Estimation of Small-Scale Vertical Diffusivity for CO2 Injected in the Deep Ocean

2009 ◽  
Author(s):  
Shinichiro Hirabayashi ◽  
Toru Sato
Keyword(s):  
Spectral Analysis ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Spatial Information ◽  
Measurement Data ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Computational Domain ◽  
Vertical Diffusivity

In this study, vertical diffusivity, the scale of which was O (10 m), at a particular site in the deep ocean was estimated by using numerical simulations with forcing low-wavenumber components, which had been reproduced from measurement data. Spatial information of velocity field was reproduced by spectral analysis of 4 sets of time-series measured simultaneously at different places in the real ocean. In order to estimate finer-scale structures, which are necessary to obtain statistical quantities such as energy dissipation rate, large eddy simulations were carried out with forcing low-wavenumber components of velocity reproduced in the spectral analysis. The low-wavenumber components generated by the nonlinear interaction of forced components and resolved components were successfully removed from the computational domain by introducing a partial spectral filter in place of the conventional FFT filter. Vertical diffusivity was estimated by using the energy dissipation rate of the reproduced flow field, which was 3.3×10−5 m2s−1 on the time average.

Numerical Simulation of Small-Scale Turbulent Diffusion for Injected CO2 in the Deep Ocean

2006 ◽  
Author(s):  
Shinichiro Hirabayashi ◽  
Toru Sato
Keyword(s):  
Energy Dissipation ◽  
Turbulent Diffusion ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Internal Tides ◽  
Time Variability ◽  
Small Scale ◽  
Computational Domain ◽  
Average Value ◽  
O 10

Small-scale turbulent diffusion is numerically simulated in relation to its time variability dependent on tidal current. From time series of 3D (3-dimensional) velocity and temperature measured at the depth of 2000 m, main constituents of internal tides are extracted. Wavenumbers of eddies, the scale of which is O (102) m, are determined by Taylor’s frozen eddy hypothesis with time-varying tidal speed taken as advection velocity. Large eddy simulation was applied to generate turbulence numerically by forcing the measured low-wavenumber components in the computational domain. The result shows that the energy dissipation rate varies in time, ranging from O (10−11) to O (10−7) m2 s−3. These values of energy dissipation correspond with vertical diffusivity of 10−6 to 10−4 m2 s−1 in this area, with temporal average value of 6.9 × 10−5 m2 s−1.

Evaluation of Turbulent Kinetic Energy Dissipation Rate in a Free Jet Flow from PIV Measurements

2012 ◽  
Vol 7 (1) ◽  
pp. 53-69
Author(s):  
Vladimir Dulin ◽  
Yuriy Kozorezov ◽  
Dmitriy Markovich
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Piv Measurements ◽  
Free Jet

The present paper reports PIV (Particle Image Velocimetry) measurements of turbulent velocity fluctuations statistics in development region of an axisymmetric free jet (Re = 28 000). To minimize measurement uncertainty, adaptive calibration, image processing and data post-processing algorithms were utilized. On the basis of theoretical analysis and direct measurements, the paper discusses effect of PIV spatial resolution on measured statistical characteristics of turbulent fluctuations. Underestimation of the second-order moments of velocity derivatives and of the turbulent kinetic energy dissipation rate due to a finite size of PIV interrogation area and finite thickness of laser sheet was analyzed from model spectra of turbulent velocity fluctuations. The results are in a good agreement with the measured experimental data. The paper also describes performance of possible ways to account for unresolved small-scale velocity fluctuations in PIV measurements of the dissipation rate. In particular, a turbulent viscosity model can be efficiently used to account for the unresolved pulsations in a free turbulent flow

scholarly journals Comparing turbulent parameters obtained from LITOS and radiosonde measurements

