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Ramsey R. Harcourt

Abstract

A prior second-moment closure (SMC) model of Langmuir turbulence in the upper ocean is modified by introduction of inhomogeneous pressure–strain rate and pressure–scalar gradient closures that are similar to the high Reynolds number, near-wall treatments for solid wall boundaries. This repairs several near-surface defects in the algebraic Reynolds stress model (ARSM) of the prior SMC by redirecting Craik–Leibovich (CL) vortex force production of turbulent kinetic energy out of the surface-normal vertical component and into a horizontal one, with an associated reduction in near-surface CL production of vertical momentum flux. A surface-proximity function introduces a new closure parameter that is tuned to previous results from large-eddy simulations (LES), and a numerical SMC model based on stability functions from the new ARSM produces improved comparisons with mean profiles of momentum and TKE components from steady-state LES results forced by aligned wind and waves. An examination of higher-order quasi-homogeneous closures and a numerical simulation of Langmuir turbulence away from the boundaries both show the near-surface inhomogeneous closure to be both necessary for consistency and preferable for simplicity.

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Ramsey R. Harcourt

Abstract

The Reynolds stress equation is modified to include the Craik–Leibovich vortex force, arising from the interaction of the phase-averaged surface wave Stokes drift with upper-ocean turbulence. An algebraic second-moment closure of the Reynolds stress equation yields an algebraic Reynolds stress model (ARSM) that requires a component of the vertical momentum flux to be directed down the gradient of the Stokes drift, in addition to the conventional component down the gradient of the ensemble-averaged Eulerian velocity. For vertical and horizontal component fluctuations, the momentum flux must be closed using the form , where the coefficient is generally distinct from the eddy viscosity or eddy diffusivity . Rational expressions for the stability functions , , and are derived for use in second-moment closure models where the turbulent velocity and length scales are dynamically modeled by prognostic equations for and . The resulting second-moment closure (SMC) includes the significant effects of the vortex force in the stability functions, in addition to source terms contributing to the and equations. Additional changes are made to the way in which is limited by proximity to boundaries or by stratification. The new SMC model is tuned to, and compared with, a suite of steady-state large-eddy simulation (LES) solutions representing a wide range of oceanic wind and wave forcing conditions. Comparisons with LES show the modified SMC captures important processes of Langmuir turbulence, but not without notable defects that may limit model generality.

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Tobias Kukulka and Ramsey R. Harcourt

Abstract

Accurately 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 z 0, and wavenumber k through the nondimensional parameters kh and kz 0. These parameters determine the rate and length scale for the dissipation of TKE produced by the CL-VF. For kz 0 ≫ 1, TKE input by the CL-VF is governed by a surface flux with TKE rapidly decaying with depth. Only for kz 0 < 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 〈w 2〉 because the CL-VF is less effective in generating larger-scale LT. Depth-averaged 〈w 2〉 scales with a modified Langmuir number Laϕ = (u */u )1/2, where u * denotes the water-side surface friction velocity and u is a depth-integrated weighted Stokes drift shear or, equivalently, a spectrally filtered surface Stokes drift.

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Ramsey R. Harcourt and Eric A. D’Asaro

Abstract

The scaling of turbulent kinetic energy (TKE) and its vertical component (VKE) in the upper ocean boundary layer, forced by realistic wind stress and surface waves including the effects of Langmuir circulations, is investigated using large-eddy simulations (LESs). The interaction of waves and turbulence is modeled by the Craik–Leibovich vortex force. Horizontally uniform surface stress τ 0 and Stokes drift profiles u S(z) are specified from the 10-m wind speed U 10 and the surface wave age CP/U 10, where CP is the spectral peak phase speed, using an empirical surface wave spectra and an associated wave age–dependent neutral drag coefficient CD. Wave-breaking effects are not otherwise included. Mixed layer depths H ML vary from 30 to 120 m, with 0.6 ≤ CP/U 10 ≤ 1.2 and 8 m s−1 < U 10 < 70 m s−1, thereby addressing most possible oceanic conditions where TKE production is dominated by wind and wave forcing.

