation occurs at the steep ridge crests due to high-mode turbulent lee waves with horizontal scales of several kilometers and vertical scales of hundreds of meters. The spatial structure and timing of the predicted velocities and dissipation agree with observations, and confirm the existence of these lee waves. The lee wave strength is greatly affected by the internal waves generated at the other ridge. When semidiurnal barotropic tides are dominant, the internal wave beams from both ridges nearly superpose after one surface reflection. The remotely generated internal waves from both ridges are therefore in phase with each other and the barotropic tides at the ridges. The barotropic to baroclinic energy conversion, energy flux divergence, ridge top velocities, and dissipation are stronger compared to the sum of the single east and west ridge cases. When diurnal tides are dominant, the wave fields are more out of phase, and the conversion, divergence, and the dissipation are less than or equal to the single ridge cases combined.

4. Klymak, J, Sonya Legg, M H Alford, M C Buijsman, R Pinkel, and J D Nash, June 2012: The direct breaking of internal waves at steep topography. Oceanography, 25(2), doi:10.5670/oceanog.2012.50.
   [ Abstract ]

   Internal waves are often observed to break close to the seafloor topography that generates them, or from which they scatter. This breaking is often spectacular, with turbulent structures observed hundreds of meters above the seafloor, and driving turbulence dissipations and mixing up to 10,000 times open-ocean levels. This article provides an overview of efforts to observe and understand this turbulence, and to parameterize it near steep "supercritical" topography (i.e., topography that is steeper than internal wave energy characteristics). Using numerical models, we demonstrate that arrested lee waves are an important turbulence-producing phenomenon. Analogous to hydraulic jumps in water flowing over an obstacle in a stream, these waves are formed and then break during each tidal cycle. Similar lee waves are also observed in the atmosphere and in shallow fjords, but in those cases, their wavelengths are of similar scale to the topography, whereas in the ocean, they are small compared to the water depth and obstacle size. The simulations indicate that these nonlinear lee waves propagate against the generating flow (usually the tide) and are arrested because they have the same phase speed as the oncoming flow. This characteristic allows estimation of their size a priori and, using a linear model of internal tide generation, computation of how much energy they trap and turn into turbulence. This approach yields an accurate parameterization of mixing in numerical models, and these models are being used to guide a new generation of observations.

5. Coles, V, L Gerber, Sonya Legg, and S Lozier, June 2011: Mentoring Groups: A non-exit strategy for women in physical oceanography. Oceanography, 24(2), doi:10.5670/oceanog.2011.43.
6. Ilicak, M, Sonya Legg, Alistair Adcroft, and Robert W Hallberg, April 2011: Dynamics of a dense gravity current flowing over a corrugation. Ocean Modelling, 38(1-2), doi:10.1016/j.ocemod.2011.02.004.
   [ Abstract ]

   In this study, we investigate the dynamics of a dense gravity currents over different sizes of ridges and canyons. We employ a high resolution idealized isopycnal model and perform a large number of experiments changing the aspect ratio of a ridge/canyon, the Coriolis parameter, the reduced gravity, the background slope and initial overflow thickness. The control run (smooth topography) is in an eddy-regime and the frequencies of the eddies coincide with those of the Filchner overflow Darelius et al., 2009. Our idealized corrugation experiments show that corrugations steer the plume downslope, and that ridges are more effective than canyons in transporting the overflow to the deep ocean. We find that a corrugation Burger number (Buc) can be used as a parameter to describe the flow over topography. Buc is a combination of a Froude number and the aspect ratio. The maximum downslope transport of a corrugation can be increased when the height of the corrugation increases (Buc increases) or when the width of the corrugation decreases (Buc increases). In addition, we propose a new parameterization of mixing as a function of Buc that can be used to account for unresolved shear in coarse resolution models. The new parameterization captures the increased local shear, thus increasing the turbulent kinetic energy and decreasing the gradient Richardson number. We find reasonable agreement in the overflow thickness and transport between the models with this parameterization and the high resolution models. We conclude that mixing effects of corrugations can be implemented as unresolved shear in an eddy diffusivity formulation and this parameterization can be used in coarse resolution models.

