Fine-scale Shear Research Articles

Energy Sinks for Lee Waves in Shear Flow

AbstractMicrostructure measurements in Drake Passage and on the flanks of Kerguelen Plateau find turbulent dissipation ratesεon average factors of 2–3 smaller than linear lee-wave generation predictions, as well as a factor of 3 smaller than the predictions of a well-established parameterization based on finescale shear and strain. Here, the possibility that these discrepancies are a result of conservation of wave actionE/ωL=E/|kU| is explored. Conservation of wave action will transfer a fraction of the lee-wave radiation back to the mean flow if the waves encounter weakening currentsU, where the intrinsic or Lagrangian frequencyωL= |kU| ↓ |f| andkthe along-stream horizontal wavenumber, wherekU≡k⋅V. The dissipative fraction of power that is lost to turbulence depends on the Doppler shift of the intrinsic frequency between generation and breaking, hence on the topographic height spectrum and bandwidthN/f. The partition between dissipation and loss to the mean flow is quantified for typical topographic height spectral shapes andN/fratios found in the abyssal ocean under the assumption that blocking is local in wavenumber. Although some fraction of lee-wave generation is always dissipated in a rotating fluid, lee waves are not as large a sink for balanced energy or as large a source for turbulence as previously suggested. The dissipative fraction is 0.44–0.56 for topographic spectral slopes and buoyancy frequencies typical of the deep Southern Ocean, insensitive to flow speedUand topographic splitting. Lee waves are also an important mechanism for redistributing balanced energy within their generating bottom current.

The Impact of Observed Variations in the Shear-to-Strain Ratio of Internal Waves on Inferred Turbulent Diffusivities

AbstractThe most comprehensive studies of the spatial and temporal scales of diffusivity rely on internal wave parameterizations that require knowledge of finescale shear and strain. Studies lacking either shear or strain measurements have to assume a constant ratio between shear and strain (Rω). Data from 14 moorings collected during five field programs are examined to determine the spatial and temporal patterns in Rω and the influence of these patterns on parameterized diffusivity. Time-mean Rω ranges from 1 to 10, with changes of order 10 observed over a broad range of scales. Temporal variability in Rω is observed at daily, weekly, and monthly scales. Observed changes in Rω could produce a 2–3 times change in parameterized diffusivity. Vertical profiles of Rω, Eshear, and Estrain (shear or strain variance relative to Garret–Munk) reveal that both local topographic properties and wind variability impact the internal wave field. Time series of Rω from each mooring have strong correlations to either shear or strain, often only at a specific range of vertical wavenumbers. Sites fall into two categories, in which Rω variability is dominated by either shear or strain. Linear fits to the dominant property (i.e., shear or strain) can be used to estimate a time series of Rω that has an RMS error that is 30% less than the RMS error from assuming Rω = 3. Shear and strain level vary in concert, as predicted by the Garret–Munk model, at high Eshear values. However, at Eshear < 5, strain variations are 3 times weaker than shear.

Numerical Modeling of Multiscale Dynamics at a High Reynolds Number: Instabilities, Turbulence, and an Assessment of Ozmidov and Thorpe Scales

Abstract A high–Reynolds number direct numerical simulation (DNS) is employed to explore the instability and turbulence dynamics accompanying an idealized multiscale flow that approximates such environments observed throughout the atmosphere. The DNS describes the superposition of a stable gravity wave (GW) and a stable, oscillatory, finescale shear flow that together yield significant wave–wave interactions, GW breaking, Kelvin–Helmholtz instabilities (KHI), fluid intrusions, and turbulence. Larger-scale GW breaking and KHI events account for the strongest turbulence intensities, with intrusions competing with KHI and GW breaking at smaller spatial scales and later times. These dynamics drive a series of sheet-and-layer structures in the velocity, stability, and dissipation fields that persist for many buoyancy periods. Measures of local turbulence intensities include energy dissipation rates, Ozmidov and Thorpe scales (LO and LT, respectively), and a buoyancy Reynolds number sufficient to ensure sustained, strong turbulence events. These exhibit significant variability between and within instability events of different types. The Ozmidov and Thorpe scales for individual events are employed to assess variations of their ratio, C = LO/LT, with time. The value of C is highly variable with event type and time but typically increases with time because significant fluid overturning most often precedes turbulence. The value of C determined for the entire domain varies from 0 prior to instability to approximately 2 or larger at late times, with minima (maxima) prior to (following) significant instability and turbulence events. This appears to preclude an assumption that C is constant in stratified flows, except perhaps as an event average that may depend on event type.

