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Eric D. Skyllingstad
and
Donald W. Denbo

Abstract

Using a two-dimensional nonhydrostatic model, experiments were performed to investigate the formation and maintenance of internal waves in the equatorial Pacific Ocean. The simulations show that internal waves are generated in the surface mixed layer by a type of Kelvin–Helmholtz instability that is dependent on both the flow Reynolds number (i.e., shear strength) and Richardson number. Because of the Richardson number dependence, the simulated internal waves exhibit a diurnal cycle, following the daily stability change in the mixed layer. The diurnal cycle is not evident when the wind stress is eastward because of a decreased mixed layer shear and corresponding Reynolds number. The amplitude, wavelength, frequency, and diurnal variability of the simulated waves are in agreement with high-resolution thermistor chain measurements. Linear theory shows that the horizontal wavelength of the internal waves depends on both the thermocline stratification and the strength of the Equatorial Undercurrent.

The simulations show that internal waves can provide an efficient mechanism for the vertical transport of horizontal momentum. In the surface mixed layer, the internal waves gain westerly momentum at the expense of the background flow. In some cases, this momentum is transferred back to the mean flow at a critical level resulting in a deceleration below the undercurrent core. Otherwise, the waves tend to decrease the current velocity above the undercurrent core.

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Eric D. Skyllingstad
and
Hemantha W. Wijesekera

Abstract

A three-dimensional large-eddy simulation (LES) model was used to examine how stratified flow interacts with bottom obstacles in the coastal ocean. Bottom terrain representing a 2D ridge was modeled using a finite-volume approach with ridge height (4.5 m) and width (∼30 m) and water depth (∼45 m) appropriate for coastal regions. Temperature and salinity profiles representative of coastal conditions giving constant buoyancy frequency were applied with flow velocities between 0.16 and 0.4 m s−1. Simulations using a free-slip lower boundary yielded flow responses ranging from transition flows with relatively high internal wave pressure drag to supercritical flow with relatively small internal wave drag. Cases with high wave drag exhibited strong lee-wave systems with wavelength of ∼100 m and regions of turbulent overturning. Application of bottom drag caused a 5–10-m-thick bottom boundary layer to form, which greatly reduced the strength of lee-wave systems in the transition cases. A final simulation with bottom drag, but with a much larger obstacle height (16 m) and width (∼400 m), produced a stronger lee-wave response, indicating that large obstacle flow is not influenced as much by bottom roughness. Flow characteristics for the larger obstacle were more similar to hydraulic flow, with lee waves that are relatively short in comparison with the obstacle width. The relatively strong effect of bottom roughness on the small obstacle wave drag suggests that small-scale bottom variations may be ignored in internal wave drag parameterizations. However, the more significant wave drag from larger-scale obstacles must still be considered and may be responsible for mixing and momentum transfer at distances far from the obstacle source.

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Eric D. Skyllingstad
and
R. M. Samelson

Abstract

Interaction between mixed layer baroclinic eddies and small-scale turbulence is studied using a nonhydrostatic large-eddy simulation (LES) model. Free, unforced flow evolution is considered, for a standard initialization consisting of an 80-m-deep mixed layer with a superposed warm filament and two frontal interfaces in geostrophic balance, on a model domain roughly 5 km × 10 km × 120 m, with an isotropic 3-m computational grid. Results from these unforced experiments suggest that shear generated in narrow frontal zones can support weak three-dimensional turbulence that is directly linked to the larger-scale baroclinic waves. Two separate but closely related issues are addressed: 1) the possible development of enhanced turbulent mixing associated with the baroclinic wave activity and 2) the existence of a downscale transfer of energy from the baroclinic wave scale to the turbulent dissipation scale. The simulations show enhanced turbulence associated with the baroclinic waves and enhanced turbulent heat flux across the isotherms of the imposed frontal boundary, relative to background levels. This turbulence develops on isolated small-scale frontal features that form as the result of frontogenetic processes operating on the baroclinic wave scale and not as the result of a continuous, inertial forward cascade through the intermediate scales. Analysis of the spectrally decomposed kinetic energy budget indicates that large-scale baroclinic eddy energy is directly transferred to small-scale turbulence, with weaker forcing at intermediate scales. For fronts with significant baroclinic wave activity, cross-frontal eddy fluxes computed from correlations of fluctuations from means along the large-scale frontal axis generally agreed with simple theoretical estimates.