7. Nikurashin, M, and Sonya Legg, February 2011: A mechanism for local dissipation of internal tides generated at rough topography. Journal of Physical Oceanography, 41(2), doi:10.1175/2010JPO4522.1.
   [ Abstract ]

   Fine- and micro-structure observations indicate that turbulent mixing is enhanced within O(1) km above rough topography. Enhanced mixing is associated with internal wave breaking and, in many regions of the ocean, has been linked to the breaking and dissipation of internal tides. The generation and dissipation of internal tides are explored in this study using a high-resolution two-dimensional nonhydrostatic numerical model, which explicitly resolves the instabilities leading to wave breaking, configured in an idealized domain with a realistic multiscale topography and flow characteristics. The control simulation, chosen to represent the Brazil Basin region, produces a vertical profile of energy dissipation and temporal characteristics of finescale motions that are consistent with observations. Results suggest that a significant fraction of mixing in the bottom O(1) km of the ocean is sustained by the transfer of energy from the large-scale internal tides to smaller-scale internal waves by nonlinear wave�wave interactions. The time scale of the energy transfer to the smaller scales is estimated to be on the order of a few days. A suite of sensitivity experiments is carried out to examine the dependence of the energy transfer time scale and energy dissipation on topographic roughness, tidal amplitude, and Coriolis frequency parameters. Implications for tidal mixing parameterizations are discussed.

8. Griffies, Stephen M., Alistair Adcroft, Anand Gnanadesikan, Robert W Hallberg, Matthew J Harrison, Sonya Legg, C M Little, M Nikurashin, A Pirani, Bonita L Samuels, J Robert Toggweiler, and Geoffrey K Vallis, et al., September 2010: Problems and prospects in large-scale ocean circulation models In Ocean Obs '09, 21-25 September, Venice, Italy, ESA Special Publication, doi:10.5270/OceanObs09.cwp.38.
   [ Abstract ]

   We overview problems and prospects in ocean circulation models, with emphasis on certain developments aiming to enhance the physical integrity and flexibility of large-scale models used to study global climate. We also consider elements of observational measures rendering information to help evaluate simulations and to guide development priorities. http://www.oceanobs09.net/blog/?p=88

9. Klymak, J, and Sonya Legg, April 2010: A simple mixing scheme for models that resolve breaking internal waves. Ocean Modelling, 33(3-4), doi:10.1016/j.ocemod.2010.02.005.
   [ Abstract ]

   Breaking internal waves in the vicinity of topography can reach heights of over 100 m and are thought to enhance basin-wide energy dissipation and mixing in the ocean. The scales at which these waves are modelled often include the breaking of large waves (10 s of meters), but not the turbulence dissipation scales (centimeters). Previous approaches to parameterize the turbulence have been to use a universally large viscosity, or to use mixing schemes that rely on Richardson-number criteria. A simple alternative is presented that enhances mixing and viscosity in the presence of breaking waves by assuming that dissipation is governed by the equivalence of the density overturning scales to the Ozmidov scale (, where LT is the size of the density overturns, and N the stratification). Eddy diffusivities and viscosities are related to the dissipation by the Osborn relation (Kz=ΓεN-2) to yield a simple parameterization , where Γ≈0.2 is the flux coefficient. This method is compared to previous schemes for flow over topography to show that, when eddy diffusivity and viscosity are assumed to be proportional, it dissipates the correct amount of energy, and that the dissipation reported by the mixing scheme is consistent with energy losses in the model. A significant advantage of this scheme is that it has no tunable parameters, apart from the turbulent Prandtl number and flux coefficient. A disadvantage is that the overturning scales of the turbulence must be relatively well-resolved.

