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.

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.

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 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.

Determination of hydraulic resistance of channels using spectral geometry methods

2021 ◽  
Author(s):  
Alex Baron
Keyword(s):  
Hydraulic Resistance ◽  
Cross Section ◽  
Dissipation Rate ◽  
Average Energy ◽  
Energy Dissipation Rate ◽  
High Accuracy ◽  
Spectral Geometry ◽  
Constant Cross Section ◽  
Theoretical Justification

Abstract In this paper, we propose a new method for calculation of hydraulic resistance of channels with constant cross-section. The method is based on the obtained estimates for the average energy dissipation rate in a turbulent flow. The first part of the paper is devoted to theoretical justification of the method. The second part is devoted to calculation of hydraulic resistance of various channels using the abovementioned method and comparison of these values with the known results. The proposed method allows for calculation of hydraulic resistance of various channels with sufficiently high accuracy and is based only on the information about the channel geometry.

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.

scholarly journals Scaling bounds on dissipation in turbulent flows

2015 ◽  
Vol 777 ◽  
pp. 591-603 ◽  
Author(s):  
Christian Seis
Keyword(s):  
Fluid Dynamics ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Equations Of Motion ◽  
Average Energy ◽  
Energy Dissipation Rate ◽  
Porous Medium Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Rigorous Method

We propose a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow, Rayleigh–Bénard convection and porous medium convection.

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.

Diapycnal Mixing in the Subthermocline of the Mariana Ridge from High-Resolution Seismic Images

2021 ◽  
Vol 51 (4) ◽  
pp. 1283-1300
Author(s):  
Qunshu Tang ◽  
Zhiyou Jing ◽  
Jianmin Lin ◽  
Jie Sun
Keyword(s):  
High Resolution ◽  
Dissipation Rate ◽  
Large Scale ◽  
Internal Tide ◽  
Ocean Model ◽  
Small Scale ◽  
Far Field ◽  
Continuous Map ◽  
Diapycnal Diffusivity ◽  
Seismic Images

AbstractThe Mariana Ridge is one of the prominent mixing hotspots of the open ocean. The high-resolution underway marine seismic reflection technique provides an improved understanding of the spatiotemporal continuous map of ocean turbulent mixing. Using this novel technique, this study quantifies the diapycnal diffusivity of the subthermocline (300–1200-m depth) turbulence around the Mariana Ridge. The autotracked wave fields on seismic images allow us to derive the dissipation rate ε and diapycnal diffusivity Kρ based on the Batchelor model, which relates the horizontal slope spectra with +1/3 slope to the inertial convective turbulence regime. Diffusivity is locally intensified around the seamounts exceeding 10−3 m2 s−1 and gradually decreases to 10−5–10−4 m2 s−1 in ~60-km range, a distance that may be associated with the internal tide beam emanating paths. The overall pattern suggests a large portion of the energy dissipates locally and a significant portion dissipates in the far field. Empirical diffusivity models Kρ(x) and Kρ(z), varying with the distance from seamounts and the height above seafloor, respectively, are constructed for potential use in ocean model parameterization. Geographic distributions of both the vertically averaged dissipation rate and diffusivity show tight relationships with the topography. Additionally, a strong agreement of the dissipation results between seismic observation and numerical simulation is found for the first time. Such an agreement confirms the suitability of the seismic method in turbulence quantification and suggests the energy cascade from large-scale tides to small-scale turbulence via possible mechanisms of local direct tidal dissipation, near-local wave–wave interactions, and far-field radiating and breaking.

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.

scholarly journals Tidally Forced Internal Waves and Overturns Observed on a Slope: Results from HOME

2006 ◽  
Vol 36 (6) ◽  
pp. 1184-1201 ◽  
Author(s):  
Murray D. Levine ◽  
Timothy J. Boyd
Keyword(s):  
Dissipation Rate ◽  
Internal Tide ◽  
Indirect Evidence ◽  
Density Field ◽  
Tidal Mixing ◽  
Vertical Shear ◽  
Buoyancy Frequency ◽  
Turbulent Dissipation ◽  
Order Of Magnitude ◽  
Highly Correlated

Abstract Tidal mixing over a slope was explored using moored time series observations on Kaena Ridge extending northwest from Oahu, Hawaii, during the Survey component of the Hawaii Ocean Mixing Experiment (HOME). A mooring was instrumented to sample the velocity and density field of the lower 500 m of the water column to look for indirect evidence of tidally induced mixing and was deployed on a slope in 1453-m water depth for 2 months beginning in November 2000. The semidiurnal barotropic tidal currents at this site have a significant cross-ridge component, favorable for exciting an internal tidal response. A large-amplitude response is expected, given that the slope of the topography (4.5°) is nearly the same as the slope of the internal wave group velocity at semidiurnal frequency. Density overturns were inferred from temperature profiles measured every 2 min. The number and strength of the overturns are greater in the 200 m nearest the bottom, with overturns exceeding 24 m present at any depth nearly 10% of the time. Estimates of turbulent dissipation rate ɛ were made for each overturn by associating the measured Thorpe scale with the Ozmidov scale. The average ɛ between 1300 and 1450 m for the entire experiment is about 10−8 m2 s−3, corresponding to an average Kρ of 10−3 m2 s−1. Both ɛ and Kρ decrease by about an order of magnitude by 1200 m. The occurrence of overturns and the magnitude of ɛ are both highly correlated with the tide: both with the spring–neap cycle as well as the phase of the semidiurnal tide itself. Dissipation rate varies by at least an order of magnitude over the spring–neap cycle. It appears that tidal frequency vertical shear within 200 m of the boundary leads to significant strain (vertical divergence). Most of the overturns occur during the few hours when the vertical strain is greatest. The buoyancy frequency N calculated from reordering these overturns is a factor of 3 lower than the background N. This is consistent with the following kinematic description: the internal tide first strains the mean density field, leading to regions of low N that subsequently overturn. Less regularly, overturns also occur when the internal tide strain has created relatively high stratification within 200 m of the bottom.

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