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  • 1
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    American Meteorological Society
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 39 (2009): 2910-2925, doi:10.1175/2009JPO4139.1.
    Description: The propagation of Rossby waves on a midlatitude β plane is investigated in the presence of density diffusion with the aid of linear hydrostatic theory. The search for wave solutions in a vertically bounded medium subject to horizontal (vertical) diffusion leads to an eigenvalue problem of second (fourth) order. Exact solutions of the problem are obtained for uniform background stratification (N), and approximate solutions are constructed for variable N using the Wentzel–Kramers–Brillouin method. Roots of the eigenvalue relations for free waves are found and discussed. The barotropic wave of adiabatic theory is also a solution of the eigenvalue problem as this is augmented with density diffusion in the horizontal or vertical direction. The barotropic wave is undamped as fluid parcels in the wave move only horizontally and are therefore insensitive to the vortex stretching induced by mixing. On the other hand, density diffusion modifies the properties of baroclinic waves of adiabatic theory. In the presence of horizontal diffusion the baroclinic modes are damped but their vertical structure remains unaltered. The ability of horizontal diffusion to damp baroclinic waves stems from its tendency to counteract the deformation of isopycnal surfaces caused by the passage of these waves. The damping rate increases (i) linearly with horizontal diffusivity and (ii) nonlinearly with horizontal wavenumber and mode number. In the presence of vertical diffusion the baroclinic waves suffer both damping and a change in vertical structure. In the long-wave limit the damping is critical (wave decay rate numerically equal to wave frequency) and increases as the square roots of vertical diffusivity and zonal wavenumber. Density diffusion in the horizontal or vertical direction reduces the amplitude of the phase speed of westward-propagating waves. Observational estimates of eddy diffusivities suggest that horizontal and vertical mixing strongly attenuates baroclinic waves in the ocean but that vertical mixing is too weak to notably modify the vertical structure of the gravest modes.
    Description: This work was supported by the U.S. National Science Foundation.
    Keywords: Rossby waves ; Extratropics ; Buoyancy ; Mixing
    Repository Name: Woods Hole Open Access Server
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  • 2
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    American Meteorological Society
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 1091-1106, doi:10.1175/2007JPO3805.1.
    Description: A model of deep ocean circulation driven by turbulent mixing is produced in a long, rectangular laboratory tank. The salinity difference is substituted for the thermal difference between tropical and polar regions. Freshwater gently flows in at the top of one end, dense water enters at the same rate at the top of the other end, and an overflow in the middle removes the same amount of surface water as is pumped in. Mixing is provided by a rod extending from top to bottom of the tank and traveling back and forth at constant speed with Reynolds numbers 〉500. A stratified upper layer (“thermocline”) deepens from the mixing and spreads across the entire tank. Simultaneously, a turbulent plume (“deep ocean overflow”) from a dense-water source descends through the layer and supplies bottom water, which spreads over the entire tank floor and rises into the upper layer to arrest the upper-layer deepening. Data are taken over a wide range of parameters and compared to scaling theory, energetic considerations, and simple models of turbulently mixed fluid. There is approximate agreement with a simple theory for Reynolds number 〉1000 in experiments with a tank depth less than the thermocline depth. A simple argument shows that mixing and plume potential energy flux rates are equal in magnitude, and it is suggested that the same is approximately true for the ocean.
    Description: The research was supported by the Ocean Climate Change Institute of Woods Hole Oceanographic Institution.
    Keywords: Ocean circulation ; Mixing ; In situ observations ; Vertical motion
    Repository Name: Woods Hole Open Access Server
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  • 3
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    American Meteorological Society
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2012. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 42 (2012): 1012–1021, doi:10.1175/JPO-D-11-0184.1.
    Description: Pacific Water flows across the shallow Chukchi Sea before reaching the Arctic Ocean, where it is a source of heat, freshwater, nutrients, and carbon. A substantial portion of Pacific Water is routed through Barrow Canyon, located in the northeast corner of the Chukchi. Barrow Canyon is a region of complex geometry and forcing where a variety of water masses have been observed to coexist. These factors contribute to a dynamic physical environment, with the potential for significant water mass transformation. The measurements of turbulent kinetic energy dissipation presented here indicate diapycnal mixing is important in the upper canyon. Elevated dissipation rates were observed near the pycnocline, effectively mixing winter and summer water masses, as well as within the bottom boundary layer. The slopes of shear/stratification layers, combined with analysis of rotary spectra, suggest that near-inertial wave activity may be important in modulating dissipation near the bottom. Because the canyon is known to be a hotspot of productivity with an active benthic community, mixing may be an important factor in maintenance of the biological environment.
