Langmuir Cells Research Articles

Influence of Stokes Drift Decay Scale on Langmuir Turbulence

AbstractAccurately scaling Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) is critical for improving ocean, weather, and climate models. The physical processes by which the structure of LT depends on surface waves’ Stokes drift decay length scale are examined. An idealized model for OSBL turbulent kinetic energy (TKE) provides a conceptual framework with three physical processes: TKE transport, dissipation, and production by the Craik–Leibovich (CL) vortex force (VF) associated with the Stokes drift shear. TKE profiles depend on OSBL depth h, surface roughness length z0, and wavenumber k through the nondimensional parameters kh and kz0. These parameters determine the rate and length scale for the dissipation of TKE produced by the CL-VF. For kz0 ≫ 1, TKE input by the CL-VF is governed by a surface flux with TKE rapidly decaying with depth. Only for kz0 < 1 can TKE penetrate deeper into the OSBL, with the TKE penetration depth controlled by kh. Turbulence-resolving large-eddy simulation results support this conceptual framework and indicate that the dominant Langmuir cell size scales with (kh)−1. Within the depth of dominant Langmuir cells, TKE dissipation is approximately balanced by CL-VF production. Shorter waves contribute less to deeper vertical velocity variance 〈w2〉 because the CL-VF is less effective in generating larger-scale LT. Depth-averaged 〈w2〉 scales with a modified Langmuir number Laϕ = (u*/usϕ)1/2, where u* denotes the water-side surface friction velocity and usϕ is a depth-integrated weighted Stokes drift shear or, equivalently, a spectrally filtered surface Stokes drift.

Reply to “Comment on ‘Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters’”

AbstractThis note is a comment in response to Gargett, who argues that a large-eddy estimate of turbulent dissipation rate using a horizontal length scale with a vertical velocity estimate, as in Greene et al., is a dubious approximation if the energy-containing eddies are anisotropic. A simulation of Langmuir cells and associated turbulence is used to support Gargett’s conclusions. This rebuttal reviews the approaches taken by Greene et al. and cites several instances of flawed reasoning by Gargett. This includes using Langmuir simulations to support the primary conclusion of Gargett, which seems unconnected to Greene et al.’s data and ignores a vast body of work on simulating Kelvin–Helmholtz instabilities, widely considered to be the dominant mechanism producing stratified turbulence.

Numerical study on the effects of progressive gravity waves on turbulence

The wind-wave-ocean system, which contains complex interactive processes, is of great importance for the momentum, heat and mass transport in the atmosphere and ocean and at their interface. In this work, we perform wave-coupled phase-resolved numerical simulations to investigate the effect of progressive gravity waves on wind and ocean turbulence. Initially homogeneous turbulence under a finite-amplitude monochromatic surface wave is simulated to reveal how the wave influences the subsurface turbulence. For the interaction between wind-driven waves and shear turbulence in the ocean, new wave-phase-resolved simulation approaches are developed to capture Langmuir cells. Lastly, wind turbulence over one and two progressive waves is simulated to elucidate the dynamics of turbulence coherent structures impacted by surface waves for improved understanding of wind-wave growth mechanism.

Line Vortices and the Vacillation of Langmuir Circulation

AbstractThree types of breakdown of Langmuir circulation (Lc) are observed, two of which are represented in large-eddy simulation (LES) models, but the third, vacillation, is not. The stability of Lc can be examined by representing the downwind-aligned vortices by line vortices that are subjected to perturbations. Earlier conclusions relating to stability in homogeneous water of infinite depth are found to be in error because no stationary unperturbed state exists. The motion of vortices is examined and shown to be consistent with an explanation of Lc devised by Csanady. Motion of line vortices in water of limited depth or bounded below by a thermocline is examined. The motion replicates some of the features of vacillation observed by Smith in deep water bounded by a thermocline, including its periodicity and fluctuations in the formation of bubble bands. Vortices describe closed orbits within the Langmuir cells. Particle motions in the vacillating Lc pattern exhibit trapping close to the line vortices or near the cell boundaries. Vacillation appears not to have been observed in water of limited depth. Here, the vacillation period is predicted to be longer than the deep-water equivalent and may be too long for vacillations to be detected.

