Abstract

Neutrally buoyant, high-drag floats were used to measure vertical velocity in the upper-ocean mixed layer during a period of rapid mixed layer deepening resulting from a storm. Salinity and temperature profiles, air–sea fluxes, and surface wave spectra were also measured. The location, Georgia Strait, British Columbia, is coastal with strong horizontal variability and may not be representative of the open ocean. The floats moved freely within the deepening mixed layer; the envelope of their motion corresponded closely to the extent of the mixed layer. The maximum vertical velocity was 0.12 m s⁻¹; the rms vertical velocity was about (0.02 m s⁻¹)². The mean square vertical velocity, excluding surface waves, was 1.5–3.0 u ²∗ , clearly higher than the upper bound of u ²∗ found in solid-wall turbulent boundary layers. The authors speculate that these anomalously high vertical velocities were due to Langmuir circulations generated by surface waves. These cannot occur in solid-wall boundary layers.

Abstract

During the winters of 1997 and 1998, a total of 24 Lagrangian floats were deployed in the Labrador Sea. These floats were designed to match the buoyancy and compressibility of seawater. They measured temperature and three-dimensional position (pressure for vertical position and RAFOS acoustic tracking for latitude and longitude) as they followed water motions three-dimensionally. This data provides direct observation of mixed layer depth and excellent estimates of vertical velocity. Floats were repeatedly carried across the convecting layer by vertical velocities averaging several centimeters per second with vertical excursions of up to one kilometer. In the horizontal, several scales of eddy motion were resolved, as was a possible float predilection toward remaining in water preconditioned for convection. Heat flux estimates from this data reveal entrainment and surface heat fluxes similar in magnitude. The mixed layer acts as a vertical conveyor belt of temperature, transporting heat from depth to the surface without requiring a net change in mixed layer temperature, since incorporation of salt from below allows an increase in density without a net change in temperature. Comparison with NCEP reanalysis meteorological heat flux and wind magnitude data shows that the vertical velocity variance can be modeled with 80% skill as a linear function of lagged buoyancy flux (with the atmosphere leading the ocean by ∼1/2 day) without using the wind estimates. Mixed layer motions are clearly driven by the surface buoyancy flux, B _o . A nonrotating scaling of vertical velocity variance, (B _o H)^1/3, provides a marginally better fit than a rotating scaling, (B _o /f)^1/2. Horizontal effects appear to play only a weak role during strong convection but result in rapid restratification when convective forcing weakens.

Abstract

D'Asaro, in previous work using nearly neutrally buoyant Lagrangian floats in a wind forced mixed layer, found 〈w ²〉 = A u ² _∗ , where 〈w ²〉 is the mean square vertical velocity and u∗ is the friction velocity estimated from shipboard meteorological measurements using bulk formulas. Depth profiles of A(z) = 〈w ²〉(z)/ u ² _∗ within the mixed layer showed a maximum value of A(z) of about 2, which is 1.75–2 times that measured in solid-wall turbulent boundary layers driven by a wall stress alone. This result implied that the ocean mixed layer was more energetic than shear-driven turbulent boundary layers driven by the same stress. Here these results are verified using observations of vertical velocity in the mixed layer from 72 float days of data from two Lagrangian floats in the North Pacific Ocean in the autumn of 2000. These floats were more neutrally buoyant than those used previously by D'Asaro, thus reducing possible biases. Wind stress was estimated from Quick Scatterometer satellite measurements and is thus subject to errors and biases different from those in D'Asaro's previous work. Despite these instrumental differences, the new results are very similar to those of the previous work, except that no corrections for internal wave velocities are needed. The values of 〈w ²〉^1/2 and u∗ are correlated well, and the maximum value of A(z) is near 2.

