scholarly journals Observations of Small-Scale Secondary Instabilities during the Shoaling of Internal Bores on a Deep-Ocean Slope

2016 ◽  
Vol 46 (1) ◽  
pp. 219-231 ◽  
Author(s):  
Frédéric Cyr ◽  
Hans van Haren
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Dissipation Rate ◽  
Deep Ocean ◽  
Temperature Sensors ◽  
Small Scale ◽  
Cooling Phase ◽  
Northeast Atlantic Ocean ◽  
Internal Bores ◽  
Secondary Instabilities

AbstractThe Rockall Bank area, located in the northeast Atlantic Ocean, is a region dominated by topographically trapped diurnal tides. These tides generate up- and downslope displacements that can be locally described as swashing motions on the bank. Using high spatial and time resolution of moored temperature sensors, the transition toward the upslope flow (cooling phase) is described as a rapid upslope-propagating bore, likely generated by breaking trapped internal waves. Buoyant anomalies are found during the bore propagation, likely resulting from small-scale instabilities. The imbalance between the rate of disappearance of available potential energy and the dissipation rate of turbulent kinetic energy suggests that these instabilities are growing (i.e., young) and have high mixing potential.

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

FLOW INTO A BLACK HOLE

1996 ◽  
Vol 11 (01) ◽  
pp. 161-170
Author(s):  
DANIELA TORDELLA ◽  
ROBERT E. BREIDENTHAL
Keyword(s):  
Black Hole ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Dissipation Rate ◽  
Rotation Period ◽  
Gravitational Potential Energy ◽  
Circular Orbits ◽  
Turbulent Eddy ◽  
Orbital Radius ◽  
Flow Speeds

A simple model is proposed to describe the flow into a black hole from the turbulent flow of matter in initially circular orbits about the black hole. Magnetic effects are not considered. The shear between fluid elements at slightly different orbital radii causes turbulent eddies to be formed. These eddies determine the dissipation rate of kinetic energy into thermal energy. For approximately circular orbits, the magnitude of the gravitational potential energy is always equal to twice the kinetic energy; the destruction of the latter resulting in a reduction in the orbital radius and hence the potential energy. In this model, the turbulent eddy rotation period is presumed to be determined by the gradient in the gravity acceleration, leading to an eddy period proportional to the orbital period. If the flow speeds are supersonic but not relativistic, then the turbulent eddy size is set by the product of the eddy rotation period and the speed of sound. At a certain smaller radius, the orbital speeds and hence the dissipation rate are so great that the speeds become relativistic and the molecular speed tends toward its limit [Formula: see text]. Then the effective eddy size is controlled by the product of the eddy rotation period and the speed of light. Using these estimates for the important eddy size, the dissipation rate, temperature, density and sinking speed as a function of the orbital radius and the rate of mass flow into the black hole are derived. Subject headings: accretion, accretion disks, stars evolution, turbulence, eddy, sonic eddy.

scholarly journals Construction of a 3D Mooring Array of Temperature Sensors

2016 ◽  
Vol 33 (10) ◽  
pp. 2247-2257 ◽  
Author(s):  
Hans van Haren ◽  
Johan van Heerwaarden ◽  
Roel Bakker ◽  
Martin Laan
Keyword(s):  
Deep Ocean ◽  
Free Fall ◽  
Temperature Sensors ◽  
Small Scale ◽  
Quantitative Studies ◽  
Diameter Structure ◽  
Inner Diameter ◽  
Ocean Topography ◽  
Free Falling ◽  
Better Than

AbstractA small-scale 3D mooring array comprising up to 550 high-resolution temperature sensors was custom designed and constructed. The stand-alone array samples ocean temperature to depths of about 3000 m, limited by the buoyancy elements, at a rate of 1 Hz, with a precision better than 0.5 mK, a noise level better than 0.1 mK, and an endurance of 1 year. Its purpose serves quantitative studies on the development of turbulent mixing by internal wave breaking above deep-ocean topography. The 3D array consists of five parallel cables 105 m long with 3.2 mm inner diameter during the first deployment, now 5.5 mm. The cables are 4 and 5.6 m apart horizontally and are held under tension of 1000 N each using heavy buoyancy elements in a single line above. The entire array is folded into a 6-m high, 3-m-diameter structure above a 750-kg weight. It is deployed in a single overboard operation similar to that of a free-falling mooring. New here is the unfolding of the compacted array when hanging overboard and prior to release into free fall.

