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## Abstract

The design and Operation of neutrally buoyant floats that attempt to track the three-dimensional motion of water parcels in highly turbulent regions of the ocean, such as the upper mixed layer, are described. These floats differ from previous floats by combining high drag, a compressibility that nearly matches that of seawater, rapid (1 Hz) sampling, and short-range, high-precision acoustic tracking. Examples of float data are shown with the twin goals of demonstrating the utility of the floats and estimating the accuracy to which they are “Lagrangian.”

The analysis indicates that these floats follow the motion of the surrounding water to better than 0.01 m s^{−1} under most circumstances. Both the net buoyancy of the float and its finite size contribute to the error. The float's buoyancy is controlled by making its compressibility very close to that of seawater, by making its drag large, by reducing air pockets and bubbles on the float, and by carefully controlling variations in the float's mass and volume between deployments. The float accurately follows that part of the velocity field with Scales much larger than its own size (1 m) but does not follow components with scales smaller than itself. A model of this dependence is presented for turbulent flows.

Several unique measurements are possible with these floats. They measure vertical displacement using pressure and therefore accurately filter out the vertical velocity of surface waves, since linear surface waves have no pressure fluctuations along Lagrangian trajectories. Accurate measurements of vertical velocity in the oceanic mixed layer are therefore possible. This, combined with temperature, can be used to measure vertical heat flux. A compass measures the spin rate of the float and thus the vertical vorticity. In fully turbulent flows with outer scales much larger than the float size, the spectra of both vertical velocity and vorticity scale with ε (the turbulent kinetic energy dissipation) over a wide range of ε values, thus allowing ε to be measured. The floats con, in principle, therefore measure many important properties of turbulent flows even in the presence of surface waves.

## Abstract

The design and Operation of neutrally buoyant floats that attempt to track the three-dimensional motion of water parcels in highly turbulent regions of the ocean, such as the upper mixed layer, are described. These floats differ from previous floats by combining high drag, a compressibility that nearly matches that of seawater, rapid (1 Hz) sampling, and short-range, high-precision acoustic tracking. Examples of float data are shown with the twin goals of demonstrating the utility of the floats and estimating the accuracy to which they are “Lagrangian.”

The analysis indicates that these floats follow the motion of the surrounding water to better than 0.01 m s^{−1} under most circumstances. Both the net buoyancy of the float and its finite size contribute to the error. The float's buoyancy is controlled by making its compressibility very close to that of seawater, by making its drag large, by reducing air pockets and bubbles on the float, and by carefully controlling variations in the float's mass and volume between deployments. The float accurately follows that part of the velocity field with Scales much larger than its own size (1 m) but does not follow components with scales smaller than itself. A model of this dependence is presented for turbulent flows.

Several unique measurements are possible with these floats. They measure vertical displacement using pressure and therefore accurately filter out the vertical velocity of surface waves, since linear surface waves have no pressure fluctuations along Lagrangian trajectories. Accurate measurements of vertical velocity in the oceanic mixed layer are therefore possible. This, combined with temperature, can be used to measure vertical heat flux. A compass measures the spin rate of the float and thus the vertical vorticity. In fully turbulent flows with outer scales much larger than the float size, the spectra of both vertical velocity and vorticity scale with ε (the turbulent kinetic energy dissipation) over a wide range of ε values, thus allowing ε to be measured. The floats con, in principle, therefore measure many important properties of turbulent flows even in the presence of surface waves.

## 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.

## 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.

## Abstract

The drag coefficient under tropical cyclones and its dependence on sea states are investigated by combining upper-ocean current observations [using electromagnetic autonomous profiling explorer (EM-APEX) floats deployed under five tropical cyclones] and a coupled ocean–wave (Modular Ocean Model 6–WAVEWATCH III) model. The estimated drag coefficient averaged over all storms is around 2–3 × 10^{−3} for wind speeds of 25–55 m s^{−1}. While the drag coefficient weakly depends on wind speed in this wind speed range, it shows stronger dependence on sea states. In particular, it is significantly reduced when the misalignment angle between the dominant wave direction and the wind direction exceeds about 45°, a feature that is underestimated by current models of sea state–dependent drag coefficient. Since the misaligned swell is more common in the far front and in the left-front quadrant of the storm (in the Northern Hemisphere), the drag coefficient also tends to be lower in these areas and shows a distinct spatial distribution. Our results therefore support ongoing efforts to develop and implement sea state–dependent parameterizations of the drag coefficient in tropical cyclone conditions.

