Quantifying mixing from standard observations: revisiting finescale parameterization in the Arctic Ocean

<p>Ocean mixing governs the vertical exchange of matter, heat and salt in the water column. In the Arctic Ocean, the vertical transport of heat due to turbulent mixing is ultimately coupled to the sea-ice cover, with immediate and far-reaching impacts on the climate and ecosystem. A detailed understanding and quantification of turbulent mixing is crucial to assess and predict the state of the changing Arctic Ocean. However, direct observations of turbulent mixing are complicated, expensive and sparse.</p><p>Finescale parameterization of turbulent energy dissipation allows for the quantification of mixing based on standard hydrographic observations such as velocity and density profiles. This method is based on the assumption that energy dissipation is achieved exclusively by cascading energy from large, observable scales to small scales by wave-to-wave interactions in the internal wave field, which in turn can be related to vertical diffusivity and hence turbulent fluxes. While the finescale parameterization is proved to be reliable at mid-latitudes, the Arctic Ocean internal wave field is distinct from the canonical mid-latitude spectrum and the applicability of the parameterization is not certain. Furthermore, in the historically quiescent Arctic, the application of finescale parameterization suffers from a generally low signal to noise ratio and processes violating the assumptions in the parameterization, such as double diffusion.  During the year-long MOSAiC expedition, both standard observations as well as specialized microstructure measurements were carried out continuously. We analyse dissipation rate and stratification measurements (from an MSS90L profiler) and 8-m vertical resolution current measurements (from a 75 kHz RDI acoustic Doppler current profiler) in the depth range from 70 -198 m, in the absence of thermohaline staircases or double-diffusive intrusions. Although the range of dissipation measurements is limited and spans 1e<sup>-11</sup> W kg<sup>-1</sup> to 8.8e<sup>-7</sup> W kg<sup>-1</sup>, direct comparisons between in-situ observations of dissipation rate and finescale parameterization provide a detailed insight into the capabilities and limitations of this method in various meteorological, oceanographic and geographic conditions. The aim is to provide guidance in how far standard oceanographic observations may be utilized to quantify mixing in past, current and future states of the Arctic Ocean.</p>

Observed Eddy–Internal Wave Interactions in the Southern Ocean

The physical mechanisms that remove energy from the Southern Ocean’s vigorous mesoscale eddy field are not well understood. One proposed mechanism is direct energy transfer to the internal wave field in the ocean interior, via eddy-induced straining and shearing of preexisting internal waves. The magnitude, vertical structure, and temporal variability of the rate of energy transfer between eddies and internal waves is quantified from a 14-month deployment of a mooring cluster in the Scotia Sea. Velocity and buoyancy observations are decomposed into wave and eddy components, and the energy transfer is estimated using the Reynolds-averaged energy equation. We find that eddies gain energy from the internal wave field at a rate of −2.2 ± 0.6 mW m−2, integrated from the bottom to 566 m below the surface. This result can be decomposed into a positive (eddy to wave) component, equal to 0.2 ± 0.1 mW m−2, driven by horizontal straining of internal waves, and a negative (wave to eddy) component, equal to −2.5 ± 0.6 mW m−2, driven by vertical shearing of the wave spectrum. Temporal variability of the transfer rate is much greater than the mean value. Close to topography, large energy transfers are associated with low-frequency buoyancy fluxes, the underpinning physics of which do not conform to linear wave dynamics and are thereby in need of further research. Our work suggests that eddy–internal wave interactions may play a significant role in the energy balance of the Southern Ocean mesoscale eddy and internal wave fields.

Dynamic Response of Steel Catenary Riser in an Internal Wave Field

This paper proposes a dynamic model for steel catenary risers (SCRs) based on the principle of virtual work, where the equations of motion are obtained by combining Euler's equation and initial conditions. The motion equations of the floating platform are transformed and combined with those of the riser to establish the complete model. Vertical structure and dispersion of the internal wave are calculated to obtain the internal wave load and combined with the floating platform motion. The whole motion equation of the riser was solved by the Newmark β method. A proprietary matlab algorithm was written to analyze the influence of different factors on the dynamic response of the riser in an internal wave field. Top tension had a significant effect on the riser dynamic characteristics and response. Floating platform movement determines the vibration frequency of the riser, considering the internal wave as an external force, to promote the whole movement of the riser. The maximum riser displacement was mainly affected by the internal wave, where the top corner was mainly from the floating platform movement.