LES and RANS simulation of wind- and wave-forced oceanic turbulent boundary layers in shallow water with wall modeling

Abstract Large-eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) simulation of wind and wave forced oceanic turbulence in unstratified shallow water are performed in order to investigate the influence of wall modeling on results. The LES is also used to investigate the dependence of results on downwind and crosswind lengths of the computational domain, representative of a shallow shelf coastal ocean (10-to-30 m deep) unaffected by lateral boundaries. In an unstratified water column, wind and surface gravity-wave forcing generate Langmuir turbulence with largest scales consisting of full-depth Langmuir circulation (LC), counter rotating vortices aligned in the direction of the wind. The LC is known to enhance vertical mixing of momentum throughout the bulk flow, inducing a deviation of the near-bottom mean downwind velocity from the classical log law. In RANS simulations, a traditional wall treatment based on the assumption that the flow satisfies the classical law of the wall is not able to lead to a good representation of the deviation from the log law caused by LC without fine-tuning of one of the coefficients in the law of the wall. An alternative RANS approach is developed via a recent wall treatment presented in [1] based on weak imposition of the no-slip bottom boundary condition, leading to an accurate representation of the log-law deviation induced by the turbulence without having to tune input coefficients. From that standpoint, this weak enforcement of bottom boundary conditions is more robust and better suited for predictive modeling of flows with full-depth LC. In the case of LES, it is found that the deviation of the downwind velocity from the log law caused by the LC is well-resolved without the need to fine tune coefficients in traditional wall treatments. Finally, the use of wall modeling facilitates simulations with expanded domains over horizontal directions (downwind and crosswind). These expanded domains allow resolution of multiple interacting full-depth Langmuir cells. It is found that the horizontal size of the domain does not greatly impact depth profiles of turbulence statistics such as mean velocity and root-mean-square of velocity.

DNS and measurements of scalar transfer across an air-water interface during inception and growth of Langmuir circulation

Direct numerical simulations (DNS) of an initially quiescent coupled air-water interface driven by an air flow with free stream speed of 5 m/s have been conducted and scalar transfer from the air side to the water side and subsequent vertical transport in the water column have been analysed. Two simulations are compared: one with a freely deforming interface, giving rise to gravity-capillary waves and aqueous Langmuir turbulence (LT) characterized by small-scale (centimeter-scale) Langmuir cells (LC), and the other with the interface intentionally held flat, i.e., without LC. It is concluded that LT serves to enhance vertical transport of the scalar in the water side and in the process increases scalar transfer efficiency from the air side to the water side relative to the shear-dominated turbulence in the flat interface case. Furthermore, transition to LT was observed to be accompanied by a spike in scalar flux characterized by an order of magnitude increase. These episodic flux increases, if linked to gusts and overall unsteadiness in the wind field, are expected to be an important contributor in determining the long-term average of the air-sea gas fluxes.

Effects of swell on transport and dispersion of oil plumes within the ocean mixed layer

AbstractThe transport in the ocean mixed layer (OML) of oil plumes originated from deepwater blowouts is studied using large eddy simulations. In particular, we focus on the effects of swell on the modulation of turbulence in the OML and its impact on oil transport. Results show that when the misalignment between the wind and the swell propagation is small, Langmuir cells develop and significantly enhance the vertical dilution of the oil plume. Conversely, when the misalignment is large, vertical dilution is suppressed when compared to the no‐swell case. Due to the strong directional shear of the mean flow within the OML, plume depth significantly impacts mean transport direction. The size of oil droplets in the plume also plays an important role in vertical dilution and mean transport direction.