## Abstract

The drag coefficient under tropical cyclones and its dependence on sea states are investigated by combining upper-ocean current observations [using electromagnetic autonomous profiling explorer (EM-APEX) floats deployed under five tropical cyclones] and a coupled ocean–wave (Modular Ocean Model 6–WAVEWATCH III) model. The estimated drag coefficient averaged over all storms is around 2–3 × 10^{−3} for wind speeds of 25–55 m s^{−1}. While the drag coefficient weakly depends on wind speed in this wind speed range, it shows stronger dependence on sea states. In particular, it is significantly reduced when the misalignment angle between the dominant wave direction and the wind direction exceeds about 45°, a feature that is underestimated by current models of sea state–dependent drag coefficient. Since the misaligned swell is more common in the far front and in the left-front quadrant of the storm (in the Northern Hemisphere), the drag coefficient also tends to be lower in these areas and shows a distinct spatial distribution. Our results therefore support ongoing efforts to develop and implement sea state–dependent parameterizations of the drag coefficient in tropical cyclone conditions.

## Abstract

A coordinated survey between a subsurface Lagrangian float and a ship-towed Triaxus profiler obtained detailed measurements of a restratifying surface intensified front (above 30 m) within the California Current System. The survey began as downfront winds incited mixing in the boundary layer. As winds relaxed and mixing subsided, the system entered a different dynamical regime as the front developed an overturning circulation with large vertical velocities that tilted isopycnals and stratified the upper ocean within a day. The horizontal buoyancy gradient was 1.5 × 10^{−6} s^{−2} and associated with vorticity, divergence, and strain that approached the Coriolis frequency. Estimates of vertical velocity from the Lagrangian float reached 1.2 × 10^{−3} m s^{−1}. These horizontal gradients and vertical velocities were consistent with submesoscale dynamics that are distinct from the classic quasigeostrophic framework used to describe larger-scale flows. Vertical and horizontal gradients of velocity and buoyancy in the vicinity of the float revealed that sheared currents differentially advected the horizontal buoyancy gradient to increase vertical stratification. This was supported by analyses of temperature and salinity gradients that composed the horizontal and vertical stratification. Potential vorticity was conserved during restratification at 16 m, consistent with adiabatic processes. Conversely, potential vorticity near the surface (8 m) increased, highlighting the role of friction in modulating near-surface stratification. The observed increase in stratification due to these submesoscale processes was equivalent to a heat flux of 2000 W m^{−2}, which is an order-of-magnitude larger than the average observed surface heat flux of 100 W m^{−2}.

## Abstract

A coordinated survey between a subsurface Lagrangian float and a ship-towed Triaxus profiler obtained detailed measurements of a restratifying surface intensified front (above 30 m) within the California Current System. The survey began as downfront winds incited mixing in the boundary layer. As winds relaxed and mixing subsided, the system entered a different dynamical regime as the front developed an overturning circulation with large vertical velocities that tilted isopycnals and stratified the upper ocean within a day. The horizontal buoyancy gradient was 1.5 × 10^{−6} s^{−2} and associated with vorticity, divergence, and strain that approached the Coriolis frequency. Estimates of vertical velocity from the Lagrangian float reached 1.2 × 10^{−3} m s^{−1}. These horizontal gradients and vertical velocities were consistent with submesoscale dynamics that are distinct from the classic quasigeostrophic framework used to describe larger-scale flows. Vertical and horizontal gradients of velocity and buoyancy in the vicinity of the float revealed that sheared currents differentially advected the horizontal buoyancy gradient to increase vertical stratification. This was supported by analyses of temperature and salinity gradients that composed the horizontal and vertical stratification. Potential vorticity was conserved during restratification at 16 m, consistent with adiabatic processes. Conversely, potential vorticity near the surface (8 m) increased, highlighting the role of friction in modulating near-surface stratification. The observed increase in stratification due to these submesoscale processes was equivalent to a heat flux of 2000 W m^{−2}, which is an order-of-magnitude larger than the average observed surface heat flux of 100 W m^{−2}.