2014 ◽  
Vol 14 (13) ◽  
pp. 19033-19053 ◽  
Author(s):  
A. Schneider ◽  
M. Gerding ◽  
F.-J. Lübken
Keyword(s):  
Spectral Analysis ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Potential Temperature ◽  
Energy Dissipation Rate ◽  
Radiosonde Data ◽  
Turbulence Measurement ◽  
Trace Species ◽  
Ozmidov Scale ◽  
Inner Scale

Abstract. Stratospheric turbulence is important for the mixing of trace species and the energy balance, but direct measurements are sparse due to the required resolution and accuracy. Recently, turbulence parameters such as the energy dissipation rate ε were inferred from standard radiosonde data by means of a Thorpe analysis. To this end, layers with vertically decreasing potential temperature are analysed, which is expected to drive turbulence. Such an application assumes a proportionality between the Thorpe length LT and the Ozmidov scale LO. While this relation is accepted for the ocean, experimental evidence for such proportionality in the stratosphere is sparse. We have developed a high-resolution (8 kHz) turbulence measurement system called LITOS, which for the first time resolves the inner scale of turbulence in the stratosphere. Therewith the energy dissipation rate ε can be determined by spectral analysis. This independent value for ε enables us to check the relation LO ∝ LT. It turns out that no proportionality can be seen in our measurements. Furthermore, dissipation rates obtained from radiosondes deviate up to a factor of ~ 3000 to those obtained by spectral analysis. Some turbulent layers measured by LITOS are not observed by the radiosonde at all, and vice versa.

scholarly journals Spectrally Resolved Energy Dissipation Rate and Momentum Flux of Breaking Waves

2008 ◽  
Vol 38 (6) ◽  
pp. 1296-1312 ◽  
Author(s):  
Johannes R. Gemmrich ◽  
Michael L. Banner ◽  
Chris Garrett
Keyword(s):  
Energy Dissipation ◽  
Wave Field ◽  
Wave Energy ◽  
Dissipation Rate ◽  
Momentum Flux ◽  
Phase Speed ◽  
Breaking Waves ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Breaking Wave

Abstract Video observations of the ocean surface taken from aboard the Research Platform FLIP reveal the distribution of the along-crest length and propagation velocity of breaking wave crests that generate visible whitecaps. The key quantity assessed is Λ(c)dc, the average length of breaking crests per unit area propagating with speeds in the range (c, c + dc). Independent of the wave field development, Λ(c) is found to peak at intermediate wave scales and to drop off sharply at larger and smaller scales. In developing seas breakers occur at a wide range of scales corresponding to phase speeds from about 0.1 cp to cp, where cp is the phase speed of the waves at the spectral peak. However, in developed seas, breaking is hardly observed at scales corresponding to phase speeds greater than 0.5 cp. The phase speed of the most frequent breakers shifts from 0.4 cp to 0.2 cp as the wave field develops. The occurrence of breakers at a particular scale as well as the rate of surface turnover are well correlated with the wave saturation. The fourth and fifth moments of Λ(c) are used to estimate breaking-wave-supported momentum fluxes, energy dissipation rate, and the fraction of momentum flux supported by air-entraining breaking waves. No indication of a Kolmogorov-type wave energy cascade was found; that is, there is no evidence that the wave energy dissipation is dominated by small-scale waves. The proportionality factor b linking breaking crest distributions to the energy dissipation rate is found to be (7 ± 3) × 10−5, much smaller than previous estimates.

Observations of Small-Scale Processes Associated with the Internal Tide Encountering an Island

2005 ◽  
Vol 35 (9) ◽  
pp. 1553-1567 ◽  
Author(s):  
Craig L. Stevens ◽  
Edward R. Abraham ◽  
C. Mark Moore ◽  
Philip W. Boyd ◽  
Jonathan Sharples
Keyword(s):  
Dissipation Rate ◽  
East Coast ◽  
Average Energy ◽  
Internal Tide ◽  
Propagation Speed ◽  
Energy Dissipation Rate ◽  
Nonstationary Time Series ◽  
Small Scale ◽  
Vertical Diffusivity ◽  
Order Of Magnitude