Response of the Internal Wave Field to Remote Wind Forcing by Tropical Cyclones

In the tropical North Atlantic, mean winds introduce relatively little energy into the internal wave field, but hurricanes act as very energetic sources for near-inertial waves. In addition to the eventlike passage of such tropical cyclones, changes in the wind speed north of the trade wind system induce a seasonal cycle in surface swell, with potential implications for the high-frequency part of the internal wave field. Using a 5-yr mooring time series in the interior of the tropical North Atlantic at 16°N, the temporal variability of internal wave energy south of the main hurricane track in different frequency bands is studied, and the magnitude of its variability, along with possible energy transfer mechanisms, is analyzed. The results show that changes in near-inertial energy are dominated by the passage of internal waves generated by hurricanes centered several hundred kilometers north of the mooring. The major role of hurricanes in the generation of near-inertial waves is also seen in an extended slab model that takes the horizontal divergence of the near-inertial current field at the mixed layer base into account. A seasonal cycle is observed in the energy at the high-frequency end (frequencies above 6 cpd) of the internal wave spectrum. It is not in phase with the near-inertial energy variability but covaries with changes in the local surface waves. These high-frequency internal waves are most energetic at times when large-amplitude surface swell with long periods and correspondingly long wavelengths is observed.

Eikonal Calculations for Energy Transfer in the Deep-Ocean Internal Wave Field near Mixing Hotspots

In the proximity of mixing hotspots in the deep ocean, the observed internal wave spectra are usually distorted from the Garrett–Munk (GM) spectrum and are characterized by the high energy level E as well as a shear–strain ratio Rω quite different from that of the GM spectrum. On the basis of the eikonal theoretical model, Ijichi and Hibiya (IH) recently proposed the revised finescale parameterization of turbulent dissipation rates in the distorted internal wave field, although the vertical velocity associated with background internal waves and the strict WKB scale separation, for example, were not taken into account. To see the effects of such simplifying assumptions on the revised parameterization, this study carries out a series of eikonal calculations for energy transfer through various internal wave spectra distorted from the GM. Although the background vertical velocity and the strict WKB scale separation somewhat affect the calculated energy transfer rates, their parameter dependence is confirmed as expected; the calculated energy transfer rates ε follow the basic scaling ε ∝ E2N2f with the local buoyancy frequency N and the local inertial frequency f and exhibit strong Rω dependence quite similar to that predicted by IH.

Revisiting the Generation of Internal Waves by Resonant Interaction with Surface Waves

Two surface waves can interact to produce an internal gravity wave by nonlinear resonant coupling. The process has been called spontaneous creation (SC) because it operates without internal waves being initially present. Previous studies have shown that the generated internal waves have high frequency close to the local Brunt–Väisälä frequency and wavelengths that are much larger than those of the participating surface waves, and that the spectral transfer rate of energy to the internal wave field is small compared to other generation processes. The aim of the present analysis is to provide a global map of the energy transfer into the internal wave field by surface–internal wave interaction, which is found to be about 10−3 TW in total, based on a realistic wind-sea spectrum (depending on wind speed), mixed layer depths, and stratification below the mixed layer taken from a state-of-the-art numerical ocean model. Unlike previous calculations of the spectral transfer rate based on a vertical mode decomposition, the authors use an analytical framework that directly derives the energy flux of generated internal waves radiating downward from the mixed layer base. Since the radiated waves are of high frequency, they are trapped and dissipated in the upper ocean. The radiative flux thus feeds only a small portion of the water column, unlike in cases of wind-driven near-inertial waves that spread over the entire ocean depth before dissipating. The authors also give an estimate of the interior dissipation and implied vertical diffusivities due to this process. In an extended appendix, they review the modal description of the SC interaction process, completed by the corresponding counterpart, the modulation interaction process (MI), where a preexisting internal wave is modulated by a surface wave and interacts with another one. MI establishes a damping of the internal wave field, thus acting against SC. The authors show that SC overcomes MI for wind speeds exceeding about 10 m s−1.

Dynamics of the Changing Near-Inertial Internal Wave Field in the Arctic Ocean

ABSTRACTThe dynamics of the wind-generated near-inertial internal wave field in the Canada Basin of the Arctic Ocean are investigated using the drifting Ice-Tethered Profiler dataset for the years 2005 to 2014, during a decade when sea ice extent and thickness decreased dramatically. This time series, with nearly 10 years of measurements and broad spatial coverage, is used to quantify a seasonal cycle and interannual trend for internal waves in the Arctic, using estimates of the amplitude of near-inertial waves derived from isopycnal displacements. The internal wave field is found to be most energetic in summer when sea ice is at a minimum, with a second maximum in early winter during the period of maximum wind speed. Amplitude distributions for the near-inertial waves are quantifiably different during summer and winter, due primarily to seasonal changes in sea ice properties that affect how the ice responds to the wind, which can be expressed through the “wind factor”—the ratio of sea ice drift speed to wind speed. A small positive interannual trend in near-inertial wave energy is linked to pronounced sea ice decline during the last decade. Overall variability in the internal wave field increases significantly over the second half of the record, with an increased probability of larger-than-average waves in both summer and winter. This change is linked to an overall increase in variability in the wind factor and sea ice drift speeds, and reflects a shift in year-round sea ice characteristics in the Arctic, with potential implications for dissipation and mixing associated with internal waves.