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.

scholarly journals Eddy-Modulated Internal Waves and Mixing on a Midocean Ridge

2012 ◽  
Vol 42 (7) ◽  
pp. 1242-1248 ◽  
Author(s):  
Xinfeng Liang ◽  
Andreas M. Thurnherr
Keyword(s):  
Kinetic Energy ◽  
Energy Content ◽  
World Ocean ◽  
Low Frequency ◽  
Mesoscale Eddies ◽  
Deep Ocean ◽  
Small Scale ◽  
Inertial Waves ◽  
Topographic Roughness ◽  
Geostrophic Flows

Abstract Mesoscale eddies are ubiquitous in the World Ocean and dominate the energy content on subinertial time scales. Recent theoretical and numerical studies suggest a connection between mesoscale eddies and diapycnal mixing in the deep ocean, especially near rough topography in regions of strong geostrophic flow. However, unambiguous observational evidence for such a connection has not yet been found, and it is still unclear what physical processes are responsible for transferring energy from mesoscale to small-scale processes. Here, the authors present observations demonstrating that finescale variability near the crest of the East Pacific Rise is strongly modulated by low-frequency geostrophic flows, including those due to mesoscale eddies. During times of strong subinertial flows, the authors observed elevated kinetic energy on vertical scales <50 m and in the near-inertial band, predominantly upward-propagating near-inertial waves, and increased incidence of layers with Richardson number . In contrast, during times of weak subinertial flows, kinetic energy in the finescale and near-inertial bands is lower, Ri values are higher, and near-inertial waves propagate predominantly downward through the water column. Diapycnal diffusivities estimated indirectly from a simple Ri-based parameterization are consistent with results from a tracer-release experiment and a microstructure survey bracketing the mooring measurements. These observations are consistent with energy transfer (a “cascade”) from subinertial flows, including mesoscale eddies, to near-inertial oscillations, turbulence, and mixing. This interpretation suggests that, in addition to topographic roughness and tidal forcing, parameterization of deep-ocean mixing should also take subinertial flows into account. The findings presented here are expected to be useful for validating and improving numerical-model parameterizations of turbulence and mixing in the ocean.

scholarly journals Deep-sea turbulence evolution observed by multiple closely spaced instruments

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chu-Fang Yang ◽  
Wu-Cheng Chi ◽  
Hans van Haren
Keyword(s):  
Kinetic Energy ◽  
Internal Waves ◽  
Deep Sea ◽  
Large Scale ◽  
Time Derivative ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Ocean Bottom ◽  
Seafloor Topography

AbstractTurbulent mixing in the deep ocean is not well understood. The breaking of internal waves on sloped seafloor topography can generate deep-sea turbulence. However, it is difficult to measure turbulence comprehensively due to its multi-scale processes, in addition to flow–flow and flow–topography interactions. Dense, high-resolution spatiotemporal coverage of observations may help shed light on turbulence evolution. Here, we present turbulence observations from four broadband ocean bottom seismometers (OBSs) and a 200-m vertical thermistor string (T-string) in a footprint of 1 × 1 km to characterize turbulence induced by internal waves at a depth of 3000 m on a Pacific continental slope. Correlating the OBS-calculated time derivative of kinetic energy and the T-string-calculated turbulent kinetic energy dissipation rate, we propose that the OBS-detected signals were induced by near-seafloor turbulence. Strong disturbances were detected during a typhoon period, suggesting large-scale inertial waves breaking with upslope transport speeds of 0.2–0.5 m s−1. Disturbances were mostly excited on the downslope side of the array where the internal waves from the Pacific Ocean broke initially and the turbulence oscillated between < 1 km small-scale ridges. Such small-scale topography caused varying turbulence-induced signals due to localized waves breaking. Arrayed OBSs can provide complementary observations to characterize deep-sea turbulence.

