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  • 1
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    Energy transfer from high-shear, low-frequency internal waves to high-frequency waves near Kaena Ridge, Hawaii (2012)
    American Meteorological Society
    Details
    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): 1524–1547, doi:10.1175/JPO-D-11-0117.1.
    Description: Evidence is presented for the transfer of energy from low-frequency inertial–diurnal internal waves to high-frequency waves in the band between 6 cpd and the buoyancy frequency. This transfer links the most energetic waves in the spectrum, those receiving energy directly from the winds, barotropic tides, and parametric subharmonic instability, with those most directly involved in the breaking process. Transfer estimates are based on month-long records of ocean velocity and temperature obtained continuously over 80–800 m from the research platform (R/P) Floating Instrument Platform (FLIP) in the Hawaii Ocean Mixing Experiment (HOME) Nearfield (2002) and Farfield (2001) experiments, in Hawaiian waters. Triple correlations between low-frequency vertical shears and high-frequency Reynolds stresses, uiw∂Ui/∂z, are used to estimate energy transfers. These are supported by bispectral analysis, which show significant energy transfers to pairs of waves with nearly identical frequency. Wavenumber bispectra indicate that the vertical scales of the high-frequency waves are unequal, with one wave of comparable scale to that of the low-frequency parent and the other of much longer scale. The scales of the high-frequency waves contrast with the classical pictures of induced diffusion and elastic scattering interactions and violates the scale-separation assumption of eikonal models of interaction. The possibility that the observed waves are Doppler shifted from intrinsic frequencies near f or N is explored. Peak transfer rates in the Nearfield, an energetic tidal conversion site, are on the order of 2 × 10−7 W kg−1 and are of similar magnitude to estimates of turbulent dissipation that were made near the ridge during HOME. Transfer rates in the Farfield are found to be about half the Nearfield values.
    Description: This work was supported by the National Science Foundation and the Office of Naval Research.
    Description: 2013-03-01
    Keywords: Diapycnal mixing ; Energy transport ; Internal waves ; Nonlinear dynamics ; Ship observations ; Spectral analysis/models/distribution
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 2
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    Parametric subharmonic instability of the internal tide at 29°N (2013)
    American Meteorological Society
    Details
    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): 17–28, doi:10.1175/JPO-D-11-0108.1.
    Description: Observational evidence is presented for transfer of energy from the internal tide to near-inertial motions near 29°N in the Pacific Ocean. The transfer is accomplished via parametric subharmonic instability (PSI), which involves interaction between a primary wave (the internal tide in this case) and two smaller-scale waves of nearly half the frequency. The internal tide at this location is a complex superposition of a low-mode waves propagating north from Hawaii and higher-mode waves generated at local seamounts, making application of PSI theory challenging. Nevertheless, a statistically significant phase locking is documented between the internal tide and upward- and downward-propagating near-inertial waves. The phase between those three waves is consistent with that expected from PSI theory. Calculated energy transfer rates from the tide to near-inertial motions are modest, consistent with local dissipation rate estimates. The conclusion is that while PSI does befall the tide near a critical latitude of 29°N, it does not do so catastrophically.
    Description: This work was sponsored by NSF OCE 04-25283.
    Description: 2013-07-01
    Keywords: Diapycnal mixing ; Internal waves ; Nonlinear dynamics
    Repository Name: Woods Hole Open Access Server
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  • 3
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    A modified leapfrog scheme for shallow water equations (2011)
    Details
    Publication Date: 2022-05-25
    Description: Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Computers & Fluids 52 (2011): 69-72, doi:10.1016/j.compfluid.2011.08.019.
    Description: In the 1D linearized shallow water equations, the Courant number should be 〈 0.5 for stability in the original Leapfrog (LF) scheme. Here, we propose using the time-averaged heights in the pressure gradient force in the momentum equations. The stability analysis shows that the new scheme is neutral when Courant number 〈1. The scheme is 2nd order accurate in both time and space. It does not require iterations and can be easily applied in 2D or 3D wave equations. The numerical simulations for 2-D linearized shallow water equations are consistent with those obtained from a 2-time-step semi-implicit scheme.