10. Klymak, J, Sonya Legg, and R Pinkel, September 2010: A simple parameterization of turbulent tidal mixing near supercritical topography. Journal of Physical Oceanography, 40(9), doi:10.1175/2010JPO4396.1.
    [ Abstract ]

    A simple parameterization for tidal dissipation near supercritical topography, designed to be applied at deep mid-ocean ridges, is presented. In this parameterization, radiation of internal tides is quantified using a linear knife-edge model. Vertical internal wave modes that have non-rotating phase speeds slower than the tidal advection speed are assumed to dissipate locally, primarily due to hydraulic effects near the ridge crest. Evidence for high modes being dissipated is given in idealized numerical models of tidal flow over a Gaussian ridge. These idealized models also give guidance for where in the water column the predicted dissipation should be placed. The dissipation recipe holds if the Coriolis frequency f is varied so long as hN/W >> f, where N is the stratification, h the topographic height, and W a width scale. This parameterization is not applicable to shallower topography, which has significantly more dissipation as near-critical process dominate the observed turbulence. The parameterization compares well against simulations of tidal dissipation at the Kauai ridge, but predicts less dissipation than estimated from observations of the full Hawaiian ridge, perhaps due to unparameterized wave-wave interactions.

11. Griffies, Stephen M., Alistair Adcroft, Ventakramani Balaji, Robert W Hallberg, Sonya Legg, T Martin, and A Pirani, et al., February 2009: Sampling Physical Ocean Field in WCRP CMIP5 Simulations: CLIVAR Working Group on Ocean Model Development (WGOMD) Committee on CMIP5 Ocean Model Output, International CLIVAR Project Office, CLIVAR Publication Series No. 137, 56pp.
    [ PDF ]
12. Legg, Sonya, Tal Ezer, Stephen M Griffies, Robert W Hallberg, and L Jackson, et al., May 2009: Improving oceanic overflow representation in climate models: The gravity current entrainment climate process team. Bulletin of the American Meteorological Society, 90(5), doi:10.1175/2008BAMS2667.1.
    [ Abstract ]

    Oceanic overflows are bottom-trapped density currents originating in semienclosed basins, such as the Nordic seas, or on continental shelves, such as the Antarctic shelf. Overflows are the source of most of the abyssal waters, and therefore play an important role in the large-scale ocean circulation, forming a component of the sinking branch of the thermohaline circulation. As they descend the continental slope, overflows mix vigorously with the surrounding oceanic waters, changing their density and transport significantly. These mixing processes occur on spatial scales well below the resolution of ocean climate models, with the result that deep waters and deep western boundary currents are simulated poorly. The Gravity Current Entrainment Climate Process Team was established by the U.S. Climate Variability and Prediction (CLIVAR) Program to accelerate the development and implementation of improved representations of overflows within large-scale climate models, bringing together climate model developers with those conducting observational, numerical, and laboratory process studies of overflows. Here, the organization of the Climate Process Team is described, and a few of the successes and lessons learned during this collaboration are highlighted, with some emphasis on the well-observed Mediterranean overflow. The Climate Process Team has developed several different overflow parameterizations, which are examined in a hierarchy of ocean models, from comparatively well-resolved regional models to the largest-scale global climate models.

13. Green, J A M., J H Simpson, Sonya Legg, and M R Palmer, 2008: Internal waves, baroclinic energy fluxes and mixing at the European shelf edge. Continental Shelf Research, 28(7), doi:10.1016/j.csr.2008.01.014.
    [ Abstract ]