Direct particle–fluid simulation of Kolmogorov-length-scale size particles in decaying isotropic turbulence

2017 ◽  
Vol 819 ◽  
pp. 188-227 ◽  
Author(s):  
Lennart Schneiders ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Kinetic Energy ◽  
Strain Rate ◽  
Viscous Dissipation ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Bulk Flow ◽  
Small Scale ◽  
Length Scale ◽  
Kolmogorov Length Scale ◽  
Scale Size

The modulation of decaying isotropic turbulence by 45 000 spherical particles of Kolmogorov-length-scale size is studied using direct particle–fluid simulations, i.e. the flow field over each particle is fully resolved by direct numerical simulations of the conservation equations. A Cartesian cut-cell method is used by which the exchange of momentum and energy at the fluid–particle interfaces is strictly conserved. It is shown that the particles absorb energy from the large scales of the carrier flow while the small-scale turbulent motion is determined by the inertial particle dynamics. Whereas the viscous dissipation rate of the bulk flow is attenuated, the particles locally increase the level of dissipation due to the intense strain rate generated near the particle surfaces due to the crossing-trajectory effect. Analogously, the rotational motion of the particles decouples from the local fluid vorticity and strain-rate field at increasing particle inertia. The high level of dissipation is partially compensated by the transfer of momentum to the fluid via forces acting at the particle surfaces. The spectral analysis of the kinetic energy budget is supported by the average flow pattern about the particles showing a nearly universal strain-rate distribution. An analytical expression for the instantaneous rate of viscous dissipation induced by each particle is derived and subsequently verified numerically. Using this equation, the local balance of fluid kinetic energy around a particle of arbitrary shape can be precisely determined. It follows that two-way coupled point-particle models implicitly account for the particle-induced dissipation rate via the momentum-coupling terms; however, they disregard the actual length scales of the interaction. Finally, an analysis of the small-scale flow topology shows that the strength of vortex stretching in the bulk flow is mitigated due to the presence of the particles. This effect is associated with the energy conversion at small wavenumbers and the reduced level of dissipation at intermediate wavenumbers. Consequently, it damps the spectral flux of energy to the small scales.

Update on the Global Energy Dissipation Rate of Deep-Ocean Low-Frequency Flows by Bottom Boundary Layer

2018 ◽  
Vol 48 (6) ◽  
pp. 1243-1255 ◽  
Author(s):  
Chao Huang ◽  
Yongsheng Xu
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Dissipation Rate ◽  
Low Frequency ◽  
Deep Ocean ◽  
Power Input ◽  
Energy Dissipation Rate ◽  
Bottom Boundary Layer ◽  
Geostrophic Currents ◽  
Bottom Boundary

AbstractThe global dissipation caused by bottom boundary layer drag is one of the major pathways for the consumption of kinetic energy in the deep ocean. However, the spatial distribution and global integral of the drag dissipation are still debatable. This paper presents an updated estimate of the dissipation rate, using the barotropic component of surface geostrophic currents and 632 in situ velocity measurements. Also, the seafloor roughness is proposed as a parameter of drag efficiency in the parameterized method. The results provide a map of the drag dissipation rate with a global integral of ~0.26 TW. Approximately 66% of this dissipation occurs in the Southern Ocean, which is consistent with the proportion of wind power input into this region. Building upon the work in previous studies on the bottom boundary layer drag, more long-period observations are used, eliminating the influence of the baroclinic contribution to the surface geostrophic currents in the construction of the bottom velocity, and taking topographic roughness into account. The estimates have implications for the maintenance of density structure in the deep ocean and understanding of the kinetic energy budget.

