Geostrophic Turbulence Theory Research Articles

Eddy Vertical Structure and Variability: Deepglider Observations in the North Atlantic

Abstract Hundreds of full-depth temperature and salinity profiles collected by Deepglider autonomous underwater vehicles (AUVs) in the North Atlantic reveal robust signals in eddy isopycnal vertical displacement and horizontal current throughout the entire water column. In separate glider missions southeast of Bermuda, subsurface-intensified cold, fresh coherent vortices were observed with velocities exceeding 20 cm s−1 at depths greater than 1000 m. With vertical resolution on the order of 20 m or less, these full-depth glider slant profiles newly permit estimation of scaled vertical wavenumber spectra from the barotropic through the 40th baroclinic mode. Geostrophic turbulence theory predictions of spectral slopes associated with the forward enstrophy cascade and proportional to inverse wavenumber cubed generally agree with glider-derived quasi-universal spectra of potential and kinetic energy found at a variety of locations distinguished by a wide range of mean surface eddy kinetic energy. Water-column average spectral estimates merge at high vertical mode number to established descriptions of internal wave spectra. Among glider mission sites, geographic and seasonal variability implicate bottom drag as a mechanism for dissipation, but also the need for more persistent sampling of the deep ocean. Significance Statement Relative to upper-ocean measurements of temperature, salinity, and velocity, deep ocean measurements (below 2000 m) are fewer in number and more difficult to collect. Deep measurements are needed, however, to explore the nature of deep ocean circulation contributing to the global redistribution of heat and to determine how upper-ocean behavior impacts or drives deep motions. Understanding of geographic and temporal variability in vertical structures of currents and eddies enables improved description of energy pathways in the ocean driven by turbulent interactions. In this study, we use newly developed autonomous underwater vehicles, capable of diving to the seafloor and back on a near daily basis, to collect high-resolution full ocean depth measurements at various locations in the North Atlantic. These measurements reveal connections between surface and deep motions, and importantly show their time evolution. Results of analyzing these vertical structures reveal the deep ocean to regularly “feel” events in the upper ocean and permit new comparisons to deep motions in climate models.

Barotropic and Baroclinic Inverse Kinetic Energy Cascade in the Antarctic Circumpolar Current

AbstractStratified geostrophic turbulence theory predicts an inverse energy cascade for the barotropic (BT) mode. Satellite altimetry has revealed a net inverse cascade in the baroclinic (BC) mode. Here the spatial variabilities of BT and BC kinetic energy fluxes in the Antarctic Circumpolar Current (ACC) were investigated using ECCO2 data, which synthesize satellite data and in situ measurements with an eddy-permitting general circulation model containing realistic bathymetry and wind forcing. The BT and BC inverse kinetic energy cascades both reveal complex spatial variations that could not be explained fully by classical arguments. For example, the BC injection scales match better with most unstable scales than with the first-mode deformation scales, but the opposite is true for the BT mode. In addition, the BT and BC arrest scales do not follow the Rhines scale well in terms of spatial variation, but show better consistency with their own energy-containing scales. The reverse cascade of the BT and BC modes was found related to their EKE, and better correlation was found between the BT inverse cascade and barotropization. Speculations of the findings were proposed; however, further observations and modeling experiments are needed to test these interpretations. Spectral flux anisotropy exhibits a feature associated with oceanic jets that is consistent with classical expectations. Specifically, the spectral flux along the along-stream direction remains negative at scales up to that of the studied domain (~2000 km), while that in the perpendicular direction becomes positive close to the scale of the width of a typical jet.

Turbulent lithosphere deformation in the Tibetan Plateau.

In this work, we show that the Tibetan Plateau deformation demonstrates turbulence-like statistics, e.g., spatial invariance across continuous scales. A dual-power-law behavior is evident to show the existence of two possible conservation laws for the enstrophy-like cascade in the range 500≲r≲2000km and kinetic-energy-like cascade in the range 50≲r≲500km. The measured second-order structure-function scaling exponents ζ(2) are similar to their counterparts in the Fourier scaling exponents observed in the atmosphere, where in the latter case the earth's rotation is relevant. The turbulent statistics observed here for nearly zero-Reynolds-number flow can be interpreted by the geostrophic turbulence theory. Moreover, the intermittency correction is recognized with an intensity close to that of the hydrodynamic turbulence of high-Reynolds-number turbulent flows, implying a universal scaling feature of very different turbulent flows. Our results not only shed new light on the debate regarding the mechanism of the Tibetan Plateau deformation but also lead to new challenges for the geodynamic modeling using Newton or non-Newtonian models because the observed turbulence-like features have to be taken into account.