    Keywords: Shallow Water Equations ; Leapfrog scheme ; Courant number ; Eigenvalue ; Semi-implicit ; Finite-volume ; Stability
    Repository Name: Woods Hole Open Access Server
    Type: Preprint
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  • 4
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    A modified atmospheric non-hydrostatic model on low aspect ratio grids (2012)
    International Meteorological Institute
    Details
    Publication Date: 2022-05-25
    Description: © The Author(s), 2012. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Tellus A 64 (2012): 17516, doi:10.3402/tellusa.v64i0.17516.
    Description: It is popular to use a horizontal explicit and a vertical implicit (HE-VI) scheme in the compressible nonhydrostatic (NH) model. However, when the aspect ratio becomes small, a small time-interval is required in HE-VI, because the Courant-Fredrich-Lewy (CFL) criterion is determined by the horizontal grid spacing. Furthermore, simulations from HE-VI can depart from the forward–backward (FB) scheme in NH even when the time interval is less than the CFL criterion allowed. Hence, a modified non-hydrostatic (MNH) model is proposed, in which the left-hand side of the continuity equation is multiplied by a parameter d (45d516, in this study). When the linearized MNH is solved by FB (can be other schemes), the eigenvalue shows that MNH can suppress the frequency of acoustic waves very effectively but does not have a significant impact on the gravity waves. Hence, MNH enables to use a longer time step than that allowed in the original NH. When the aspect ratio is small, MNH solved by FB can be more accurate and efficient than the NH solved by HE-VI. Therefore, MNH can be very useful to study cloud, Large Eddy Simulation (LES), turbulence, flow over complex terrains, etc., which require fine resolution in both horizontal and vertical directions.
    Keywords: Non-hydrostatic model ; Forward-backward ; HE-VI ; Eigenvalue ; LES ; Aspect ratio
    Repository Name: Woods Hole Open Access Server
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  • 5
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    A modified atmospheric non-hydrostatic model on low aspect ratio grids : part II (2013)
    International Meteorological Institute
    Details
    Publication Date: 2022-05-25
    Description: © The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Tellus A 65 (2013): 19681, doi:10.3402/tellusa.v65i0.19681.
    Description: Sun et al. (2012) proposed a modified non-hydrostatic model (MNH), in which the left-hand side of the continuity equation is multiplied by a parameter δ(4 ≤ δ≤16 in the article) to suppress high-frequency acoustic waves. They showed that the MNH allows a longer time step than the original non-hydrostatic model (NH). The MNH is also more accurate and efficient than the horizontal explicit and vertical implicit scheme (HEVI) when the aspect ratio (Δx/Δz) is small. In addition to multiplying a parameter δ, here we propose to add a smoothing on the right-hand side of the continuity equation in the MNH to damp shortest sound waves. Linear stability analysis and non-linear model simulations show that the MNH with smoothing (henceforth abbreviated as MNHS) can use twice the time interval of the MNH while maintaining the same accuracy. The MNHS is also more accurate and efficient than HEVI when the aspect ratio is small.
    Keywords: Non-hydrostatic model ; Eigenvalue ; Forwardbackward ; Aspect ratio ; Gravity wave ; HEVI
    Repository Name: Woods Hole Open Access Server
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  • 6
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    Subharmonic energy transfer from the semidiurnal internal tide to near-diurnal motions over Kaena Ridge, Hawaii (2013)
    American Meteorological Society
    Details
    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): 766–789, doi:10.1175/JPO-D-12-0141.1.