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Martín S. Hoecker-Martínez
,
William D. Smyth
, and
Eric D. Skyllingstad

Abstract

The dominant processes governing ocean mixing during an active phase of the Madden–Julian oscillation are identified. Air–sea fluxes and upper-ocean currents and hydrography, measured aboard the R/V Revelle during boreal fall 2011 in the Indian Ocean at 0°, 80.5°E, are integrated by means of a large-eddy simulation (LES) to infer mixing mechanisms and quantify the resulting vertical property fluxes. In the simulation, wind accelerates the mixed layer, and shear mixes the momentum downward, causing the mixed layer base to descend. Turbulent kinetic energy gains due to shear production and Langmuir circulations are opposed by stirring gravity and frictional losses. The strongest stirring of buoyancy follows precipitation events and penetrates to the base of the mixed layer. The focus here is on the initial 24 h of an unusually strong wind burst that began on 24 November 2011. The model shows that Langmuir turbulence influences only the uppermost few meters of the ocean. Below the wave-energized region, shear instability responds to the integrated momentum flux into the mixed layer, lagging the initial onset of the storm. Shear below the mixed layer persists after the storm has weakened and decelerates the surface jet slowly (compared with the acceleration at the peak of the storm). Slow loss of momentum from the mixed layer extends the effect of the surface wind burst by energizing the fluid at the base of the mixed layer, thereby prolonging heat uptake due to the storm. Ocean turbulence and air–sea fluxes contribute to the cooling of the mixed layer approximately in the ratio 1:3, consistent with observations.

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Eric D. Skyllingstad
,
W. D. Smyth
, and
G. B. Crawford

Abstract

The role of resonant wind forcing in the ocean boundary layer was examined using an ocean large-eddy simulation (LES) model. The model simulates turbulent flow in a box, measuring ∼100–300 m on a side, whose top coincides with the ocean surface. Horizontal boundary conditions are periodic, and time-dependent wind forcing is applied at the surface. Two wind forcing scenarios were studied: one with resonant winds, that is, winds that rotated at exactly the inertial frequency (at 45°N), and a second with off-resonance winds from a constant direction. The evolution of momentum and temperature for both cases showed that resonant wind forcing produces much stronger surface currents and vertical mixing in comparison to the off-resonance case. Surface wave effects were also examined and found to be of secondary importance relative to the wind forcing.

The main goal was to quantify the main processes via which kinetic energy input by the wind is converted to potential energy in the form of changes in the upper-ocean temperature profile. In the resonant case, the initial pathway of wind energy was through the acceleration of an inertially rotating current. About half of the energy input into the inertial current was dissipated as the result of a turbulent energy cascade. Changes in the potential energy of the water column were ∼7% of the total input wind energy. The off-resonance case developed a much weaker inertial current system, and consequently less mixing because the wind acted to remove energy after ∼¼ inertial cycle. Local changes in the potential energy were much larger than the integrated values, signifying the vertical redistribution of water heated during the summer season.

Visualization of the LES results revealed coherent eddy structures with scales from 30–150 m. The largest-scale eddies dominated the vertical transport of heat and momentum and caused enhanced entrainment at the boundary layer base. Near the surface, the dominant eddies were driven by the Stokes vortex force and had the form of Langmuir cells. Near the base of the mixed layer, turbulent motions were driven primarily by the interaction of the inertial shear with turbulent Reynolds stresses. Bulk Richardson number and eddy diffusivity profiles from the model were consistent with one-dimensional model output using the K-profile parameterization.

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Eric D. Skyllingstad
,
Jenessa Duncombe
, and
Roger M. Samelson

Abstract

Generation of ocean surface boundary layer turbulence and coherent roll structures is examined in the context of wind-driven and geostrophic shear associated with horizontal density gradients using a large-eddy simulation model. Numerical experiments over a range of surface wind forcing and horizontal density gradient strengths, combined with linear stability analysis, indicate that the dominant instability mechanism supporting coherent roll development in these simulations is a mixed instability combining shear instability of the ageostrophic, wind-driven flow with symmetric instability of the frontal geostrophic shear. Disruption of geostrophic balance by vertical mixing induces an inertially rotating ageostrophic current, not forced directly by the wind, that initially strengthens the stratification, damps the instabilities, and reduces vertical mixing, but instability and mixing return when the inertial buoyancy advection reverses. The resulting rolls and instabilities are not aligned with the frontal zone, with an oblique orientation controlled by the Ekman-like instability. Mean turbulence is enhanced when the winds are destabilizing relative to the frontal orientation, but mean Ekman buoyancy advection is found to be relatively unimportant in these simulations. Instead, the mean turbulent kinetic energy balance is dominated by mechanical shear production that is enhanced when the wind-driven shear augments the geostrophic shear, while the resulting vertical mixing nearly eliminates any effective surface buoyancy flux from near-surface, cold-to-warm, Ekman buoyancy advection.