The Role of Intermittency in Internal-Wave Shear Dispersion

AbstractThis paper revisits a long-standing discrepancy between (i) 1–5-km isopycnal diffusivities of O(1) m2 s−1 based on dye spreading and (ii) inferences of O(0.1) m2 s−1 from internal-wave shear dispersion Kh ~ 〈Kz〉〈〉/f2 in several studies in the stratified ocean interior, where 〈Kz〉 is the bulk average diapycnal diffusivity, 〈〉 the finescale shear variance, and f the Coriolis frequency. It is shown that, taking into account (i) the intermittency of shear-driven turbulence, (ii) its lognormality, and (iii) its correlation with unstable finescale near-inertial shear, internal-wave shear dispersion cannot necessarily be discounted based on available information. This result depends on an infrequent occurrence of turbulence bursts, as is observed, and a correlation between diapycnal diffusivity Kz and the off-diagonal vertical strain, or the vertical gradient of horizontal displacement, |χz| = |∫Vz dt|, which is not well known and may vary from region to region. Taking these factors into account, there may be no need to invoke additional submesoscale mixing mechanisms such as vortical-mode stirring or internal-wave Stokes drift to explain the previously reported discrepancies.

The Latitudinal Dependence of Shear and Mixing in the Pacific Transiting the Critical Latitude for PSI

AbstractTurbulent mixing rates are inferred from measurements spanning 25°–37°N in the Pacific Ocean. The observations were made as part of the Internal Waves Across the Pacific experiment, designed to investigate the long-range fate of the low-mode internal tide propagating north from Hawaii. Previous and companion results argue that, near a critical latitude of 29°N, the internal tide loses energy to high-mode near-inertial motions through parametric subharmonic instability. Here, the authors estimate mixing from several variations of the finescale shear–strain parameterization, as well as Thorpe-scale analysis of overturns. Though all estimated diffusivities are modest in magnitude, average diffusivity in the top kilometer shows a factor of 2–4 elevation near and equatorward of 29°N. However, given intrinsic uncertainty and the strong temporal variability of diffusivity observed in long mooring records, the meridional mixing pattern is found to be near the edge of statistical significance.

Scaling turbulent dissipation in an Arctic fjord

Abstract In September 2003, microstructure and fine-scale shear (vertical derivative of horizontal current) and strain (vertical derivative of isopycnal displacements) profiles were collected in Storfjorden, Svalbard Archipelago. Storfjorden is a sill-fjord of significant dense water production and the period of observations corresponds to weak overflow conditions of the dense water. The data set comprises fine-scale measurements combined with simultaneous dissipation and buoyancy frequency profiles and allows for evaluation of various turbulence scalings and internal wave–wave interaction models. Microstructure profiles identified high levels of background vertical diffusivity, K ρ , O (10 −4 ) m 2 s −1 , which increased by one order within the overflow. Fine-scale shear and strain spectral levels were found to be elevated above those of Garrett–Munk, consistent with the observed enhanced mixing, whereas their average ratio was comparable to that of Garrett–Munk. Among the internal wave–wave interaction models, a shear–strain model agreed with the observations (between the surface and bottom mixed layers) within a factor of 2, on the average. A scaling of the dissipation, e , in the form of total-energy× N suggests that approximately 0.5% of the energy is dissipated per buoyancy period, 2 π / N . The best-fit power-law scaling between diffusivity and N is K ρ ∝ N −1.4 (±0.2) . For this environment, a parameterization of the form of Pacanowski–Philander is suggested with background levels of eddy viscosity and diffusivity elevated by an order of magnitude.