Abstract

Intensive data collection in the region of the Labrador Sea northwest of former Ocean Weather Station Bravo during the winter of 1998 allowed examination of the meso- and submesoscale structure during active convection. Data used include shipboard CTDs, shipboard underway data, isobaric CTD profiling floats, and high-drag floats whose trajectories were approximately Lagrangian in the horizontal and vertical directions. On the mesoscale, O(20 km), horizontal variability was nearly 1°C and 0.1 psu. An anticyclonic eddy of 40-km diameter was found. On a smaller scale, O(5 km), variability of 0.04 psu and 0.3°C was found. By utilizing data from fully Lagrangian floats, this smaller-scale field was found to be organized into eddies of 1–12-km radius. Both cyclonic and anticyclonic features were found, with the anticyclones being larger. This observation may explain the excess of anticyclones reported in previous studies having lower spatial resolution. These features were unsteady, with an anticyclone doubling in size in less than a week. There was communication between eddies, with four of five floats escaping an anticyclone. This exchange produced horizontal diffusivities (250–350 m² s⁻¹) on the order of basin-scale values, implying these small-scale features could produce the majority of the stirring. The influence of these structures on convection was explored: convection occurred throughout the region sampled despite the presence of eddies, the deepest mixed layers were found within an anticyclone, and convective trajectories within small cyclones were found to be significantly tilted so as to avoid the surface centers of the cyclones.

Abstract

Stratified flows are often a mixture of waves and turbulence. Here, Lagrangian frequency is used to distinguish these two types of motion.

A set of 52 Lagrangian float trajectories from Knight Inlet and 10 trajectories from below the mixed layer in the wintertime northeast Pacific were analyzed using frequency spectra. A subset of 28 trajectories transit the Knight Inlet sill where energetic internal waves and strong turbulent mixing coexist.

Vertical velocity spectra show a progression from a nearly Garrett–Munk internal wave spectrum at low energies to a shape characteristic of homogeneous turbulence at high energies. All spectra show a break in slope at a frequency close to the buoyancy frequency N. Spectra from the Knight Inlet sill are analyzed in more detail. For “subbuoyant” frequencies (less than N) all 28 spectra exhibit a ratio of vertical-to-horizontal kinetic energy that varies with frequency as predicted by the linear internal wave equations. All spectra have a shape similar to that of the Garrett–Munk internal wave spectrum at subbuoyant frequencies. These motions are much more like waves than turbulence. For “superbuoyant” frequencies (greater than N) all 28 spectra are isotropic and exhibit the −2 spectral slope of inertial subrange homogeneous turbulence. These motions appear to be turbulent.

These data suggest that stratified flows may be modeled as the sum of nearly isotropic turbulence with superbuoyant Lagrangian frequencies and anisotropic internal waves with subbuoyant Lagrangian frequencies. The horizontal velocities are larger than the vertical velocities for the internal wave component but approximately equal for the turbulent component. Vertical kinetic energy is therefore a better indicator of turbulent kinetic energy than is horizontal or total kinetic energy.

Abstract

Mixing in a stratified ocean is controlled by different physics, depending on the large-scale Richardson number. At high Richardson numbers, mixing is controlled by interactions between internal wave modes. At Richardson numbers of order 1, mixing is controlled by instabilities of the large-scale wave modes. A “wave–turbulence” (W–T) transition separates these two regimes. This paper investigates the W–T transition, using observed oceanic and atmospheric spectra and parameterizations. Viewed in terms of Lagrangian (intrinsic) frequency spectra, the transition occurs when the inertial subrange of turbulence, confined to frequencies greater than the buoyancy frequency N, reaches the level of the internal waves, confined to frequencies less than N. Viewed in terms of vertical wavenumber spectra, the W–T transition occurs when the bandwidth of internal waves becomes small. Both of these singularities occur when the typical internal wave velocity becomes comparable to the phase speed of the lowest internal wave mode. At energies below that of the W–T transition, the dissipation rate varies as the energy squared; above the transition the dependence is linear. The transition occurs at lower shear and dissipation rates where the phase speed of the lowest mode is smaller, that is, in shallower water for the same stratification. Traditional turbulence closure models, which ignore internal waves, can be accurate only at energies above the W–T transition.