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Natalie Perlin
,
Eric D. Skyllingstad
,
Roger M. Samelson
, and
Philip L. Barbour

Abstract

Air–sea coupling during coastal upwelling was examined through idealized three-dimensional numerical simulations with a coupled atmosphere–ocean mesoscale model. Geometry, topography, and initial and boundary conditions were chosen to be representative of summertime coastal conditions off the Oregon coast. Over the 72-h simulations, sea surface temperatures were reduced several degrees near the coast by a wind-driven upwelling of cold water that developed within 10–20 km off the coast. In this region, the interaction of the atmospheric boundary layer with the cold upwelled water resulted in the formation of an internal boundary layer below 100-m altitude in the inversion-capped boundary layer and a reduction of the wind stress in the coupled model to half the offshore value. Surface heat fluxes were also modified by the coupling. The simulated modification of the atmospheric boundary layer by ocean upwelling was consistent with recent moored and aircraft observations of the lower atmosphere off the Oregon coast during the upwelling season. For these 72-h simulations, comparisons of coupled and uncoupled model results showed that the coupling caused measurable differences in the upwelling circulation within 20 km off the coast. The coastal Ekman transport divergence was distributed over a wider offshore extent and a thinner ocean surface boundary layer, with consistently smaller offshore and depth-integrated alongshore transport formed in the upwelling region, in the coupled case relative to the uncoupled case. The results indicate that accurate models of coastal upwelling processes can require representations of ocean–atmosphere interactions on short temporal and horizontal scales.

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Eric D. Skyllingstad
,
W. D. Smyth
,
J. N. Moum
, and
H. Wijesekera

Abstract

The response of the upper ocean to westerly wind forcing in the western equatorial Pacific was modeled by means of large-eddy simulation for the purpose of comparison with concurrent microstructure observations. The model was initialized using currents and hydrography measured during the Coupled Ocean–Atmosphere Response Experiment (COARE) and forced using measurements of surface fluxes over a 24-h period. Comparison of turbulence statistics from the model with those estimated from concurrent measurements reveals good agreement within the mixed layer. The shortcomings of the model appear in the stratified fluid below the mixed layer, where the vertical length scales of turbulent eddies are limited by stratification and are not adequately resolved by the model. Model predictions of vertical heat and salt fluxes in the entrainment zone at the base of the mixed layer are very similar to estimates based on microstructure data.

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Leif N. Thomas
,
Eric D. Skyllingstad
,
Luc Rainville
,
Verena Hormann
,
Luca Centurioni
,
James N. Moum
,
Olivier Asselin
, and
Craig M. Lee

Abstract

Along with boundary layer turbulence, downward radiation of near-inertial waves (NIWs) damps inertial oscillations (IOs) in the surface ocean; however, the latter can also energize abyssal mixing. Here we present observations made from a dipole vortex in the Iceland Basin where, after the period of direct wind forcing, IOs lost over half their kinetic energy (KE) in two inertial periods to radiation of NIWs with minimal turbulent dissipation of KE. The dipole’s vorticity gradient led to a rapid reduction in the NIW’s lateral wavelength via ζ refraction that was accompanied by isopycnal undulations below the surface mixed layer. Pressure anomalies associated with the undulations were correlated with the NIW’s velocity yielding an energy flux of 310 mW m−2 pointed antiparallel to the vorticity gradient and a downward flux of 1 mW m−2 capable of driving the observed drop in KE. The minimal role of turbulence in the energetics after the IOs had been generated by the winds was confirmed using a large-eddy simulation driven by the observed winds.

Significance Statement

We report direct observational estimates of the vector wave energy flux of a near-inertial wave. The energy flux points from high to low vorticity in the horizontal, consistent with the theory of ζ refraction. The downward energy flux dominates the observed damping of inertial motions over turbulent dissipation and mixing.

Open access
Eric D. Skyllingstad
,
Roger M. Samelson
,
Harper Simmons
,
Lou S. Laurent
,
Sophia Merrifield
,
Thilo Klenz
, and
Luca Centurioni

Abstract

The observed development of deep mixed layers and the dependence of intense, deep-mixing events on wind and wave conditions are studied using an ocean LES model with and without an imposed Stokes-drift wave forcing. Model results are compared to glider measurements of the ocean vertical temperature, salinity, and turbulence kinetic energy (TKE) dissipation rate structure collected in the Icelandic Basin. Observed wind stress reached 0.8 N m−2 with significant wave height of 4–6 m, while boundary layer depths reached 180 m. We find that wave forcing, via the commonly used Stokes drift vortex force parameterization, is crucial for accurate prediction of boundary layer depth as characterized by measured and predicted TKE dissipation rate profiles. Analysis of the boundary layer kinetic energy (KE) budget using a modified total Lagrangian-mean energy equation, derived for the wave-averaged Boussinesq equations by requiring that the rotational inertial terms vanish identically as in the standard energy budget without Stokes forcing, suggests that wind work should be calculated using both the surface current and surface Stokes drift. A large percentage of total wind energy is transferred to model TKE via regular and Stokes drift shear production and dissipated. However, resonance by clockwise rotation of the winds can greatly enhance the generation of inertial current mean KE (MKE). Without resonance, TKE production is about 5 times greater than MKE generation, whereas with resonance this ratio decreases to roughly 2. The results have implications for the problem of estimating the global kinetic energy budget of the ocean.

Open access