Abstract Current-meter, temperature, and microstructure observations of the large-amplitude internal tide shoaling on the continental shelf of the east coast of northern New Zealand show the complexity of the internal kinematics and mixing. The propagation speed of the main internal wave was around 0.3 m s−1, and nonstationary time series analysis was used to locate the trailing short-wavelength internal waves in frequency (periods of around 40 min) and tidal-phase space. The average energy dissipation rate (5 × 10−8 m2 s−3) was an order of magnitude smaller than that observed on the open shelf in other studies, but peaks in dissipation rate were measured to be much greater. The vertical diffusivity of heat was around 10−4 m2 s−1, comparable to, or greater than, other studies. Examples of the scale and sporadic nature of larger mixing events were observed. The behavior was complicated by the nearby steeply shoaling coast of the Poor Knight Islands. Consistent reflected wave energy was not apparent.

scholarly journals High-Resolution In Situ Profiling through the Stable Boundary Layer: Examination of the SBL Top in Terms of Minimum Shear, Maximum Stratification, and Turbulence Decrease

2006 ◽  
Vol 63 (4) ◽  
pp. 1291-1307 ◽  
Author(s):  
B. B. Balsley ◽  
R. G. Frehlich ◽  
M. L. Jensen ◽  
Y. Meillier
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
High Resolution ◽  
Stable Boundary Layer ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Horizontal Wind ◽  
Small Scale ◽  
Stable Boundary ◽  
Stable Conditions

Abstract Some 50 separate high-resolution profiles of small-scale turbulence defined by the energy dissipation rate (ɛ), horizontal wind speed, and temperature from near the surface, through the nighttime stable boundary layer (SBL), and well into the residual layer are used to compare the various definitions of SBL height during nighttime stable conditions. These profiles were obtained during postmidnight periods on three separate nights using the Tethered Lifting System (TLS) during the Cooperative Atmosphere–Surface Exchange Study (CASES-99) campaign in east-central Kansas, October 1999. Although the number of profiles is insufficient to make any definitive conclusions, the results suggest that, under most conditions, the boundary layer top can be reasonably estimated in terms of a very significant decrease in the energy dissipation rate (i.e., the mixing height) with height. In the majority of instances this height lies slightly below the height of a pronounced minimum in wind shear and slightly above a maximum in N 2, where N is the Brunt–Väisälä frequency. When combined with flux measurements and vertical velocity variance data obtained from the nearby 55-m tower, the results provide additional insights into SBL processes, even when the boundary layer, by any definition, extends to heights well above the top of the tower. Both the TLS profiles and tower data are then used for preliminary high-resolution studies into various categories of SBL structure, including the so-called upside-down boundary layer.

The multifractal lagrangian nature of turbulence

1993 ◽  
Vol 342 (1665) ◽  
pp. 379-411 ◽  
Keyword(s):  
Fixed Point ◽  
Energy Dissipation ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Small Volume ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Fractal Curve ◽  
Multifractal Formalism ◽  
Lagrangian Statistics

The multifractal formalism for the eulerian statistics of small-scale dynamics in turbulent flows is reviewed. Theoretical extensions of these results (the statistics of small volume averages of the energy dissipation rate) are used to predict properties of the probability distribution of the local energy dissipation rate at a fixed point. The improved parametrization of the eulerian statistics allows the lagrangian statistics (those for a fixed fluid particle in contrast to the eulerian statistics at a fixed point) to be determined exactly by using results derived as a consequence of incompressibility. Several properties of particle trajectories in a turbulent flow can be predicted with these new lagrangian statistics. In particular, a trajectory is typically smooth and generally unremarkable in its features. This contrasts the often suggested description: that of a highly convoluted and intricately structured ‘fractal’ curve. Some of the traditional dispersion results, which depend on the lagrangian statistics, are shown to be only weakly influenced by the intermittency inherent in the multifractal character of turbulence.