    Description: ELS was supported as a WHOI Postdoctoral Scholar through the WHOI Ocean and Climate Change Institute.
    Description: 2012-12-01
    Keywords: Arctic ; Continental shelf/slope ; Mixing ; Small scale processes
    Repository Name: Woods Hole Open Access Server
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  • 4
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Atmospheric and Oceanic Technology 30 (2013): 1767–1788, doi:10.1175/JTECH-D-12-00140.1.
    Description: Seismic images of oceanic thermohaline finestructure record vertical displacements from internal waves and turbulence over large sections at unprecedented horizontal resolution. Where reflections follow isopycnals, their displacements can be used to estimate levels of turbulence dissipation, by applying the Klymak–Moum slope spectrum method. However, many issues must be considered when using seismic images for estimating turbulence dissipation, especially sources of random and harmonic noise. This study examines the utility of seismic images for estimating turbulence dissipation in the ocean, using synthetic modeling and data from two field surveys, from the South China Sea and the eastern Pacific Ocean, including the first comparison of turbulence estimates from seismic images and from vertical shear. Realistic synthetic models that mimic the spectral characteristics of internal waves and turbulence show that reflector slope spectra accurately reproduce isopycnal slope spectra out to horizontal wavenumbers of 0.04 cpm, corresponding to horizontal wavelengths of 25 m. Using seismic reflector slope spectra requires recognition and suppression of shot-generated harmonic noise and restriction of data to frequency bands with signal-to-noise ratios greater than about 4. Calculation of slope spectra directly from Fourier transforms of the seismic data is necessary to determine the suitability of a particular dataset to turbulence estimation from reflector slope spectra. Turbulence dissipation estimated from seismic reflector displacements compares well to those from 10-m shear determined by coincident expendable current profiler (XCP) data, demonstrating that seismic images can produce reliable estimates of turbulence dissipation in the ocean, provided that random noise is minimal and harmonic noise is removed.
    Description: This work was funded by NSF Grants 0452744, 0405654, and 0648620, and ONR/DEPSCoR Grant DODONR40027.
    Description: 2014-02-01
    Keywords: Mixing ; Thermocline ; Acoustic measurements/effects
    Repository Name: Woods Hole Open Access Server
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  • 5
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 45 (2015): 2006–2024, doi:10.1175/JPO-D-14-0234.1.
    Description: The effects of wind-driven whitecapping on the evolution of the ocean surface boundary layer are examined using an idealized one-dimensional Reynolds-averaged Navier–Stokes numerical model. Whitecapping is parameterized as a flux of turbulent kinetic energy through the sea surface and through an adjustment of the turbulent length scale. Simulations begin with a two-layer configuration and use a wind that ramps to a steady stress. This study finds that the boundary layer begins to thicken sooner in simulations with whitecapping than without because whitecapping introduces energy to the base of the boundary layer sooner than shear production does. Even in the presence of whitecapping, shear production becomes important for several hours, but then inertial oscillations cause shear production and whitecapping to alternate as the dominant energy sources for mixing. Details of these results are sensitive to initial and forcing conditions, particularly to the turbulent length scale imposed by breaking waves and the transfer velocity of energy from waves to turbulence. After 1–2 days of steady wind, the boundary layer in whitecapping simulations has thickened more than the boundary layer in simulations without whitecapping by about 10%–50%, depending on the forcing and initial conditions.
    Description: We thank Skidmore College for financial and infrastructure support, and Skidmore and the National Science Foundation for funding travel to meetings where early versions of this work were presented. We also thank the National Science Foundation, Oregon State University, Jonathan Nash, and Joe Jurisa for funding and hosting a workshop on River Plume Mixing in October, 2013, where ideas and context for this paper were developed.
    Description: 2016-02-01
    Keywords: Circulation/ Dynamics ; Mixing ; Turbulence ; Wave breaking ; Wind stress ; Atm/Ocean Structure/ Phenomena ; Mixed layer
    Repository Name: Woods Hole Open Access Server
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  • 6
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in he balance of salinity variance in a partially stratified estuary: Implications for exchange flow, mixing, and stratification. Journal of Physical Oceanography, 48(12), (2018) 2887-2899., doi: 10.1175/JPO-D-18-0032.1.