Comparison of deep-ocean finescale shear at two sites along the Mid-Atlantic Ridge

Abstract Four drifting floats were used to measure the magnitude of the vertical derivative of horizontal velocity in waters above the rough bathymetry of the Mid-Atlantic Ridge. This derivative is typically the dominant component of the velocity gradient (the shear). Two floats were at the site of the Brazil Basin Tracer Release Experiment (BBTRE) in the South Atlantic, and two were near the site of the Guiana Abyssal Gyre Experiment (GAGE) in the North Atlantic. Floats operated for 1 year except for one BBTRE float, which operated for 100 days. Shear was measured over a vertical span of 9.5 m using drag elements that caused the floats to rotate slowly in response to shear. For each float, the first, second and fourth moments of shear were elevated above levels associated with the Garrett–Munk model internal-wave spectrum. Three of the four floats were tracked as they moved over mountainous terrain, allowing shear intensity to be measured as a function of height above the bottom. A deep BBTRE float showed enhancement of rms shear near the bottom. Floats at both areas provided measurements at 2000 m above the bottom, with differing results: the GAGE site had a lower fourth moment of shear (diapycnal diffusivity proxy) than the BBTRE site. However, application of normalization factors accounting for differences between the sites in bottom roughness, latitude-dependent internal-wave dynamics, and tidal current speeds brings the results into agreement.

Measurements of the Turbulent Energy Dissipation Rate around the Shelf Break in the East China Sea

Using the micro-structure profiler, TurboMAP, large values for the turbulent energy dissipation rate e were found just above the bottom of the shelf and around the thermocline near the continental shelf break in the East China Sea. The values found above the bottom are produced by the bottom stress due to tidal currents, resulting in a distinct bottom mixed layer where the vertical eddy diffusivity Kz is also large. Distinct maxima in the values of e detected around the thermocline are located at the depth of the fine-scale shear maxima detected with the moored ADCP. The vertical profiles of e were compared with those of the current velocity, and it was found that the maxima in e appear to correspond to those of the shear with fine scale. The magnitude of the observed e coincided approximately with the e calculated from the fine-scale shear and the buoyancy frequency according to the parameterization proposed by Gregg (1989), if the large-scale mean shear caused by the Kuroshio is subtracted. However, it is not clear whether the parameterization for the internal wave fields in the open ocean is applicable to the estimation of e in the shelf break. Whereas the most predominant value of e was found just above the bottom and around the thermocline, the maxima of e could be found in the internal area. They could have been caused by the propagation of the vertically high wave number internal tides along the characteristic ray.

Observations of turbulent energy dissipation rate ε in the Japan Sea

Abstract Measurements of turbulent energy dissipation rate e were obtained in the southern Japan Sea during experimental campaigns in June 2000 and 2001, and November 2001. The data sets show markedly different vertical structures of e between the two seasons, suggesting that wind stirring is a dominant process in the vertical heat exchange between the upper 200 m and the deeper layers. In June, values of eddy diffusivity Kz computed from e and buoyancy frequency N2 are generally around 10−6 m2 s−1, reaching 10−4 near the surface and in subsurface mixing patches. In November, Kz is around 10−4 in the surface mixing layer and around 10−5 in the deeper layer below 200 m. During the November observations, fine-scale current velocity shear was obtained with lowered ADCP. Vertical profiles of the Richardson number Ri calculated from the fine-scale velocity shear and N2 show that relatively large values of e tend to correspond to small values of Ri at the subsurface deeper than 100 m. It is inferred that the energy source of turbulence away from the surface is supplied mainly by near-inertial currents.

Mixing estimates from a large-scale hydrographic survey in the North Atlantic

[1] A large-scale hydrographic survey from 2003 (RV Meteor cruise M59/2) is used to map turbulent mixing by means of eddy diffusivities from finescale shear and strain in the subpolar North Atlantic, covering various hydrographic and bathymetric conditions. Results from the analysis indicate small (O(10−5) m2s−1) diffusivities below the Labrador Sea Water layer at mid-depth in the open ocean. Higher values exceeding 10−4 m2s−1 are found in the abyss close to rough topography and over the flanks of the Mid-Atlantic Ridge. The strongest mixing with diffusivities of 10−3 m2s−1 occurs in the Deep Western Boundary Current off Flemish Cap. The results of this study convey the need to map mixing globally from existing sets of CTD/LADCP data as well as its feasibility: the similarities and differences in mixing patterns as compared to other studies indicate that large scale patterns of small scale processes are still not well known and understood.

