scholarly journals Time-Dependent Eddy-Mean Energy Diagrams and Their Application to the Ocean

2016 ◽  
Vol 46 (9) ◽  
pp. 2827-2850 ◽  
Author(s):  
Ru Chen ◽  
Andrew F. Thompson ◽  
Glenn R. Flierl
Keyword(s):  
Large Scale ◽  
Energy Exchange ◽  
Temporal Variations ◽  
Turnover Time ◽  
Time Dependent ◽  
Global Ocean ◽  
Mean Flow ◽  
Flow Interactions ◽  
The Mean ◽  
Three Components

AbstractInsight into the global ocean energy cycle and its relationship to climate variability can be gained by examining the temporal variability of eddy–mean flow interactions. A time-dependent version of the Lorenz energy diagram is formulated and applied to energetic ocean regions from a global, eddying state estimate. The total energy in each snapshot is partitioned into three components: energy in the mean flow, energy in eddies, and energy temporal anomaly residual, whose time mean is zero. These three terms represent, respectively, correlations between mean quantities, correlations between eddy quantities, and eddy-mean correlations. Eddy–mean flow interactions involve energy exchange among these three components. The temporal coherence about energy exchange during eddy–mean flow interactions is assessed. In the Kuroshio and Gulf Stream Extension regions, a suppression relation is manifested by a reduction in the baroclinic energy pathway to the eddy kinetic energy (EKE) reservoir following a strengthening of the barotropic energy pathway to EKE; the baroclinic pathway strengthens when the barotropic pathway weakens. In the subtropical gyre and Southern Ocean, a delay in energy transfer between different reservoirs occurs during baroclinic instability. The delay mechanism is identified using a quasigeostrophic, two-layer model; part of the potential energy in large-scale eddies, gained from the mean flow, cascades to smaller scales through eddy stirring before converting to EKE. The delay time is related to this forward cascade and scales linearly with the eddy turnover time. The relation between temporal variations in wind power input and eddy–mean flow interactions is also assessed.

A Simple Dynamical Model with Features of Convective Momentum Transport

2009 ◽  
Vol 66 (2) ◽  
pp. 373-392 ◽  
Author(s):  
Andrew J. Majda ◽  
Samuel N. Stechmann
Keyword(s):  
Dynamic Model ◽  
Large Scale ◽  
Intraseasonal Oscillation ◽  
Momentum Transport ◽  
Linear Stability Theory ◽  
Westerly Wind ◽  
Mean Flow ◽  
Flow Interactions ◽  
The Mean ◽  
Convective Momentum Transport

Abstract Convective momentum transport (CMT) plays a central role in interactions across multiple space and time scales. However, because of the multiscale nature of CMT, quantifying and parameterizing its effects is often a challenge. Here a simple dynamic model with features of CMT is systematically derived and studied. The model includes interactions between a large-scale zonal mean flow and convectively coupled gravity waves, and convection is parameterized using a multicloud model. The moist convective wave–mean flow interactions shown here have several interesting features that distinguish them from other classical wave–mean flow settings. First an intraseasonal oscillation of the mean flow and convectively coupled waves (CCWs) is described. The mean flow oscillates due to both upscale and downscale CMT, and the CCWs weaken, change their propagation direction, and strengthen as the mean flow oscillates. The basic mechanisms of this oscillation are corroborated by linear stability theory with different mean flow background states. Another case is set up to imitate the westerly wind burst phase of the Madden–Julian oscillation (MJO) in the simplified dynamic model. In this case, CMT first accelerates the zonal jet with the strongest westerly wind aloft, and then there is deceleration of the winds due to CMT; this occurs on an intraseasonal time scale and is in qualitative agreement with actual observations of the MJO. Also, in this case, a multiscale envelope of convection propagates westward with smaller-scale convection propagating eastward within the envelope. The simplified dynamic model is able to produce this variety of behavior even though it has only a single horizontal direction and no Coriolis effect.

scholarly journals Spatiotemporal Variability of the Global Ocean Internal Processes Inferred from Satellite Observations

2019 ◽  
Vol 49 (8) ◽  
pp. 2147-2164 ◽  
Author(s):  
Yang Yang ◽  
X. San Liang
Keyword(s):  
Southern Ocean ◽  
Large Scale ◽  
Kuroshio Extension ◽  
Spatiotemporal Variability ◽  
Global Ocean ◽  
Western Boundary ◽  
Analysis Tool ◽  
Mean Flow ◽  
Annual Fluctuation ◽  
The Mean

AbstractUsing a new analysis tool, namely, multiscale window transform (MWT), and the MWT-based theory of canonical transfer, this study investigates the spatiotemporal variations of the nonlinear interactions among the mean flows, interannual variabilities, quasi-annual fluctuations, and eddies in the global ocean. It is found that the canonical kinetic energy (KE) transfers are highly inhomogeneous in space, maximized in the western boundary current (WBC), Southern Ocean, and equatorial regions. In contrast to the equatorial and WBC regions where the temporal KE cascades are mainly forward, the Southern Ocean is the very place where coherent large-scale patterns of inverse KE cascade take place. The canonical transfers are also found to be highly variable in time. Specifically, in the Kuroshio Extension, the transfer from the mean flow to the interannual variability is in pace with the external winds from the eastern North Pacific; in the subtropical gyre, the mean flow-to-eddy transfer is responsible for the variability of the eddy kinetic energies (EKE) at both interannual and seasonal scales; in the tropics, the downscale transfers to the eddies from the other three scales all contribute to the interannual modulation of the EKE, and these transfers tend to decrease (increase) during El Niño (La Niña) events. In the Southern Ocean, the high-frequency eddies are found to feed KE to the low-frequency variability through temporal inverse cascade processes, which have been strengthened due to the enhanced eddy activities in the recent decade. Also discussed here is the relation between the seasonal EKE variability and the eddy–quasi-annual fluctuation interaction.