The mixed layer–averaged “bulk” VKE 〈w 2〉/u*2 is equally sensitive to the nondimensional Stokes e-folding depth D*S/H ML and to the turbulent Langmuir number Lat = u*/US, where u* = |τ0|/ρw in water density ρw and US = |u S|z=0. Use of a D*S scale-equivalent monochromatic wave does not accurately reproduce the results using a full-surface wave spectrum with the same e-folding depth. The bulk VKE for both monochromatic and broadband spectra is accurately predicted using a surface layer (SL) Langmuir number LaSL = u*/〈uSSL, where 〈u SSL is the average Stokes drift in a surface layer 0 > z > − 0.2H ML relative to that near the bottom of the mixed layer. In the wave-dominated limit LaSL → 0, turbulent vertical velocity scales as w rmsu*La−2/3 SL. The mean profile (z) of VKE is characterized by a subsurface peak, the depth of which increases with D*S/H ML to a maximum near 0.22H ML as its relative magnitude /〈w 2〉 decreases. Modestly accurate scalings for these variations are presented. The magnitude of the crosswind velocity convergence scales differently from VKE. These results predict that for pure wind seas and H ML ≅ 50 m, 〈w 2〉/u*2 varies from less than 1 for young waves at U 10 = 10 m s−1 to about 2 for mature seas at winds greater than U 10 = 30 m s−1. Preliminary comparisons with Lagrangian float data account for invariance in 〈w 2〉/u*2 measurements as resulting from an inverse relationship between U 10 and CP/U 10 in observed regimes.

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Ramsey R. Harcourt and Eric A. D’Asaro

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The effects of upward buoyancy on the accuracy with which Lagrangian floats can measure the Eulerian mean variance 〈wwE and skewness SwE of vertical fluid velocity w in the wind-driven upper-ocean boundary layer is investigated using both simulated floats in large-eddy simulation (LES) models and two float datasets. Nearly neutrally buoyant floats are repeatedly advected by the turbulent velocities across the boundary layer. Their vertical position Z is determined from pressure measurements; their W variance 〈WWF and skewness SWE are determined from the time series of float W = dZ/dt. If the float buoyancy is small, then the simulated floats measure the Eulerian velocity accurately; that is, δW 2 = 〈WWF − 〈wwE and δSW = SWFSwE are small compared to 〈wwE and SwE respectively. If the floats are buoyant, and thus have an upward vertical velocity W bias relative to the water, then δW 2 and δSW can become significant. Buoyancy causes the floats to oversample both shallow depths and strong vertical velocities, leading to positive values of δW 2 and negative values of δSW. The skewness S Z F of depth measures the degree to which shallow depths are oversampled; it is shown to be a good predictor of W bias/〈WWF 1/2, δW 2/〈WWF〉, and δSW/SWF over a wide range of float buoyancies and boundary layer forcings. Float data collected during two deployments confirm these results, but averaging times of several float days are typically required to obtain stable statistics. Significant differences in the magnitude of the effect may occur between datasets from different ocean forcing regimes and float designs. Other measures of float buoyancy are also useful predictors. These results can be used to correct existing float measurements of 〈wwE for the effects of buoyancy and also can be used as a means to operationally assess and control float buoyancy.

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Zhihua Zheng, Ramsey R. Harcourt, and Eric A. D’Asaro

Abstract

Monin-Obukhov Similarity Theory (MOST) provides important scaling laws for flow properties in the surface layer of the atmosphere and has contributed to most of our understanding of the near-surface turbulence. The prediction of near-surface vertical mixing in most operational ocean models is largely built upon this theory. However, the validity of MOST in the upper ocean is questionable due to the demonstrated importance of surface waves in the region. Here we examine the validity of MOST in the statically unstable oceanic surface layer, using data collected from two open ocean sites with different wave conditions. The observed vertical temperature gradients are found to be about half of those predicted by MOST. We hypothesize this is attributable to either the breaking of surface waves, or Langmuir turbulence generated by the wave-current interaction. Existing turbulence closure models for surface wave breaking and for Langmuir turbulence are simplified to test these two hypotheses. Although both models predict reduced temperature gradients, the simplified Langmuir turbulence model matches observations more closely, when appropriately tuned.

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Ramsey R. Harcourt, Elizabeth L. Steffen, Roland W. Garwood, and Eric A. D'Asaro

Abstract

Measurements of deep convection from fully Lagrangian floats deployed in the Labrador Sea during February and March 1997 are compared with results from model drifters embedded in a large eddy simulation (LES) of the rapidly deepening mixed layer. The deep Lagrangian floats (DLFs) have a large vertical drag, and are designed to nearly match the density and compressibility of seawater. The high-resolution numerical simulation of deep convective turbulence uses initial conditions and surface forcing obtained from in situ oceanic and atmospheric observations made by the R/V Knorr. The response of model floats to the resolved large eddy fields of buoyancy and velocity is simulated for floats that are 5 g too buoyant, as well as for floats that are correctly ballasted. Mean profiles of potential temperature, Lagrangian rates of heating and acceleration, vertical turbulent kinetic energy (TKE), vertical heat flux, potential temperature variance, and float probability distribution functions (PDFs) are compared for actual and model floats.

Horizontally homogeneous convection, as represented by the LES model, accounts for most of the first and second order statistics from float observations, except that observed temperature variance is several times larger than model variance. There are no correspondingly large differences in vertical TKE, heat flux, or mixed layer depth. The augmented temperature variance may be due to mixing across large-scale temperature and salinity gradients that are largely compensated in buoyancy. The rest of the DLF statistics agree well with the response of correctly ballasted model floats in the lowest 75% of the mixed layer, and are less consistent with results from buoyantly ballasted model floats.