Observations of Energetic High-Wavenumber Internal Waves in the Kuroshio

Abstract Intense and spatially coherent shear layers were detected in and under the Kuroshio in an April 2000 survey in the East China Sea. The sloping layers, revealed by shipboard Doppler sonars on the R/V Roger Revelle, appeared to cross isopycnal surfaces. Except in a small region near the Kuroshio shelfbreak front, the rms finescale shear associated with the layers significantly exceeded the geostrophic shear. An April 2002 follow-on cruise was organized to establish whether these motions were propagating internal waves. Shipboard and lowered ADCPs were both operated from the R/V Melville. In addition to CTD-sonar transects, a 30-h time series of currents and shear was obtained in the core of the Kuroshio near the island of Kyushu, Japan. The shear structures were indeed found to be propagating, with both up- and down-going internal wave motions present. In comparison with the nearby open ocean, the finescale (<160 m) vertical shear variance is increased by a factor of 3 in the Kuroshio and by a fact...

Finescale Shear at 1660 and 2850 dbar over the Mid-Atlantic Ridge in the Eastern Brazil Basin*

Abstract Two drifting Shearmeter instruments have provided records of the magnitude of shear (the magnitude of the vertical derivative of horizontal velocity), measured over a 10-m aperture, in the vicinity of the Brazil Basin Tracer Release Experiment. The floats drifted at roughly 1660 and 2850 dbar, where the buoyancy frequencies were N = 1.1 and 0.5 cph, respectively. Two additional floats provided deep trajectories but no shear data. The records of hourly mean values of shear magnitude (with mean values denoted Sh) exhibit strong temporal variability, with time scales comparable to those of fortnightly tidal modulation. The deep record exhibits stronger mean Sh near the seafloor than above, with the exception of the bin closest to the seafloor; Sh from neither float correlates strictly with tidal forcing. Shallow Sh varies in apparent response to atmospheric forcing. The mean squared shear of the shallow record is 4 times the N-dependent value associated with the Garrett–Munk spectral model, and that...

Idealized Solutions for the Energy Balance of the Finescale Internal Wave Field*

Abstract Recent fine- and microstructure observations indicate enhanced finescale shear and strain in conjunction with bottom-intensified turbulent dissipation above rough bathymetry in the Brazil Basin. Such observations implicate the bottom boundary as an energy source for the finescale internal wave field. Simple analytical and numerical solutions to an equation governing the spatial and temporal evolution of the finescale wave field are described here. The governing equation implicitly treats the effects of wave breaking on the vertical propagation of internal waves through a flux representation of nonlinear transports associated with internal wave–wave interactions. These solutions identify the rate of dissipation of turbulent kinetic energy with downscale energy transports at high vertical wavenumber, resulting in an estimate of dissipation versus depth. The sensitivity of the turbulent dissipation depth profile to various environmental parameters is examined. Observed dissipation profiles and shear...

Patterns of Shear and Turbulence across the Florida Current

Abstract Measurements by the Multi-Scale Profiler (MSP) at seven stations spanning the Straits of Florida characterize levels and patterns of internal wave activity and mixing in this vertically sheared environment. Contrasting properties suggest five mixing regimes. The largest and most vast is the interior regime, where the background flow has an inverse Richardson number (Ri−1) ranging up to 0.55, shear is dominated by fluctuations that are 1–4 times stronger than in the open ocean, and turbulent diffusivities are similarly moderate at (1–4) × 10−5 m2 s−1. The high-velocity core of the current, near the surface at midchannel, is associated with weak mixing. To its west is a zone of high mean shear, where strong stratification results in background Ri−1 of only 0.4, fluctuations are weak, and diffusivity is moderate. Intermittent shear features beneath the core have mean Ri−1 > 1 and strong turbulence. Two regimes are related to channel topography. Adjacent to the steep eastern slope, finescale shear is...