    The energy flux in internal waves generated at the Celtic Sea shelf break was estimated by (i) applying perturbation theory to a week-long dataset from a mooring at 200�m depth, and (ii) using a 2D non-hydrostatic circulation model over the shelf break. The dataset consisted of high resolution time-series of currents and vertical stratification together with two 25-h sets of vertical profiles of the dissipation of turbulent kinetic energy. The observations indicated an average energy flux of 139�W�m⁻¹, travelling along the shelf break towards the northwest. The average energy flux across the shelf break at the mooring was only 8�W�m⁻¹. However, the waves propagating onshelf transported up to 200�W�m⁻¹, but they were only present 51% of the time. A comparison between the divergence of the baroclinic energy flux and observed dissipation within the seasonal thermocline at the mooring showed that the dissipation was at least one order of magnitude larger. Results from a 2D model along a transect perpendicular to the shelf break showed a time-averaged onshelf energy flux of 153�425�W�m⁻¹, depending on the magnitude of the barotropic forcing. A divergence zone of the energy flux was found a few kilometre offshore of the location of the observations in the model results, and fluxes on the order of several kW�m⁻¹ were present in the deep waters further offshelf from the divergence zone. The modelled fluxes exhibited qualitative agreements with the phase and hourly onshelf magnitudes of the observed energy fluxes. Both the observations and the model results show an intermittent onshelf energy flux of 100�200�W�m⁻¹, but these waves could only propagate 20�30�km onshore before dissipating. This conclusion was supported by a 25-h dataset sampled some 180�km onto the shelf, where a weak wave energy flux was found going towards the shelf break. We therefore conclude that shelf break generated internal waves are unlikely to be the main source of energy for mixing on the inner part of the shelf.

14. Jackson, L, Robert W Hallberg, and Sonya Legg, May 2008: A Parameterization of shear-driven turbulence for ocean climate models. Journal of Physical Oceanography, 38(5), doi:10.1175/2007JPO3779.1.
    [ Abstract ]

    This paper presents a new parameterization for shear-driven, stratified, turbulent mixing that is pertinent to climate models, in particular the shear-driven mixing in overflows and the Equatorial Undercurrent. This parameterization satisfies a critical requirement for climate applications by being simple enough to be implemented implicitly and thereby allowing the parameterization to be used with time steps that are long compared to both the time scale on which the turbulence evolves and the time scale with which it alters the large-scale ocean state. The mixing is expressed in terms of a turbulent diffusivity that is dependent on the shear forcing and a length scale that is the minimum of the width of the low Richardson number region (Ri = N²/|u_z|², where N is the buoyancy frequency and |u_z| is the vertical shear) and the buoyancy length scale over which the turbulence decays [L_b = Q^1/2/N, where Q is the turbulent kinetic energy (TKE)]. This also allows a decay of turbulence vertically away from the low Richardson number region over the buoyancy scale, a process that the results show is important for mixing across a jet. The diffusivity is determined by solving a vertically nonlocal steady-state TKE equation and a vertically elliptic equilibrium equation for the diffusivity itself. High-resolution nonhydrostatic simulations of shear-driven stratified mixing are conducted in both a shear layer and a jet. The results of these simulations support the theory presented and are used, together with discussions of various limits and reviews of previous work, to constrain parameters.

15. Legg, Sonya, L Jackson, and Robert W Hallberg, 2008: Eddy-resolving modeling of overflows In Ocean Modeling in an Eddying Regime, Geophysical Monograph 177, M. W. Hecht, and H. Hasumi, eds., Washington, DC, American Geophysical Union, 63-82.
16. Legg, Sonya, and J Klymak, September 2008: Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge. Journal of Physical Oceanography, 38(9), doi:10.1175/2008JPO3777.1.
    [ Abstract ]

    Recent observations from the Hawaiian Ridge indicate episodes of overturning and strong dissipation coupled with the tidal cycle near the top of the ridge. Simulations with realistic topography and stratification suggest that this overturning has its origins in transient internal hydraulic jumps that occur below the shelf break at maximum ebb tide, and then propagate up the slope as internal bores when the flow reverses. A series of numerical simulations explores the parameter space of topographic slope, barotropic velocity, stratification, and forcing frequency to identify the parameter regime in which these internal jumps are possible. Theoretical analysis predicts that the tidally driven jumps may occur when the vertical tidal excursion is large, which is shown to imply steep topographic slopes, such that dh/dxN/ω > 1. The vertical length scale of the jumps is predicted to depend on the flow speed such that the jump Froude number is of order unity. The numerical results agree with the theoretical predictions, with finite-amplitude internal hydraulic jumps and overturning forming during strong offslope tidal flow over steep slopes. These results suggest that internal hydraulic jumps may be an important mechanism for local tidally generated mixing at tall steep topography.