    Description: Salinity variance dissipation is related to exchange flow through the salinity variance balance equation, and meanwhile its magnitude is also proportional to the turbulence production and stratification inside the estuary. As river flow increases, estuarine volume-integrated salinity variance dissipation increases owing to more variance input from the open boundaries driven by exchange flow and river flow. This corresponds to the increased efficient conversion of turbulence production to salinity variance dissipation due to the intensified stratification with higher river flow. Through the spring–neap cycle, the temporal variation of salinity variance dissipation is more dependent on stratification than turbulence production, so it reaches its maximum during the transition from neap to spring tides. During most of the transition time from spring to neap tides, the advective input of salinity variance from the open boundaries is larger than dissipation, resulting in the net increase of variance, which is mainly expressed as vertical variance, that is, stratification. The intensified stratification in turn increases salinity variance dissipation. During neap tides, a large amount of enhanced salinity variance dissipation is induced by the internal shear stress near the halocline. During most of the transition time from neap to spring tides, dissipation becomes larger than the advective input, so salinity variance decreases and the stratification is destroyed.
    Description: TW was supported by the National Key R&D Program of China (Grant 2017YFA0604104), National Natural Science Foundation of China (Grant 41706002), Natural Science Foundation of Jiangsu Province (Grant BK20170864), and MEL Visiting Fellowship (MELRS1617). WRG was supported by NSF Grant OCE 1736539. Part of this work is finished during TW’s visit in MEL and WHOI. We would like to acknowledge John Warner for providing the codes of the Hudson estuary model, and Parker MacCready, the editor, and two reviewers for their insightful suggestions on improving the manuscript.
    Description: 2019-06-06
    Keywords: Estuaries ; Dynamics ; Mixing ; Density Currents
    Repository Name: Woods Hole Open Access Server
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  • 7
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 909–917, doi:10.1175/2007JPO3535.1.
    Description: The classical two-box model of Stommel is extended in two directions: replacing the buoyancy constraint with an energy constraint and including the wind-driven gyre. Stommel postulated a buoyancy constraint for the thermohaline circulation, and his basic idea has evolved into the dominating theory of thermohaline circulation; however, recently, it is argued that the thermohaline circulation is maintained by mechanical energy from wind stress and tides. The major difference between these two types of models is the bifurcation structure: the Stommel-like model has two thermal modes (one stable and another one unstable) and one stable haline mode, whereas the energy-constraint model has one stable thermal mode and two saline modes (one stable and another one unstable). Adding the wind-driven gyre changes the threshold value of thermohaline bifurcation greatly; thus, the inclusion of the wind-driven gyre is a vital step in completely modeling the physical processes related to thermohaline circulation.
    Description: YPG was supported by the National Science Foundation of China (NSFC, 40676022), the National Basic Research Program of China (2006CB403605), and the Guangdong Natural Science Foundation (5003672). RXH was supported by the National Oceanic and Atmospheric Administration through CICOR Cooperative Agreement NA17RJ1223 to the Woods Hole Oceanographic Institution.
    Keywords: Thermohaline circulation ; Mixing ; Wind stress ; Buoyancy ; Energy budget
    Repository Name: Woods Hole Open Access Server
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  • 8
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 37 (2007): 1859-1877, doi:10.1175/jpo3088.1.
    Description: A series of dye releases in the Hudson River estuary elucidated diapycnal mixing rates and temporal variability over tidal and fortnightly time scales. Dye was injected in the bottom boundary layer for each of four releases during different phases of the tide and of the spring–neap cycle. Diapycnal mixing occurs primarily through entrainment that is driven by shear production in the bottom boundary layer. On flood the dye extended vertically through the bottom mixed layer, and its concentration decreased abruptly near the base of the pycnocline, usually at a height corresponding to a velocity maximum. Boundary layer growth is consistent with a one-dimensional, stress-driven entrainment model. A model was developed for the vertical structure of the vertical eddy viscosity in the flood tide boundary layer that is proportional to u2*/N∞, where u* and N∞ are the bottom friction velocity and buoyancy frequency above the boundary layer. The model also predicts that the buoyancy flux averaged over the bottom boundary layer is equal to 0.06N∞u2* or, based on the structure of the boundary layer equal to 0.1NBLu2*, where NBL is the buoyancy frequency across the flood-tide boundary layer. Estimates of shear production and buoyancy flux indicate that the flux Richardson number in the flood-tide boundary layer is 0.1–0.18, consistent with the model indicating that the flux Richardson number is between 0.1 and 0.14. During ebb, the boundary layer was more stratified, and its vertical extent was not as sharply delineated as in the flood. During neap tide the rate of mixing during ebb was significantly weaker than on flood, owing to reduced bottom stress and stabilization by stratification. As tidal amplitude increased ebb mixing increased and more closely resembled the boundary layer entrainment process observed during the flood. Tidal straining modestly increased the entrainment rate during the flood, and it restratified the boundary layer and inhibited mixing during the ebb.