Abstract

Taylor's single-particle dispersion model is revisited and applied to unstratified and density stratified flows using observationally based and theoretical models of the Lagrangian velocity and density spectra, which are compared with existing parameterizations of diapycnal diffusion in these flows. For unstratified homogeneous turbulence, the vertical particle dispersion coefficient K _z computed from model Lagrangian velocity spectra agrees well with contemporary estimates of the diffusivity. For internal waves with no mixing, a large apparent dispersion occurs for times somewhat larger than the inverse buoyancy frequency 1/N. No dispersion occurs at long times. For stratified homogeneous turbulence with energy dissipation rate ε, K _z = Γ _d εN ⁻², the same form as Osborn, but with Γ _d of about 2.5. This high value is attributed to apparent dispersion due to internal waves and an improper form of the model spectra that allows internal waves to exist at low frequencies. A diapycnal dispersion coefficient K∗ is formulated based on a white spectrum of Lagrangian density change Dρ/Dt with level β _ρ χ, where χ is the rate of dissipation of density variance. This yields K∗ = (π/2)β _ρ χ/ ρ ⁻² _z , where ρ _z is the mean vertical density gradient. This has the same form as the Osborn and Cox model for diapycnal diffusivity if β _ρ = 1/π.

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 C_P /U ₁₀, where C_P is the spectral peak phase speed, using an empirical surface wave spectra and an associated wave age–dependent neutral drag coefficient C_D . Wave-breaking effects are not otherwise included. Mixed layer depths H _ML vary from 30 to 120 m, with 0.6 ≤ C_P /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 La _t = u*/U_S , where u* = | τ ₀|/ρ_w in water density ρ_w and U_S = |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 La_SL = u*/〈u ^S 〉_SL , where 〈u ^S 〉_SL 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 La_SL → 0, turbulent vertical velocity scales as w _rms ∼ u*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 C_P /U ₁₀ in observed regimes.

Abstract

This paper describes the instrumentation and techniques for long-term targeted observation of the centimeter-scale velocity structure within the oceanic surface boundary layer, made possible by the recent developments in capabilities of autonomous platforms and self-contained pulse-coherent acoustic Doppler current profilers (ADCPs). Particular attention is paid to the algorithms of ambiguity resolution (“unwrapping”) of pulse-coherent Doppler velocity measurements. The techniques are demonstrated using the new Nortek Signature1000 ADCP mounted on a Lagrangian float, a combination shown to be capable of observing ocean turbulence in a number of recent studies. Statistical uncertainty of the measured velocities in relation to the ADCP setup is also evaluated. Described techniques and analyses should be broadly applicable to other autonomous and towed applications of pulse-coherent ADCPs.

Abstract

The Lagrangian properties of a high-resolution, three-dimensional, direct numerical simulation of Kelvin– Helmholtz (K–H) instability are examined with the goal of assessing the ability of Lagrangian measurements to determine rates and properties of ocean mixing events. The size and rotation rates of the two-dimensional K–H vortices are easily determined even by individual trajectories. Changes in density along individual trajectories unambiguously show diapycnal mixing. These changes are highly structured during the early phases of the instability but become more random once the flow becomes turbulent. Only 36 particles were tracked, which is not enough to usefully estimate volume-averaged fluxes from the average rates of temperature change. Similarly, time-and volume-averaged vertical advective flux can be estimated to only 20% accuracy. Despite the relatively low Reynolds number of the flow, R _λ ≈ 100, the dissipation rates of energy ɛ and density variance χ are correlated with the spectral levels of transverse velocity and density in an inertial subrange, as expected for high-Reynolds-number turbulence. The Kolmogorov constants are consistent with previous studies. This suggests that these inertial dissipation methods are the most promising techniques for making useful measurements of diapycnal mixing rates from practical Lagrangian floats because they converge rapidly and have a clear theoretical basis.