Surface boundary layer evolution and near‐inertial wind power input

AbstractDeep weakly stratified surface layers in the Southern Ocean complicate the identification of the mixed‐layer base, which is critical in estimating the wind power input through the ocean surface. Typically used mixed‐layer depth criteria often ignore weak stratification, which traps momentum near the surface and significantly enhances the near‐inertial‐band wind power input. The thickness of the active mixing‐layer, the turbulent layer in contact with wind stress, is needed to accurately estimate wind power input. A fine‐density‐threshold criterion of 0.005 kg m−3, just above the noise floor of most autonomous instruments, was applied to observed profiles of potential density to estimate the thickness of the actively mixing‐layer. Vertical shear, Langmuir cells, and buoyant convection are investigated as possible mechanisms maintaining turbulence within the mixing‐layer. Over 90% of the observed variance of the mixing‐layer thickness is explained by either shear‐driven entrainment, which is simulated using the Price‐Weller‐Pinkel model, or by a parameterization of downwelling plumes due to Langmuir cell convergence. In general, surface buoyancy fluxes are too weak to drive mixed‐layer turbulence. Comparison of National Oceanographic Data Center (NODC) climatological mixed‐layer thickness to those determined using the 0.005 kg m−3 density threshold suggests a multiplicative seasonally varying correction of 1.5–3.5 should be applied to wind work estimates made using the NODC climatological mixed‐layer thickness in the Southern Ocean.

Numerical Evidence of Turbulence Generated by Nonbreaking Surface Waves

AbstractNumerical simulation of monochromatic surface waves propagating over a turbulent field is conducted to reveal the mechanism of turbulence production by nonbreaking waves. The numerical model solves the primitive equations subject to the fully nonlinear boundary conditions on the exact water surface. The result predicts growth rates of turbulent kinetic energy consistent with previous measurements and modeling. It also validates the observed horizontal anisotropy of the near-surface turbulence that the spanwise turbulent intensity exceeds the streamwise component. Such a flow structure is found to be attributed to the formation of streamwise vortices near the water surface, which also induces elongated surface streaks. The averaged spacing between the streaks and the depth of the vortical cells approximates that of Langmuir turbulence. The strength of the vortices arising from the wave–turbulence interaction, however, is one order of magnitude less than that of Langmuir cells, which arises from the interaction between the surface waves and the turbulent shear flow. In contrast to Langmuir turbulence, production from the Stokes shear does not dominate the energetics budget in wave-induced turbulence. The dominant production is the advection of turbulence by the velocity straining of waves.

Observations and numerical simulations of large‐eddy circulation in the ocean surface mixed layer

AbstractTwo near‐surface dye releases were mapped on scales of minutes to hours temporally, meters to order 1 km horizontally, and 1–20 m vertically using a scanning, depth‐resolving airborne lidar. In both cases, dye evolved into a series of rolls with their major axes approximately aligned with the wind and/or near‐surface current. In both cases, roll spacing was also of order 5–10 times the mixed layer depth, considerably larger than the 1–2 aspect ratio expected for Langmuir cells. Numerical large‐eddy simulations under similar forcing showed similar features, even without Stokes drift forcing. In one case, inertial shear driven by light winds induced large aspect ratio large‐eddy circulation. In the second, a preexisting lateral mixed layer density gradient provided the dominant forcing. In both cases, the growth of the large‐eddy structures and the strength of the resulting dispersion were highly dependent on the type of forcing.

Turbulence structure in the upper ocean: a comparative study of observations and modeling

Observations of turbulent dissipation rates measured by two independent instruments are compared with numerical model runs to investigate the injection of turbulence generated by sea surface gravity waves. The near-surface observations are made by a moored autonomous instrument, fixed at approximately 8 m below the sea surface. The instrument is equipped with shear probes, a high-resolution pressure sensor, and an inertial motion package to measure time series of dissipation rate and nondirectional surface wave energy spectrum. A free-falling profiler is used additionally to collect vertical microstructure profiles in the upper ocean. For the model simulations, we use a one-dimensional mixed layer model based on a k–ε type second moment turbulence closure, which is modified to include the effects of wave breaking and Langmuir cells. The dissipation rates obtained using the modified k–ε model are elevated near the sea surface and in the upper water column, consistent with the measurements, mainly as a result of wave breaking at the surface, and energy drawn from wave field to the mean flow by Stokes drift. The agreement between observed and simulated turbulent quantities is fairly good, especially when the Stokes production is taken into account.