## Abstract

A coordinated multiplatform campaign collected detailed measurements of a restratifying surface intensified upwelling front within the California Current System. A companion paper outlined the evolution of the front, revealing the importance of lateral advection at tilting isopycnals and increasing stratification in the surface boundary layer with a buoyancy flux equivalent to 2000 W m^{−2}. Here, observations were compared with idealized models to explore the dynamics contributing to the stratification. A 2D model combined with a reduced form of the horizontal momentum equations highlight the importance of transient Ekman dynamics, turbulence, and thermal wind imbalance at modulating shear in the boundary layer. Specifically, unsteady frictional adjustment to the rapid decrease in wind stress created vertically sheared currents that advected horizontal gradients to increase vertical stratification on superinertial time scales. The magnitude of stratification depended on the strength of the horizontal buoyancy gradient. This enhanced stratification due to horizontal advection inhibited nighttime mixing that would have otherwise eroded stratification from the diurnal warm layer. This underscores the importance of near-surface lateral restratification for the upper ocean buoyancy budget on diel time scales.

## Abstract

A coordinated multiplatform campaign collected detailed measurements of a restratifying surface intensified upwelling front within the California Current System. A companion paper outlined the evolution of the front, revealing the importance of lateral advection at tilting isopycnals and increasing stratification in the surface boundary layer with a buoyancy flux equivalent to 2000 W m^{−2}. Here, observations were compared with idealized models to explore the dynamics contributing to the stratification. A 2D model combined with a reduced form of the horizontal momentum equations highlight the importance of transient Ekman dynamics, turbulence, and thermal wind imbalance at modulating shear in the boundary layer. Specifically, unsteady frictional adjustment to the rapid decrease in wind stress created vertically sheared currents that advected horizontal gradients to increase vertical stratification on superinertial time scales. The magnitude of stratification depended on the strength of the horizontal buoyancy gradient. This enhanced stratification due to horizontal advection inhibited nighttime mixing that would have otherwise eroded stratification from the diurnal warm layer. This underscores the importance of near-surface lateral restratification for the upper ocean buoyancy budget on diel time scales.

## Abstract

Oceanic surface submesoscale currents are characterized by anisotropic fronts and filaments with widths from 100 m to a few kilometers; an *O*(1) Rossby number; and large magnitudes of lateral buoyancy and velocity gradients, cyclonic vorticity, and convergence. We derive an asymptotic model of submeoscale frontogenesis—the rate of sharpening of submesoscale gradients—and show that in contrast with “classical” deformation frontogenesis, the near-surface convergent motions, which are associated with the ageostrophic secondary circulation, determine the gradient sharpening rates. Analytical solutions for the inviscid Lagrangian evolution of the gradient fields in the proposed asymptotic regime are provided, and emphasize the importance of ageostrophic motions in governing frontal evolution. These analytical solutions are further used to derive a scaling relation for the vertical buoyancy fluxes that accompany the gradient sharpening process. Realistic numerical simulations and drifter observations in the northern Gulf of Mexico during winter confirm the applicability of the asymptotic model to strong frontogenesis. Careful analysis of the numerical simulations and field measurements demonstrates that a subtle balance between boundary layer turbulence, pressure, and Coriolis effects (e.g., turbulent thermal wind; Gula et al. 2014) leads to the generation of the surface convergent motions that drive frontogenesis in this region. Because the asymptotic model makes no assumptions about the physical mechanisms that initiate the convergent frontogenetic motions, it is generic for submesoscale frontogenesis of *O*(1) Rossby number flows.

## Abstract

Oceanic surface submesoscale currents are characterized by anisotropic fronts and filaments with widths from 100 m to a few kilometers; an *O*(1) Rossby number; and large magnitudes of lateral buoyancy and velocity gradients, cyclonic vorticity, and convergence. We derive an asymptotic model of submeoscale frontogenesis—the rate of sharpening of submesoscale gradients—and show that in contrast with “classical” deformation frontogenesis, the near-surface convergent motions, which are associated with the ageostrophic secondary circulation, determine the gradient sharpening rates. Analytical solutions for the inviscid Lagrangian evolution of the gradient fields in the proposed asymptotic regime are provided, and emphasize the importance of ageostrophic motions in governing frontal evolution. These analytical solutions are further used to derive a scaling relation for the vertical buoyancy fluxes that accompany the gradient sharpening process. Realistic numerical simulations and drifter observations in the northern Gulf of Mexico during winter confirm the applicability of the asymptotic model to strong frontogenesis. Careful analysis of the numerical simulations and field measurements demonstrates that a subtle balance between boundary layer turbulence, pressure, and Coriolis effects (e.g., turbulent thermal wind; Gula et al. 2014) leads to the generation of the surface convergent motions that drive frontogenesis in this region. Because the asymptotic model makes no assumptions about the physical mechanisms that initiate the convergent frontogenetic motions, it is generic for submesoscale frontogenesis of *O*(1) Rossby number flows.