Internal Waves in Monterey Submarine Canyon

Velocity, temperature, and salinity profile surveying in Monterey Submarine Canyon during spring tide reveals an internal wave field almost an order of magnitude more energetic than that in the open ocean. Semidiurnal fluctuations and their harmonics dominate, near-inertial motions are absent. The ratio of horizontal kinetic to available potential energy is less than one in much of the canyon, inconsistent with hydrostatic internal waves. The excess potential energy may be due to isopycnal displacements induced by barotropic tide flow over the sloping bottom. Removal of the expected barotropic contribution raises the energy ratio to 2.04–2.10, in line with the semidiurnal internal wave value of 2.13. Finescale shear and strain are also elevated. Finescale parameterizations for turbulent eddy diffusivities, which have proven successful in the open ocean, underestimate upper-canyon microstructure estimates of 100 × 10−4 m2 s−1 by a factor of 30. Energy fluxes and near-bottom velocities are strongly steered by the sinuous canyon topography. A vertically integrated influx of 5 kW m−1 at the mouth diminishes to ±1 kW m−1 toward the shallow end of the canyon. Both sinks and sources of internal wave energy are indicated by energy-flux convergences and divergences along the canyon axis. Along-axis energy-flux convergences are consistent with microstructure dissipation rates ϵ. The high diapycnal eddy diffusivities may drive strong nutrient fluxes to enhance bioproductivity.

Turbulence in Plant Canopies

▪ Abstract The single-point statistics of turbulence in the ‘roughness sub-layer’ occupied by the plant canopy and the air layer just above it differ significantly from those in the surface layer. The mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium. Velocity moments scale with single length and time scales throughout the layer rather than depending on height. Large coherent structures control turbulence dynamics. Sweeps rather than ejections dominate eddy fluxes and a typical large eddy consists of a pair of counter-rotating streamwise vortices, the downdraft between the vortex pair generating the sweep. Comparison with the statistics and instability modes of the plane mixing layer shows that the latter rather than the boundary layer is the appropriate model for canopy flow and that the dominant large eddies are the result of an inviscid instability of the inflected mean velocity profile. Aerodynamic drag on the foliage is the cause both of the unstable inflected velocity profile and of a ‘spectral short cut’ mechanism that removes energy from large eddies and diverts it to fine scales, where it is rapidly dissipated, bypassing the inertial eddy-cascade. Total dissipation rates are very large in the canopy as a result of the fine-scale shear layers that develop around the foliage.

Estimates of the Vertical Wavenumber–Frequency Spectra of Vertical Shear and Strain

Abstract Measurements of vertical shear and strain were acquired from the research platform FLIP during the PATCHEX experiment in October, 1986 (34°N, 127°W). Vertical sheer was shear from two separate Doppler sonar systems. A long-range sonar, with independent estimates every 18 m, sampled from 150–1200 m in depth. A short-range sonar measured fine-scale shear over 150–180 m depth, with 1.5 m vertical resolution. Vertical strain, ∂η/∂z, was estimated from two repeatedly profiling CTDs. These sampled to 560 m once every three minutes. The time variation of the strain field is monitored in both Eulerian (fixed-depth) and semi-Lagrangian (isopycnal-following) reference frames, from 150–406 m depth. Eulerian vertical wavenumber-frequency (m, ω) spectra of vertical shear and strain exhibit a frequency dependency which is a strong function of wavenumber (ω−2–ω0 for m = 0.01–0.3 cpm). In contrast the semi-Lagrangian strain spectrum is more nearly separable in frequency and wavenumber, in closer agreement with t...

Finescale Velocity-Density Characteristics and Richardson Number Statistics of the Eastern Equatorial Pacific

Abstract An analysis of finescale horizontal-velocity shear and density data collected along 110°W longitude in the equatorial Pacific is presented. The measurements were made with the free-fall velocity–density profiler, TOPS. Twenty-five deployments are used to investigate the variability in the depth interval 150–900 m. In this interval the shear and strain fields are dominated by finescale structures. The extra-equatorial latitude band 4–10°N exhibits shear and strain spectra as well as Richardson number (Ri) statistics that are consistent with midlatitude internal-wave model predictions. Approaching the equator, an enhancement of shear and strain variance is found along with an accompanying increase in the occurrence of Ri less than ¼. Consistent with previous studies, the present measurement suggest that the 13°C thermostad is turbulently mixed. A high occurrence of Ri less than ¼ is also found below the thermostad and in the latitude range 2–4°S. The implications of these observations are discussed...