Inhibition of oil plume dilution in Langmuir ocean circulation

Oil spills from deep‐water blowouts rise through and interact with the ocean mixed layer and Langmuir turbulence, leading to considerable diversity of oil slick dilution patterns observed on the ocean surface. Certain conditions can drive oil droplet plumes to organize into distinct bands called windrows, inhibiting oil dilution. Observations of blurred or even diffused plumes are also common, but conditions under which these various dilution regimes emerge are not well understood. Here we use large eddy simulations to explain and quantify the dilution patterns and their dependence on relevant physical parameters. Two mechanisms, the downwelling and dilution due to Langmuir cells and the inhibition of dilution due to buoyancy of oil droplets, compete. This competition can be characterized by the ratio of Stokes drift to droplet rise velocity—the drift‐to‐buoyancy parameter, Db. We find that plume appearance and quantitative measures of relative dilution depend mainly on Db.

Characteristics of interfacial signatures on a wind-driven gravity-capillary wave

[1] Direct numerical simulation of a wind-driven gravity-capillary wave and the underlying turbulent flow is conducted to identify the characteristic signatures of various surface parameters, including temperature, gas flux, velocities, and roughness, and to reveal the impacts of the nonbreaking surface waves on these surface flow and tracer parameters. Three characteristic surface signatures and the corresponding flow processes are identified: the carrier gravity wave, the parasitic capillary wavelets, and the elongated streaks. The elongated streaks are induced by both the coherent streamwise vortices formed within the turbulent shear layer and the Langmuir circulations arising from nonlinear interaction between the carrier gravity wave and the drift current. All three surface signatures can be observed in the distributions of various quantities, although some are more apparent than the others. Image-processing techniques, employing empirical mode decomposition and phase averaging, are developed to decompose the distinct signatures thus to quantify the contributions by the responsible flow processes. It is found that elongated streaks prevail the distribution of surface temperature and gas flux, indicating that Langmuir cells and the coherent eddies contribute to the major interfacial heat and gas transport. These eddies also induced strong cross-stream velocity divergence at the water surface, which exhibits resemblant elongated distribution as that of gas flux (correlation coefficient � 0.6). High correlation between the surface distributions of temperature and gas flux is observed (correlation coefficient � 0.8 to 0.9), suggesting that the spatial and temporal distribution of surface temperature is a good proxy tracer of interfacial gas transfer.

Transient Evolution of Langmuir Turbulence in Ocean Boundary Layers Driven by Hurricane Winds and Waves

Abstract A large-eddy simulation (LES) model, which adopts wave-averaged equations with vortex force, is used to investigate Langmuir turbulence and ocean boundary layer (OBL) dynamics in high-wind hurricane conditions. The temporally evolving spatially asymmetric wind and wave Stokes drift velocity imposed in the LES are generated by a spectral wave prediction model adapted to Hurricane Frances traveling at a speed of 5.5 m s−1. The potency of Langmuir turbulence depends on the turbulent Langmuir number, the wind–Stokes drift alignment, and the depth scale of the Stokes profile Ds relative to the OBL depth h. At the time of maximum winds, large-scale vigorous coherent cells develop on the right-hand side of the storm under the inertially rotating winds; the Stokes drift velocity is well tuned to the surface winds. Much weaker cells develop on the left-hand side of the storm, partly because of reduced Stokes production. With misaligned winds and waves the vertical momentum fluxes can be counter to the gradient of Stokes drift, and the cell orientation tracks the direction of the mean Lagrangian shear. The entrainment flux is increased by 20% and the sea surface temperature is 0.25 K cooler on the right-hand side of the storm in the presence of Langmuir turbulence. Wave effects impact entrainment when the ratio Ds/|h| > 0.75. Because of wind–wave asymmetry Langmuir cells add quantitatively to the left–right asymmetry already understood for hurricanes due to resonance. And the transient evolution of the OBL cannot be understood simply in terms of equilibrium snapshots.