Energy Cascades and Loss of Balance in a Reentrant Channel Forced by Wind Stress and Buoyancy Fluxes

AbstractA large fraction of the kinetic energy in the ocean is stored in the “quasigeostrophic” eddy field. This “balanced” eddy field is expected, according to geostrophic turbulence theory, to transfer energy to larger scales. In order for the general circulation to remain approximately steady, instability mechanisms leading to loss of balance (LOB) have been hypothesized to take place so that the eddy kinetic energy (EKE) may be transferred to small scales where it can be dissipated. This study examines the kinetic energy pathways in fully resolved direct numerical simulations of flow in a flat-bottomed reentrant channel, externally forced by surface buoyancy fluxes and wind stress in a configuration that resembles the Antarctic Circumpolar Current. The flow is allowed to reach a statistical steady state at which point it exhibits both a forward and an inverse energy cascade. Flow interactions with irregular bathymetry are excluded so that bottom drag is the sole mechanism available to dissipate the upscale EKE transfer. The authors show that EKE is dissipated preferentially at small scales near the surface via frontal instabilities associated with LOB and a forward energy cascade rather than by bottom drag after an inverse energy cascade. This is true both with and without forcing by the wind. These results suggest that LOB caused by frontal instabilities near the ocean surface could provide an efficient mechanism, independent of boundary effects, by which EKE is dissipated. Ageostrophic anticyclonic instability is the dominant frontal instability mechanism in these simulations. Symmetric instability is also important in a “deep convection” region, where it can be sustained by buoyancy loss.

The Effects of Altimeter Instrument Noise on the Estimation of the Wavenumber Spectrum of Sea Surface Height

Abstract The wavenumber spectrum of sea surface height (SSH) observed by satellite altimetry was analyzed by Xu and Fu. The spectral shape in the wavelength range of 70–250 km was approximated by a power law, representing a regime governed by geostrophic turbulence theories. The effects of altimeter instrument noise were assumed insignificant at wavelengths longer than 70 km. The authors reexamined the assumption in the study. Using nearly simultaneous observations made by Jason-1 and Jason-2 during their cross-calibration phase, this study found that the white noise level of altimetry measurement was best estimated from the spectral values at wavelengths from 25 to 35 km. After removing a white noise level based on such estimate from the SSH spectrum, the spectral slope values changed significantly over most of the oceans. A key finding is that the spectral slopes are generally steeper than k−2 (k is wavenumber) poleward of the 20° latitudes, where flatter spectral slopes in some regions have previously caused problems for dynamic interpretations. The new results indicate that the spectral slopes in the core regions of the major ocean current systems have values between the original geostrophic turbulence theory and the surface quasigeostrophic theory. The near k−4 spectrum suggests that the sea surface height variability at these wavelengths in the high eddy energy regions might be governed by frontogenesis.

Length Scales of Eddy Generation and Nonlinear Evolution of the Seasonally Modulated South Pacific Subtropical Countercurrent

AbstractThe dynamical processes behind the seasonal modulation of the two-dimensional eddy kinetic energy (EKE) wavenumber spectrum in the Subtropical Countercurrent region of the South Pacific are investigated with 14 yr of satellite altimeter data and climatological hydrographic data. The authors find a seasonally modulated generation of EKE via baroclinic instability in modes with larger meridional length scales. Subsequent nonlinear eddy–eddy interactions redistribute the EKE to larger total horizontal length scales, and larger zonal scales in particular. This is confirmed by diagnosing the spectral transfer of EKE in the surface geostrophic flow, which is found to drive an anisotropic inverse cascade, being redirected in the sense consistent with the β effect, as predicted by geostrophic turbulence theory on the β plane. Because of the seasonal renewal of meridionally elongated anomalies by baroclinic instability and possibly because of the barotropization process, however, the net outcome for the formation of surface zonal flows is observed to be limited.

Direct Evidence of an Oceanic Inverse Kinetic Energy Cascade from Satellite Altimetry

AbstractSea surface height measurements from satellites reveal the turbulent properties of the South Pacific Ocean surface geostrophic circulation, both supporting and challenging different aspects of geostrophic turbulence theory. A near-universal shape of the spectral kinetic energy flux is found and provides direct evidence of a source of kinetic energy near to or smaller than the deformation radius, consistent with linear instability theory. The spectral kinetic energy flux also reveals a net inverse cascade (i.e., a cascade to larger spatial scale), consistent with two-dimensional turbulence phenomenology. However, stratified geostrophic turbulence theory predicts an inverse cascade for the barotropic mode only; energy in the large-scale baroclinic modes undergoes a direct cascade toward the first-mode deformation scale. Thus if the surface geostrophic flow is predominately the first baroclinic mode, as expected for oceanic stratification profiles, then the observed inverse cascade contradicts geostrophic turbulence theory. The latter interpretation is argued for. Furthermore, and consistent with this interpretation, the inverse cascade arrest scale does not follow the Rhines arrest scale, as one would expect for the barotropic mode. A tentative revision of theory is proposed that would resolve the conflicts; however, further observations and idealized modeling experiments are needed to confirm, or refute, the revision. It is noted that no inertial range was found for the inverse cascade range of the spectrum, implying inertial range scaling, such as the established K−5/3 slope in the spectral kinetic energy density plot, is not applicable to the surface geostrophic flow.