scholarly journals Comparing turbulent parameters obtained from LITOS and radiosonde measurements

2015 ◽  
Vol 15 (4) ◽  
pp. 2159-2166 ◽  
Author(s):  
A. Schneider ◽  
M. Gerding ◽  
F.-J. Lübken
Keyword(s):  
Spectral Analysis ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Potential Temperature ◽  
Energy Dissipation Rate ◽  
Radiosonde Data ◽  
Turbulence Measurement ◽  
Trace Species ◽  
Ozmidov Scale ◽  
Inner Scale

Abstract. Stratospheric turbulence is important for the mixing of trace species and the energy balance, but direct measurements are sparse due to the required resolution and accuracy. Recently, turbulence parameters such as the energy dissipation rate ε were inferred from standard radiosonde data by means of a Thorpe analysis. To this end, layers with vertically decreasing potential temperature are analysed, which is expected to indicate turbulence. Such an application assumes a proportionality between the Thorpe length LT and the Ozmidov scale LO. While this relation is accepted for the ocean, experimental evidence for such proportionality in the stratosphere is sparse. We have developed a high-resolution (8 kHz) turbulence measurement system called LITOS (Leibniz Institute Turbulence Observations in the Stratosphere), which for the first time resolves the inner scale of turbulence in the stratosphere. Therewith the energy dissipation rate ε can be determined by spectral analysis. This independent value for ε enables us to check the relation LO ∝ LT. In our measurements no such proportionality can be seen, although the mean of the ratio LO/LT is close to what is assumed in radiosonde analyses. Dissipation rates for individual layers obtained from radiosondes deviate up to a factor of ~3000 from those obtained by spectral analysis. Some turbulent layers measured by LITOS are not observed by the radiosonde at all, and vice versa. However, statements about the statistical mean seem to be possible by Thorpe analysis.

Stochastic models for the droplet motion and evaporation in under-resolved turbulent flows at a large Reynolds number

2021 ◽  
Vol 932 ◽  
Author(s):  
M.A. Gorokhovski ◽  
S.K. Oruganti
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Stochastic Models ◽  
Dissipation Rate ◽  
High Speed ◽  
Evaporation Rate ◽  
Energy Dissipation Rate ◽  
Large Reynolds Number ◽  
Small Scale ◽  
Droplet Motion

In this work we introduce a Lagrangian stochastic model for particle motion and evaporation to be used in large-eddy simulations (LES) of turbulent liquid sprays. Effects of small-scale intermittency, usually under-resolved in LES, are explicitly included via modelling of the energy dissipation rate seen by a droplet along its trajectory. Namely, the dissipation rate is linked to the norm of the droplet sub-filtered acceleration which is included in the droplet motion equation. This norm, along with the direction of the droplet sub-filtered acceleration, is simulated as a stochastic process. With increasing Reynolds number, the distribution of the sub-filtered acceleration develops longer tails, with a slower decay in auto-correlation functions of the norm and direction of this acceleration. The stochastic models are specified for particles larger and smaller the Kolmogorov length scale. The assumption of the droplet evaporation model is similar, i.e. the evaporation rate is strongly enhanced when a droplet is subjected to very localized zones of intense velocity gradients. Thereby, the overall evaporation process is assumed to be a succession of two steady-state sub-processes with equal intensities, i.e. evaporation and vapour mixing. Then the stochastic properties of the overall evaporation rate are also controlled by fluctuations of the energy dissipation rate along the droplet path, and with increasing Reynolds number, the intensity of fluctuations of this rate is also increasing. The assessment of the presented stochastic models in LES of high-speed non-evaporating and evaporating sprays show the accurate prediction of experimental data on relatively coarser grids along with a remarkably weaker sensitivity to the grid spacing. The joint statistics and Voronoi tessellations exhibit strong intermittency of evaporation rate. The intensity of turbulence along the droplet pathway substantially promotes the vaporization rate.

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