    Description: Nonlinear energy transfers from the semidiurnal internal tide to high-mode, near-diurnal motions are documented near Kaena Ridge, Hawaii, an energetic generation site for the baroclinic tide. Data were collected aboard the Research Floating Instrument Platform (FLIP) over a 35-day period during the fall of 2002, as part of the Hawaii Ocean Mixing Experiment (HOME) Nearfield program. Energy transfer terms for a PSI resonant interaction at midlatitude are identified and compared to those for near-inertial PSI close to the M2 critical latitude. Bispectral techniques are used to demonstrate significant energy transfers in the Nearfield, between the low-mode M2 internal tide and subharmonic waves with frequencies near M2/2 and vertical wavelengths of O(120 m). A novel prefilter is used to test the PSI wavenumber resonance condition, which requires the subharmonic waves to propagate in opposite vertical directions. Depth–time maps of the interactions, formed by directly estimating the energy transfer terms, show that energy is transferred predominantly from the tide to subharmonic waves, but numerous reverse energy transfers are also found. A net forward energy transfer rate of 2 × 10−9 W kg−1 is found below 400 m. The suggestion is that the HOME observations of energy transfer from the tide to subharmonic waves represent a first step in the open-ocean energy cascade. Observed PSI transfer rates could account for a small but significant fraction of the turbulent dissipation of the tide within 60 km of Kaena Ridge. Further extrapolation suggests that integrated PSI energy transfers equatorward of the M2 critical latitude may be comparable to PSI energy transfers previously observed near 28.8°N.
    Description: This work was supported by the National Science Foundation and the Office of Naval Research.
    Description: 2013-10-01
    Keywords: Diapycnal mixing ; Energy transport ; Internal waves ; Nonlinear dynamics ; Topographic effects ; In situ oceanic observations
    Repository Name: Woods Hole Open Access Server
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  • 7
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    Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate (2014)
    American Meteorological Society
    Details
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2014. 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 44 (2014): 1854–1872, doi:10.1175/JPO-D-13-0104.1.
    Description: The authors present inferences of diapycnal diffusivity from a compilation of over 5200 microstructure profiles. As microstructure observations are sparse, these are supplemented with indirect measurements of mixing obtained from (i) Thorpe-scale overturns from moored profilers, a finescale parameterization applied to (ii) shipboard observations of upper-ocean shear, (iii) strain as measured by profiling floats, and (iv) shear and strain from full-depth lowered acoustic Doppler current profilers (LADCP) and CTD profiles. Vertical profiles of the turbulent dissipation rate are bottom enhanced over rough topography and abrupt, isolated ridges. The geography of depth-integrated dissipation rate shows spatial variability related to internal wave generation, suggesting one direct energy pathway to turbulence. The global-averaged diapycnal diffusivity below 1000-m depth is O(10−4) m2 s−1 and above 1000-m depth is O(10−5) m2 s−1. The compiled microstructure observations sample a wide range of internal wave power inputs and topographic roughness, providing a dataset with which to estimate a representative global-averaged dissipation rate and diffusivity. However, there is strong regional variability in the ratio between local internal wave generation and local dissipation. In some regions, the depth-integrated dissipation rate is comparable to the estimated power input into the local internal wave field. In a few cases, more internal wave power is dissipated than locally generated, suggesting remote internal wave sources. However, at most locations the total power lost through turbulent dissipation is less than the input into the local internal wave field. This suggests dissipation elsewhere, such as continental margins.
    Description: This research was funded by the Climate Process Team (CPT) on internal wave–driven mixing throughNSF GrantOCE-0968721. GSC acknowledges support from NSF Grants OCE-0825266 (EXITS), OCE-1029483 (SPAM), and OCE-1029722 (MIXET). LDT and CBW acknowledge support from NSF Grant OCE-0927650. SWand ACNG acknowledge support from NERC Grant NE/G001510/1 (SOFine).
    Description: 2015-01-01
    Keywords: Circulation/ Dynamics ; Diapycnal mixing ; Internal waves
    Repository Name: Woods Hole Open Access Server
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  • 8
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    Scaling turbulent dissipation in the transition layer (2014)
    American Meteorological Society
    Details
    Publication Date: 2022-05-26
    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): 2475–2489, doi:10.1175/JPO-D-13-057.1.