    Description: The work was supported by the National Science Foundation Grant OCE00-95972 (W. Geyer, J. Lerczak), OCE00-99310 (R. Houghton), and OCE00-95913 (R. Chant, E. Hunter).
    Keywords: Estuaries ; Boundary layer ; Mixing ; Tides ; Friction
    Repository Name: Woods Hole Open Access Server
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  • 9
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2012. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 25 (2012): 1096–1115, doi:10.1175/2011JCLI4228.1.
    Description: Ventilation, including subduction and obduction, for the global oceans was examined using Simple Ocean Data Assimilation (SODA) outputs. The global subduction rate averaged over the period from 1959 to 2006 is estimated at 505.8 Sv (1 Sv ≡ 106 m3 s−1), while the corresponding global obduction rate is estimated at 482.1 Sv. The annual subduction/obduction rates vary greatly on the interannual and decadal time scales. The global subduction rate is estimated to have increased 7.6% over the past 50 years, while the obduction rate is estimated to have increased 9.8%. Such trends may be insignificant because errors associated with the data generated by ocean data assimilation could be as large as 10%. However, a major physical mechanism that induced these trends is primarily linked to changes in the Southern Ocean. While the Southern Ocean plays a key role in global subduction and obduction rates and their variability, both the Southern Ocean and equatorial regions are critically important sites of water mass formation/erosion.
    Description: This work was supported by the Key State Basic Research Program of China under Grant 2012CB417401, the National Natural Science Foundation of China (Grants 40906007, 40890152), and the Open Foundation of Physical Oceanography Laboratory, OUC, under Grant 200902.
    Description: 2012-08-15
    Keywords: Decadal variability ; Southern Ocean ; Trends ; Water masses ; Convergence ; Mixing
    Repository Name: Woods Hole Open Access Server
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  • 10
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    American Meteorological Society
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 43 (2013): 698–705, doi:10.1175/JPO-D-12-0119.1.
    Description: Owing to the larger thermal expansion coefficient at higher temperatures, more buoyancy is put into the ocean by heating than is removed by cooling at low temperatures. The authors show that, even with globally balanced thermal and haline surface forcing at the ocean surface, there is a negative density flux and hence a positive buoyancy flux. As shown by McDougall and Garrett, this must be compensated by interior densification on mixing due to the nonlinearity of the equation of state (cabbeling). Three issues that arise from this are addressed: the estimation of the annual input of density forcing, the effects of the seasonal cycle, and the total cabbeling potential of the ocean upon complete mixing. The annual expansion through surface density forcing in a steady-state ocean driven by balanced evaporation–precipitation–runoff (E–P–R) and net radiative budget at the surface Qnet is estimated as 74 000 m3 s−1 (0.07 Sv; 1 Sv ≡ 106 m3 s−1), which would be equivalent to a sea level rise of 6.3 mm yr−1. This is equivalent to approximately 3 times the estimated rate of sea level rise or 450% of the average Mississippi River discharge. When seasonal variations are included, this density forcing increases by 35% relative to the time-mean case to 101 000 m3 s−1 (0.1 Sv). Likely bounds are established on these numbers by using different Qnet and E–P–R datasets and the estimates are found to be robust to a factor of ~2. These values compare well with the cabbeling-induced contraction inferred from independent thermal dissipation rate estimates. The potential sea level decrease upon complete vertical mixing of the ocean is estimated as 230 mm. When horizontal mixing is included, the sea level drop is estimated as 300 mm.
    Description: The authors would like to acknowledge support from the National Aeronautics and Space Administration, Grant NNX12AF59G and the National Science Foundation, Grant OCE-0647949.
    Description: 2013-10-01
    Keywords: Buoyancy ; Conservation equations ; Diapycnal mixing ; Heating ; Mixing ; Heat budgets/fluxes
    Repository Name: Woods Hole Open Access Server
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