The form and orientation of Langmuir cells for misaligned winds and waves

Large eddy simulations of the Craik‐Leibovich equations are used to assess the effect of misaligned Stokes drift and wind direction on Langmuir cells in the ocean mixed layer. Misalignments from 0° to 135° are examined and Langmuir turbulence structures are evident in all cases. The Stokes drift is modeled using a broadband empirical spectrum, and cases with and without the Coriolis effect, wind waves, and an initial mixed layer are examined. The expected scaling for the vertical velocity variance is recovered in the aligned simulations and is adapted here to the misaligned cases. The adjusted scaling projects the friction velocity (aligned with the wind stress) into the dominant axial direction of the Langmuir cells. The turbulent Langmuir number is generalized through a similar projection into the axial direction of the Langmuir cells, which reduces its value in realistic conditions. For known Langmuir cell orientations, the strength of Langmuir turbulence for misaligned cases can be estimated using the projected Langmuir number. A prediction for the angle between the wind stress and cell direction is obtained using the law of the wall; this prediction only requires the wind stress, Stokes drift, and boundary layer depth. Conditional analyses show that, with increasing misalignment, the typically antisymmetric Langmuir cell pairs become asymmetric. This asymmetry is due, in part, to the advection by cross cell flow of vorticity from one vortex tube onto the other, and in part due to an asymmetry induced by the stretching of vertical vorticity into cross cell vorticity.

The influence of crosswind tidal currents on Langmuir circulation in a shallow ocean

[1] Langmuir circulation (LC) is a turbulent process driven by wind and surface waves that plays a key role in transferring momentum, heat, and mass in the oceanic surface layer. On the coastal shelves the largest-scale LC span the whole water column and thus couple the surface and bottom boundary layers and enhance turbulent mixing. Observations and large eddy simulations (LES) of a shallow coastal ocean demonstrate that these relatively large scale Langmuir cells are strongly influenced by crosswind tidal currents. Two mechanisms by which crosswind tidal shear may distort and disrupt Langmuir cells are proposed. The first mechanism involves cell shearing due to differential advection across the whole cell. For the second mechanism, middepth vertical LC currents advect sheared mean crosswind current, leading to the attraction of upwelling and downwelling regions, so that LC cells are unsustainable when both regions overlap. Scaling arguments indicate that LC cells are more susceptible to crosswind shear distortion for smaller LC surface velocity convergence and greater cell aspect ratio (vertical to horizontal LC scale), which is consistent with the results obtained from the observations and LES. These results imply that scaling of LC characteristics in a coastal ocean differs from that in the open ocean, which has important practical implications for parameterizing enhanced mixing due to LC.

Contribution of coherent vortices such as Langmuir cells to wind‐driven surface layer mixing

The wind blowing over the water surface causes, even for low wind speeds, Langmuir circulation in addition to shear‐generated turbulence. Both of these mechanisms mix the upper layer of oceans and lakes, but since the mixing efficiency of Langmuir cells is unknown, their relevance to mixed layer deepening is still an open question. In order to estimate the contribution to mixing by Langmuir vortex cells relative to shear‐induced mixing, we employ results on entrainment rate obtained from laboratory experiments with turbulent Taylor vortex cells. These are coherent horizontal vortices analogous to Langmuir cells. To relate the two, we define a surface friction velocity u* that would be necessary to drive cells of strength equivalent to the Taylor vortices. It is then shown that up to a friction Richardson number of Ri* ≈ 50, layer deepening is predominantly caused by shear‐generated turbulence, whereas for Ri* > 50, the contribution by turbulent coherent vortices (Langmuir cells) dominates the mixing process. For Richardson numbers Ri* > 120, the entrainment rate decreases, but there is no criterion for the arrest of mixing by turbulent Langmuir cells as was previously suggested. The present results confirm observations that shear‐generated turbulence dominates during initial layer deepening under relatively weak buoyancy effects and that subsequently Langmuir cell mixing dominates the mixed layer deepening. The entrainment rates obtained from laboratory experiments are discussed and predict values for the mixed layer deepening that are in good agreement with in situ observations.