    Description: Data from three midlatitude, month-long surveys are examined for evidence of enhanced vertical mixing associated with the transition layer (TL), here defined as the strongly stratified layer that exists between the well mixed layer and the thermocline below. In each survey, microstructure estimates of turbulent dissipation were collected concurrently with fine-structure stratification and shear. Survey-wide averages are formed in a “TL coordinate” zTL, which is referenced around the depth of maximum stratification for each profile. Averaged profiles show characteristic TL structures such as peaks in stratification N2 and shear variance S2, which fall off steeply above zTL = 0 and more gradually below. Turbulent dissipation rates ɛ are 5–10 times larger than those found in the upper thermocline (TC). The gradient Richardson number Ri = N2/S2 becomes unstable (Ri 〈 0.25) within ~10 m of the TL upper boundary, suggesting that shear instability is active in the TL for zTL 〉 0. Ri is stable for zTL ≤ 0. Turbulent dissipation is found to scale exponentially with depth for zTL ≤ 0, but the decay scales are different for the TL and upper TC: ɛ scales well with either N2 or S2. Owing to the strong correlation between S2 and N2, existing TC scalings of the form ɛ ~ |S|p|N|q overpredict variations in ɛ. The scale dependence of shear variance is not found to significantly affect the scalings of ɛ versus N2 and S2 for zTL ≤ 0. However, the onset of unstable Ri at the top of the TL is sensitively dependent to the resolution of the shears.
    Description: This work was funded by NSF Grant OCE-0968787 as part of a Climate Process Team for internal wave-driven mixing.
    Keywords: Atm/Ocean Structure/ Phenomena ; Diapycnal mixing ; Mixed layer ; Thermocline ; Physical Meteorology and Climatology ; Heat budgets/fluxes ; Observational techniques and algorithms ; In situ oceanic observations ; Profilers, oceanic
    Repository Name: Woods Hole Open Access Server
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  • 9
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    Climate Process Team on internal wave–driven ocean mixing (2017)
    American Meteorological Society
    Details
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 98 (2017): 2429-2454, doi:10.1175/BAMS-D-16-0030.1.
    Description: Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.
    Description: We are grateful to U.S. CLIVAR for their leadership in instigating and facilitating the Climate Process Team program. We are indebted to NSF and NOAA for sponsoring the CPT series.
    Description: 2018-06-01
    Repository Name: Woods Hole Open Access Server
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  • 10
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    A modified atmospheric non-hydrostatic model on low aspect ratio grids (2012)
    Co-Action Publishing
    In: Tellus A
    Details
    Publication Date: 2012-04-19
    Description: It is popular to use a horizontal explicit and a vertical implicit (HE-VI) scheme in the compressible nonhydrostatic (NH) model. However, when the aspect ratio becomes small, a small time-interval is required in HE-VI, because the Courant-Fredrich-Lewy (CFL) criterion is determined by the horizontal grid spacing. Furthermore, simulations from HE-VI can depart from the forward–backward (FB) scheme in NH even when the time interval is less than the CFL criterion allowed. Hence, a modified non-hydrostatic (MNH) model is proposed, in which the left-hand side of the continuity equation is multiplied by a parameter d (45d516, in this study). When the linearized MNH is solved by FB (can be other schemes), the eigenvalue shows that MNH can suppress the frequency of acoustic waves very effectively but does not have a significant impact on the gravity waves. Hence, MNH enables to use a longer time step than that allowed in the original NH. When the aspect ratio is small, MNH solved by FB can be more accurate and efficient than the NH solved by HE-VI. Therefore, MNH can be very useful to study cloud, Large Eddy Simulation (LES), turbulence, flow over complex terrains, etc., which require fine resolution in both horizontal and vertical directions. Keywords: non-hydrostatic model, forward-backward, HE-VI, eigenvalue, LES, aspect ratio (Published: 17 April 2012) Citation: Tellus A 2012, 64 , 17516, http://dx.doi.org/10.3402/tellusa.v64i0.17516
    Print ISSN: 0280-6495
    Electronic ISSN: 1600-0870
    Topics: Geography , Geosciences , Physics
    Published by Co-Action Publishing on behalf of The International Meteorological Institute in Stockholm.
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