Other differences between observation and simulation in the mean profiles of heat flux, vertical TKE, and Lagrangian heating and vertical acceleration rates are confined to the upper quarter of the mixed layer. These differences are small contributions to layer-averaged quantities, but represent statistically significant profile features. Larger observed values of heat flux and vertical TKE in the upper quarter of the mixed layer are more consistent with model floats ballasted light. Float buoyancy, however, cannot fully account for the observed PDFs, temperature profiles, and Lagrangian rates of heating and acceleration. A test of Lagrangian self-consistency comparing vertical TKE and Lagrangian acceleration also shows that DLF measurements are not significantly affected by excess float buoyancy. These upper mixed layer features may instead be due to the interaction of wind-driven currents and baroclinicity.

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Eleanor Frajka-Williams, Charles C. Eriksen, Peter B. Rhines, and Ramsey R. Harcourt

Abstract

Vertical velocities in the world’s oceans are typically small, less than 1 cm s−1, posing a significant challenge for observational techniques. Seaglider, an autonomous profiling instrument, can be used to estimate vertical water velocity in the ocean. Using a Seaglider’s flight model and pressure observations, vertical water velocities are estimated along glider trajectories in the Labrador Sea before, during, and after deep convection. Results indicate that vertical velocities in the stratified ocean agree with the theoretical Wentzel–Kramers–Brillouin (WKB) scaling of w; and in the turbulent mixed layer, scale with buoyancy, and wind forcing. It is estimated that accuracy is to within 0.5 cm s−1. Because of uncertainties in the flight model, velocities are poor near the surface and deep apogees, and during extended roll maneuvers. Some of this may be improved by using a dynamic flight model permitting acceleration and by better constraining flight parameters through pilot choices during the mission.

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Andrey Y. Shcherbina, Michael C. Gregg, Matthew H. Alford, and Ramsey R. Harcourt

Abstract

A monthlong field survey in July 2007, focused on the North Pacific subtropical frontal zone (STFZ) near 30°N, 158°W, combined towed depth-cycling conductivity–temperature–depth (CTD) profiling with shipboard current observations. Measurements were used to investigate the distribution and structure of thermohaline intrusions. The study revealed that local extrema of vertical salinity profiles, often used as intrusion indicators, were only a subset of a wider class of distortions in thermohaline fields due to interleaving processes. A new method to investigate interleaving based on diapycnal spiciness curvature was used to describe an expanded class of laterally coherent intrusions. STFZ intrusions were characterized by their overall statistics and by a number of case studies. Thermohaline interleaving was particularly intense within 5 km of two partially compensated fronts, where intrusions with both positive and negative salinity anomalies were widespread. The vertical and cross-frontal scales of the intrusions were on the order of 10 m and 5 km, respectively. Though highly variable, the slopes of these features were typically intermediate between those of isopycnals and isohalines. Although the influence of double-diffusive processes sometime during the evolution of intrusions could not be excluded, the broad spectrum of the observed features suggests that any role of double diffusion was secondary.

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Tyler J. Rabe, Tobias Kukulka, Isaac Ginis, Tetsu Hara, Brandon G. Reichl, Eric A. D’Asaro, Ramsey R. Harcourt, and Peter P. Sullivan

Abstract

Extreme winds and complex wave fields drive upper-ocean turbulence in tropical cyclone conditions. Motivated by Lagrangian float observations of bulk vertical velocity variance (VVV) under Hurricane Gustav (2008), upper-ocean turbulence is investigated based on large-eddy simulation (LES) of the wave-averaged Navier–Stokes equations. To realistically capture wind- and wave-driven Langmuir turbulence (LT), the LES model imposes the Stokes drift vector from spectral wave simulations; both the LES and wave model are forced by the NOAA Hurricane Research Division (HRD) surface wind analysis product. Results strongly suggest that without LT effects simulated VVV underestimates the observed VVV. LT increases the VVV, indicating that it plays a significant role in upper-ocean turbulence dynamics. Consistent with observations, the LES predicts a suppression of VVV near the hurricane eye due to wind-wave misalignment. However, this decrease is weaker and of shorter duration than that observed, potentially due to large-scale horizontal advection not present in the LES. Both observations and simulations are consistent with a highly variable upper ocean turbulence field beneath tropical cyclone cores. Bulk VVV, a TKE budget analysis, and anisotropy coefficient (ratio of horizontal to vertical velocity variances) profiles all indicate that LT is suppressed to levels closer to that of shear turbulence (ST) due to misaligned wind and wave fields. VVV approximately scales with the directional surface layer Langmuir number. Such a scaling provides guidance for the development of an upper-ocean boundary layer parameterization that explicitly depends on sea state.

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