scholarly journals Energetics of small scale turbulence in the lower stratosphere from high resolution radar measurements

2001 ◽  
Vol 19 (8) ◽  
pp. 945-952 ◽  
Author(s):  
J. Dole ◽  
R. Wilson ◽  
F. Dalaudier ◽  
C. Sidi
Keyword(s):  
High Resolution ◽  
Kinetic Energy ◽  
Dissipation Rate ◽  
Lower Stratosphere ◽  
Inertial Subrange ◽  
Small Scale ◽  
Temperature Variance ◽  
Dissipation Rates ◽  
High Resolution Radar ◽  
Radar Measurements

Abstract. Very high resolution radar measurements were performed in the troposphere and lower stratosphere by means of the PROUST radar. The PROUST radar operates in the UHF band (961 MHz) and is located in St. Santin, France (44°39’ N, 2°12’ E). A field campaign involving high resolution balloon measurements and the PROUST radar was conducted during April 1998. Under the classical hypothesis that refractive index inhomogeneities at half radar wavelength lie within the inertial subrange, assumed to be isotropic, kinetic energy and temperature variance dissipation rates were estimated independently in the lower stratosphere. The dissipation rate of temperature variance is proportional to the dissipation rate of available potential energy. We therefore estimate the ratio of dissipation rates of potential to kinetic energy. This ratio is a key parameter of atmospheric turbulence which, in locally homogeneous and stationary conditions, is simply related to the flux Richardson number, Rf .Key words. Meteorology and atmospheric dynamics (turbulence) – Radio science (remote sensing)

scholarly journals Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers

2017 ◽  
Vol 825 ◽  
pp. 213-244 ◽  
Author(s):  
A. K. Kaminski ◽  
C. P. Caulfield ◽  
J. R. Taylor
Keyword(s):  
Kinetic Energy ◽  
Dissipation Rate ◽  
Richardson Number ◽  
Initial Perturbation ◽  
Necessary Condition ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Buoyancy Frequency ◽  
Strongly Nonlinear ◽  
Perturbation Energy

The Miles–Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the minimum gradient Richardson number, $Ri_{g,min}$, is less than $1/4$ somewhere in the flow. However, the non-normality of the Navier–Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times. We calculate numerically the linear optimal perturbations which maximize the perturbation energy gain for a stably stratified shear layer consisting of a hyperbolic tangent velocity distribution with characteristic velocity $U_{0}^{\ast }$ and a uniform stratification with constant buoyancy frequency $N_{0}^{\ast }$. We vary the bulk Richardson number $Ri_{b}=N_{0}^{\ast 2}h^{\ast 2}/U_{0}^{\ast 2}$ (corresponding to $Ri_{g,min}$) between 0.20 and 0.50 and the Reynolds numbers $\mathit{Re}=U_{0}^{\ast }h^{\ast }/\unicode[STIX]{x1D708}^{\ast }$ between 1000 and 8000, with the Prandtl number held fixed at $\mathit{Pr}=1$. We find the transient growth of non-normal perturbations may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow even in flows where $Ri_{g,min}>1/4$. We show that the effects of nonlinearity are more significant for flows with higher $\mathit{Re}$, lower $Ri_{b}$ and higher initial perturbation amplitude $E_{0}$. Enhanced kinetic energy dissipation is observed for higher-$Re$ and lower-$Ri_{b}$ flows, and the mixing efficiency, quantified here by $\unicode[STIX]{x1D700}_{p}/(\unicode[STIX]{x1D700}_{p}+\unicode[STIX]{x1D700}_{k})$ where $\unicode[STIX]{x1D700}_{p}$ is the dissipation rate of density variance and $\unicode[STIX]{x1D700}_{k}$ is the dissipation rate of kinetic energy, is found to be approximately 0.35 for the most strongly nonlinear cases.

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