17. Riemenschneider, U, and Sonya Legg, 2007: Regional simulations of the Faroe Bank Channel overflow in a level model. Ocean Modelling, 17(2), doi:10.1016/j.ocemod.2007.01.003.
    [ Abstract ]

    The work presented in this paper is part of an effort to understand and improve the representation of overflows in large scale, coarse resolution ocean climate models. To this end we developed a regional model of the Faroe Bank Channel overflow using the MITgcm (Massachusetts Institute of Technology General Circulation Model), a typical global ocean model using discrete levels as the vertical co-ordinate. In order to isolate the numerical diffusion resulting from the advection of tracers, the model is run without any turbulence closure schemes, without convective adjustment or any other physically based parameterization of mixing. Comparison between the model results and recent observations of the Faroe Bank Channel plume allows assessment of the model performance, including its ability to correctly represent the mixing and the downslope transport in the plume. It is found that at the highest resolution used in this paper (2.5 km � horizontal and 25 m � vertical) the structure of the modeled plume and the magnitude of the entrainment is comparable to the observed plume. The dependence of the mixing on various model parameters, such as vertical and horizontal resolution, vertical viscosity, drag coefficient and inflow forcing, is tested extensively. The numerical mixing in the model is found to be most sensitive to changes in the horizontal resolution, and to a lesser extent on vertical resolution and vertical viscosity. The inflow forcing and drag coefficient show only a very minor effect on the mixing. The results presented in the paper identify the shortcomings of the model at coarser resolutions which need to be addressed when attempting to represent such overflows realistically in large scale climate and ocean models.

18. Legg, Sonya, Robert W Hallberg, and J B Girton, 2006: Comparison of entrainment in overflows simulated by z-coordinate, isopycnal and non-hydrostatic models. Ocean Modelling, 11(1-2), doi:10.1016/j.ocemod.2004.11.006.
    [ Abstract ]

    A series of idealised numerical simulations of dense water flowing down a broad uniform slope are presented, employing both a z-coordinate model (the MIT general circulation model) and an isopycnal coordinate model (the Hallberg Isopycnal Model). Calculations are carried out at several different horizontal and vertical resolutions, and for a range of physical parameters. A subset of calculations are carried out at very high resolution using the non-hydrostatic variant of the MITgcm. In all calculations dense water descends the slope while entraining and mixing with ambient fluid. The dependence of entrainment, mixing and down-slope descent on resolution and vertical coordinate are assessed. At very coarse resolutions the z-coordinate model generates excessive spurious mixing, and dense water has difficulty descending the slope. However, at intermediate resolutions the mixing in the z-coordinate model is less than found in the high-resolution non-hydrostatic simulations, and dense water descends further down the slope. Isopycnal calculations show less resolution dependence, although entrainment and mixing are both reduced slightly at coarser resolution. At intermediate resolutions the z-coordinate and isopycnal models produce similar levels of mixing and entrainment. These results provide a benchmark against which future developments in overflow entrainment parameterizations in both z-coordinate and isopycnal models may be compared.

19. Legg, Sonya, and K M H Huijts, 2006: Preliminary simulations of internal waves and mixing generated by finite amplitude tidal flow over isolated topography. Deep-Sea Research, Part II, 53(1-2), doi:10.1016/j.dsr2.2005.09.014.
    [ Abstract ]

    Much recent observational evidence suggests that energy from the barotropic tides can be used for mixing in the deep ocean. Here the process of internal-tide generation and dissipation by tidal flow over an isolated Gaussian topography is examined, using two-dimensional numerical simulations employing the MITgcm. Four different topographies are considered, for five different amplitudes of barotropic forcing, thereby allowing a variety of combinations of key nondimensional parameters. While much recent attention has focused on the role of relative topographic steepness and height in modifying the rate of conversion of energy from barotropic to baroclinic modes, here attention is focused on parameters dependent on the flow amplitude. For narrow topography, large amplitude forcing gives rise to baroclinic responses at higher harmonics of the forcing frequency. Tall narrow topographies are found to be the most conducive to mixing. Dissipation rates in these calculations are most efficient for the narrowest topography.

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