scholarly journals Tidal bending of ice shelves as a mechanism for large-scale temporal variations in ice flow

2018 ◽  
Vol 12 (5) ◽  
pp. 1699-1713 ◽  
Author(s):  
Sebastian H. R. Rosier ◽  
G. Hilmar Gudmundsson
Keyword(s):  
Stream Flow ◽  
Large Scale ◽  
Temporal Variations ◽  
Mean Flow ◽  
Ice Shelf ◽  
Ice Flow ◽  
Ice Shelves ◽  
The Mean ◽  
Viscoelastic Modelling ◽  
Shelf Flow

Abstract. GPS measurements reveal strong modulation of horizontal ice shelf and ice stream flow at a variety of tidal frequencies, most notably a fortnightly (Msf) frequency not present in the vertical tides themselves. Current theories largely fail to explain the strength and prevalence of this signal over floating ice shelves. We show how well-known non-linear aspects of ice rheology can give rise to widespread, long-periodic tidal modulation in ice shelf flow, generated within ice shelves themselves through tidal flexure acting at diurnal and semidiurnal frequencies. Using full-Stokes viscoelastic modelling, we show that inclusion of tidal bending within the model accounts for much of the observed tidal modulation of ice shelf flow. Furthermore, our model shows that, in the absence of vertical tidal forcing, the mean flow of the ice shelf is reduced by almost 30 % for the geometry that we consider.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Analysis of Turbulence in the Tip Region of a Waterjet Pump Rotor

2010 ◽  
Author(s):  
Huixuan Wu ◽  
Rinaldo L. Miorini ◽  
Joseph Katz
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Multiple Scales ◽  
Tip Clearance ◽  
Mean Flow ◽  
Production Characteristic ◽  
Pump Rotor ◽  
The Mean ◽  
Turbulence Production ◽  
Waterjet Pump

A series of high resolution planar particle image velocimetry measurements performed in a waterjet pump rotor reveal the inner structure of the tip leakage vortex (TLV) which dominates the entire flow field in the tip region. Turbulence generated by interactions among the TLV, the shear layer that develops as the backward leakage flow emerges from the tip clearance as a “wall jet”, the passage flow, and the endwall is highly inhomogeneous and anisotropic. We examine this turbulence in both RANS and LES modelling contexts. Spatially non-uniform distributions of Reynolds stress components are explained in terms of the local mean strain field and associated turbulence production. Characteristic length scales are also inferred from spectral analysis. Spatial filtering of instantaneous data enables the calculation of subgrid scale (SGS) stresses, along with the SGS energy flux (dissipation). The data show that the SGS energy flux differs from the turbulence production rate both in trends and magnitude. The latter is dominated by energy flux from the mean flow to the large scale turbulence, which is resolved in LES, whereas the former is dominated by energy flux from the mean flow to the SGS turbulence. The SGS dissipation rate is also used for calculating the static and dynamic Smagorinsky coefficients, the latter involving filtering at multiple scales; both vary substantially in the tip region, and neither is equal to values obtained in isotropic turbulence.

Advancing the simulation of mesoscale eddies: Backscatter schemes in eddy-permitting ocean simulations

2021 ◽  
Author(s):  
Stephan Juricke ◽  
Sergey Danilov ◽  
Marcel Oliver ◽  
Nikolay Koldunov ◽  
Dmitry Sidorenko ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Large Scale ◽  
Mesoscale Eddy ◽  
Ocean Model ◽  
Mean Flow ◽  
Ocean Coupling ◽  
Climate Simulations ◽  
Flow Interactions ◽  
To Come ◽  
Eddy Dynamics

&lt;p&gt;Capturing mesoscale eddy dynamics is crucial for accurate simulations of the large-scale ocean currents as well as oceanic and climate variability. Eddy-mean flow interactions affect the position, strength and variations of mean currents and eddies are important drivers of oceanic heat transport and atmosphere-ocean-coupling. However, simulations at eddy-permitting resolutions are substantially underestimating eddy variability and eddy kinetic energy many times over. Such eddy-permitting simulations will be in use for years to come, both in coupled and uncoupled climate simulations. We present a set of kinetic energy backscatter schemes with different complexity as alternative momentum closures that can alleviate some eddy related biases such as biases in the mean currents, in sea surface height variability and in temperature and salinity. The complexity of the schemes reflects in their computational costs, the related simulation improvements and their adaptability to different resolutions. However, all schemes outperform classical viscous closures and are computationally less expensive than a related necessary resolution increase to achieve similar results. While the backscatter schemes are implemented in the ocean model FESOM2, the concepts can be adjusted to any ocean model including NEMO.&lt;/p&gt;

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

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