## Abstract

Estimates of drag coefficients beneath Typhoon Megi (2010) are calculated from roughly hourly velocity profiles of three EM-APEX floats, air launched ahead of the storm, and from air-deployed dropsondes measurements and microwave estimates of the 10-m wind field. The profiles are corrected to minimize contributions from tides and low-frequency motions and thus isolate the current induced by Typhoon Megi. Surface wind stress is computed from the linear momentum budget in the upper 150 m. Three-dimensional numerical simulations of the oceanic response to Typhoon Megi indicate that with small corrections, the linear momentum budget is accurate to 15% before the passage of the eye but cannot be applied reliably thereafter. Monte Carlo error estimates indicate that stress estimates can be made for wind speeds greater than 25 m s^{−1}; the error decreases with greater wind speeds. Downwind and crosswind drag coefficients are computed from the computed stress and the mapped wind data. Downwind drag coefficients increase to 3.5 ± 0.7 × 10^{−3} at 31 m s^{−1}, a value greater than most previous estimates, but decrease to 2.0 ± 0.4 × 10^{−3} for wind speeds > 45 m s^{−1}, in agreement with previous estimates. The crosswind drag coefficient of 1.6 ± 0.5 × 10^{−3} at wind speeds 30–45 m s^{−1} implies that the wind stress is about 20° clockwise from the 10-m wind vector and thus not directly downwind, as is often assumed.

## Abstract

Estimates of drag coefficients beneath Typhoon Megi (2010) are calculated from roughly hourly velocity profiles of three EM-APEX floats, air launched ahead of the storm, and from air-deployed dropsondes measurements and microwave estimates of the 10-m wind field. The profiles are corrected to minimize contributions from tides and low-frequency motions and thus isolate the current induced by Typhoon Megi. Surface wind stress is computed from the linear momentum budget in the upper 150 m. Three-dimensional numerical simulations of the oceanic response to Typhoon Megi indicate that with small corrections, the linear momentum budget is accurate to 15% before the passage of the eye but cannot be applied reliably thereafter. Monte Carlo error estimates indicate that stress estimates can be made for wind speeds greater than 25 m s^{−1}; the error decreases with greater wind speeds. Downwind and crosswind drag coefficients are computed from the computed stress and the mapped wind data. Downwind drag coefficients increase to 3.5 ± 0.7 × 10^{−3} at 31 m s^{−1}, a value greater than most previous estimates, but decrease to 2.0 ± 0.4 × 10^{−3} for wind speeds > 45 m s^{−1}, in agreement with previous estimates. The crosswind drag coefficient of 1.6 ± 0.5 × 10^{−3} at wind speeds 30–45 m s^{−1} implies that the wind stress is about 20° clockwise from the 10-m wind vector and thus not directly downwind, as is often assumed.

## Abstract

A crucial region of the ocean surface boundary layer (OSBL) is the strongly sheared and strongly stratified transition layer (TL) separating the mixed layer from the upper pycnocline, where a diverse range of waves and instabilities are possible. Previous work suggests that these different waves and instabilities will lead to different OSBL behaviors. Therefore, understanding which physical processes occur is key for modeling the TL. Here we present observations of the TL from a Lagrangian float deployed for 73 days near Ocean Weather Station Papa (50°N, 145°W) during fall 2018. The float followed the vertical motion of the TL, continuously measuring profiles across it using an ADCP, temperature chain, and salinity sensors. The temperature chain made depth–time images of TL structures with a resolution of 6 cm and 3 s. These showed the frequent occurrence of very sharp interfaces, dominated by temperature jumps of *O*(1)°C over 6 cm or less. Temperature inversions were typically small (

## Abstract

A crucial region of the ocean surface boundary layer (OSBL) is the strongly sheared and strongly stratified transition layer (TL) separating the mixed layer from the upper pycnocline, where a diverse range of waves and instabilities are possible. Previous work suggests that these different waves and instabilities will lead to different OSBL behaviors. Therefore, understanding which physical processes occur is key for modeling the TL. Here we present observations of the TL from a Lagrangian float deployed for 73 days near Ocean Weather Station Papa (50°N, 145°W) during fall 2018. The float followed the vertical motion of the TL, continuously measuring profiles across it using an ADCP, temperature chain, and salinity sensors. The temperature chain made depth–time images of TL structures with a resolution of 6 cm and 3 s. These showed the frequent occurrence of very sharp interfaces, dominated by temperature jumps of *O*(1)°C over 6 cm or less. Temperature inversions were typically small (