Turbulent behavior of a fine mesh (1/12°) numerical simulation of the North Atlantic

The geostrophic turbulent behavior of a fine mesh (1/12°) numerical simulation of the North Atlantic is discussed and compared to observations and coarser numerical simulations. The Miami Isopycnic Coordinate Ocean Model (MICOM) was configured for the North and Equatorial Atlantic (28°S–65°N) with a horizontal resolution of 1/12° (average mesh size on the order of 6 km) and 16 layers in the vertical. Such a set-up demands the latest in high performance computing. The unique aspects of this simulation are (a) a correct Gulf Stream separation from the North American coast and (b) high eddy activity. These results support the view that an inertial boundary layer (which results from the fine resolution) is an important factor in the separation process and that resolution of the first Rossby radius of deformation is necessary for a correct representation of baroclinic instabilities. Sea surface height variability spectra are computed from the model results and compared to observations and previous models, within the framework of the geostrophic turbulence theory. Length scales representative of the simulated eddy field compare well with observations based on altimeter data. Despite higher eddy activity, there is no significant geographic variation in spectral slope in the inertial ranges consistent with previous simulations with coarser resolution. Observations, on the other hand, show a flattening in the spectra derived from altimeter data in weakly energetic areas when compared to spectra from highly energetic areas of the Atlantic. The possible impact of mechanisms not represented in the model, such as high frequency and high wave number wind forcing, is then discussed.

Towed thermistor chain observations of fronts in the subtropical North Pacific

A thermistor chain was towed 1400 km through the eastern North Pacific subtropical frontal zone in January 1980. The observations resolve surface layer temperature features with horizontal wavelengths of 0.2–200 km and vertical scales of 10–70 m. The dominant features, which have horizontal wavelengths of 10–100 km, amplitudes of 0.2°‐1.0°C, and random orientation, likely arise from baroclinic instability. Associated with them is a plateau below 0.1 cpkm in the horizontal temperature gradient spectrum. Strong temperature fronts O(1°–2°C/3–10 km) are observed near 33°N, 31°N, and 27°N. Temperature variability is partially density compensated by salinity, with the fraction of compensation increasing northward. There is evidence of vertical mixing during high winds. Temperature at 15‐m depth is roughly normally distributed around the climatological surface mean, with a standard deviation of approximately 0.5°C. The standard deviation would correspond to an adiabatic meridional displacement of 80–100 km in the mean gradient. Horizontal temperature gradient at 15‐m depth has maximum values in excess of 0.25°C/100 m and kurtosis near 80. In the band 0.10–1 cpkm, the 15‐m gradient spectrum is inversely proportional to wave number, consistent with predictions from geostrophic turbulence theory, while the spectrum at 70‐m depth has additional variance that is consistent with Garrett‐Munk internal wave displacements.

Horizontal spectra of atmospheric tracers measured during the Global Atmospheric Sampling Program

Variance power spectra of potential temperature, ozone, carbon monoxide, and water vapor at airliner cruise altitudes are presented. These results are based on data collected aboard commercial airlines at cruise altitudes during the Global Atmospheric Sampling Program (GASP). The horizontal scales (wavelengths) resolved by these data extend from 2.6–2400 km for temperature, 10–2400 km for ozone, 150–3000 km for water vapor, and 300–2500 km for carbon monoxide. The results divide into two distinct regimes in most cases, with the transition found at 500‐ to 800‐km wavelength. The long wavelength regime of temperature behaves as predicted by geostrophic turbulence theory, but only some of the chemical tracer results fit this model. At scales less than 500–800 km, spectral shapes of all tracers follow an approximately −5/3 power law dependence on wave number. At scales less than about 100 km, tropospheric ozone spectra follow a −1 power law. Spectral amplitudes of potential temperature and ozone are larger in the stratosphere than in the troposphere, while spectral amplitudes of carbon monoxide and water vapor are larger in the troposphere. The horizontal fluctuations giving rise to these spectra apparently result from that component of a spectrum of quasi‐horizontal displacements which acts orthogonal to the background gradient of each tracer. Numerical checks support this hypothesis for each of the chemical tracers, assuming the tracers are horizontally stratified. Finally, it is found that the frequency distribution of ozone spectral magnitude at a given wave number is approximately lognormal.

Hemispheric Spectral Statistics of Available Potential Energy

Abstract Analysis of hemispheric temperature variance data on five isobaric surfaces in terms of two-dimensional spectral decomposition shows that the available potential energy distributes with a slope in the neighborhood of −3 for the scale range 14≤n≤25. Although this slope varies with pressure, indications are that the observations substantiate the expectations of geostrophic turbulence theory. The noted deviations from −3 are discussed in terms of the distribution of energy in vertical modes which are not in the range in which −3 statistics should be expected. Vertical scales necessary for a three-dimensional spectral representation are considered with regard to the Brunt-Vaisala frequency distribution.