Effect of Langmuir cells on bubble dissolution and air‐sea gas exchange

Gases are exchanged between the atmosphere and ocean by diffusion through the sea surface and by dissolution of air bubbles injected by breaking wind waves. Langmuir cells enhance the contribution from bubbles by keeping them under water for longer thus increasing their dissolution. We determine the importance of Langmuir cells by using a bubble model to calculate the amount of gas that dissolves from bubbles as a function of wind speed, gas saturation, and injection depth and a Langmuir cell model to estimate the effect of the associated downwelling currents on bubble dissolution. The calculations are preformed for the eight gases N2, O2, CO2, He, Ne, Ar, Kr, and Xe, and the results are then compared with the total gas exchange determined by common descriptions of air‐sea gas exchange. The contribution of gas bubbles to air‐sea gas exchange increases with wind speed and can reach 77% for O2, 98% for N2, and 16% for CO2 at a wind speed of 20 m s−1 and a gas saturation of 95%. The additional effect of Langmuir cells on the total gas exchange at a gas saturation of 95% is 19% for O2, 35% for N2, and 0.7% for CO2. The importance of Langmuir cells for air‐sea gas exchange generally increases with gas saturation and decreases with the solubility of the gas.

Spreading of floating particles by Langmuir circulation

Particles floating on the sea surface, in particular buoyant algae, are drawn into bands by the converging flow between neighbouring Langmuir cells. Floating bands subsequently amalgamate as a result of Langmuir turbulence. Simple models are developed to describe the rearrangement and dispersion of the floating particles. If the production of floating particles has ceased, the mean separation of the bands of particles increases with time and eventually becomes unrelated to the mean distance between the lines of convergence resulting from Langmuir circulation. The concentration of particles in the bands, proportional to the width of bands, and the separation of bands with a given concentration of particles, both increase with time. Care is needed in estimating the width of Langmuir cells to distinguish between surface bands of floating material that is continuously being produced and bands made visible by some earlier, but discontinued, generation. An alternative mechanism for the generation of dense bands of floating algae is proposed.

Optics and remote sensing of Bahamian carbonate sediment whitings and potential relationship to wind-driven Langmuir circulation

Abstract. Regions of milky white seas or "whitings" periodically occur to the west of Andros Island along the Great Bahama Bank where the bottom sediment consists of fine-grained aragonite mud. We present measurements of inherent optical properties within a sediment whiting patch and discuss the potential for monitoring the frequency, extent, and quantity of suspended matter from ocean colour satellite imagery. Sea spectral reflectance measured in situ and remotely from space revealed highly reflective waters elevated across the visible spectrum (i.e., "whitened") with a peak at 490 nm. Particulate backscattering was an order of magnitude higher than that measured at other stations throughout the region. The whiting also had one of the highest backscattering ratios measured in natural waters (0.05–0.06) consistent with water dominated by aragonite particles with a high index of refraction. Regular periodicity of 40 and 212 s evident in the light attenuation coefficient over the sampling period indicated patches of fluctuating turbidity on spatial scales that could be produced from regular rows of Langmuir cells penetrating the 5-m water column. We suggest that previously described mechanisms for sediment resuspension in whitings, such as tidal bursting and fish activity, are not fully consistent with these data and propose that wind-driven Langmuir cells reaching the full-depth of the water column may represent a plausible mechanism for sediment resuspension and subsequent whiting formation. Optics and remote sensing provide important tools for quantifying the linkages between physical and biogeochemical processes in these dynamic shallow water ecosystems.