Dissipation of Synoptic-Scale Flow by Small-Scale Turbulence

2008 ◽  
Vol 65 (3) ◽  
pp. 766-791 ◽  
Author(s):  
K. Ngan ◽  
P. Bartello ◽  
D. N. Straub
Keyword(s):  
Normal Modes ◽  
Base Flow ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Synoptic Scale ◽  
Boussinesq Model ◽  
Weak Stratification ◽  
Balanced Flow ◽  
Scale Turbulence ◽  
Scale Motion

Abstract Although it is now accepted that imbalance in the atmosphere and ocean is generic, the feedback of the unbalanced motion on the balanced flow has not received much attention. In this work the parameterization problem is examined in the context of rotating stratified turbulence, that is, with a nonhydrostatic Boussinesq model. Using the normal modes as a first approximation to the balanced and unbalanced flow, the growth of ageostrophic perturbations to the quasigeostrophic flow and the associated feedback are studied. For weak stratification, there are analogies with the three-dimensionalization of decaying 2D turbulence: the growth rate of the ageostrophic perturbation follows a linear estimate, geostrophic energy is extracted from the base flow, and the associated damping on the geostrophic base flow (the “eddy viscosity”) is peaked at large horizontal scales. For strong stratification, the transfer spectra and eddy viscosities maintain this structure if there is synoptic-scale motion and the buoyancy scale is adequately resolved. This has been confirmed for global Rossby and Froude numbers of O(0.1). Implications for atmospheric and oceanic modeling are discussed.

Triadic scale interactions in a turbulent boundary layer

2015 ◽  
Vol 767 ◽  
Author(s):  
Subrahmanyam Duvvuri ◽  
Beverley J. McKeon
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Small Scale ◽  
Velocity Signal ◽  
Small Scales ◽  
Amplitude Modulation Coefficient ◽  
Scale Turbulence ◽  
Scale Motion ◽  
Phase Relationships

AbstractA formal relationship between the skewness and the correlation coefficient of large and small scales, termed the amplitude modulation coefficient, is established for a general statistically stationary signal and is analysed in the context of a turbulent velocity signal. Both the quantities are seen to be measures of phase in triadically consistent interactions between scales of turbulence. The naturally existing phase relationships between large and small scales in a turbulent boundary layer are then manipulated by exciting a synthetic large-scale motion in the flow using a spatially impulsive dynamic wall roughness perturbation. The synthetic scale is seen to alter the phase relationships, or the degree of modulation, in a quasi-deterministic manner by exhibiting a phase-organizing influence on the small scales. The results presented provide encouragement for the development of a practical framework for favourable manipulation of energetic small-scale turbulence through large-scale inputs in a wall-bounded turbulent flow.

scholarly journals Investigations of non-hydrostatic, stably stratified and rapidly rotating flows

2016 ◽  
Vol 801 ◽  
pp. 430-458 ◽  
Author(s):  
David Nieves ◽  
Ian Grooms ◽  
Keith Julien ◽  
Jeffrey B. Weiss
Keyword(s):  
Large Scale ◽  
Boussinesq Equations ◽  
Reduced Model ◽  
Small Scale ◽  
Net Energy ◽  
Stratified Turbulence ◽  
Stochastic Forcing ◽  
Barotropic Mode ◽  
Energy Exchanges ◽  
Scale Turbulence

We present an investigation of rapidly rotating (small Rossby number $Ro\ll 1$) stratified turbulence where the stratification strength is varied from weak (large Froude number $Fr\gg 1$) to strong ($Fr\ll 1$). The investigation is set in the context of a reduced model derived from the Boussinesq equations that retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave–eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes only. The simulations reveal two regimes: characterized by the presence of well-formed, persistent and thin turbulent layers of locally weakened stratification at small Froude numbers, and by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole enclosed by small-scale turbulence. When the Reynolds number is not too large, a direct cascade of barotropic kinetic energy is observed, leading to total energy equilibration. We examine net energy exchanges that occur through vortex stretching and vertical buoyancy flux and diagnose the horizontal scales active in these exchanges. We find that the baroclinic motions inject energy directly to the largest scales of the barotropic mode, implying that the large-scale barotropic dipole is not the end result of an inverse cascade within the barotropic mode.

Evolution of stream wise vortices and generation of small-scale motion in a plane mixing layer

1991 ◽  
Vol 231 ◽  
pp. 257-301 ◽  
Author(s):  
K. J. Nygaard ◽  
A. Glezer
Keyword(s):  
Surface Film ◽  
Mixing Layer ◽  
Excitation Frequency ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Base Flow ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Plane Mixing Layer ◽  
Scale Motion

The evolution of streamwise vortices in a plane mixing layer and their role in the generation of small-scale three-dimensional motion are studied in a closed-return water facility. Spanwise-periodic streamwise vortices are excited by a time-harmonic wavetrain with span wise-periodic amplitude variations synthesized by a mosaic of 32 surface film heaters flush-mounted on the flow partition. For a given excitation frequency, virtually any span wise wavelength synthesizable by the heating mosaic can be excited and can lead to the formation of streamwise vortices before the rollup of the primary vortices is completed. The onset of streamwise vortices is accompanied by significant distortion in the transverse distribution of the streamwise velocity component. The presence of inflexion points, absent in corresponding velocity distributions of the unforced flow, suggests the formation of locally unstable regions of large shear in which broadband perturbations already present in the base flow undergo rapid amplification, followed by breakdown to small-scale motion. Furthermore, as a result of spanwise-non-uniform excitation the cores of the primary vortices are significantly altered. The three-dimensional features of the streamwise vortices and their interaction with the base flow are inferred from surfaces of r.m.s. velocity fluctuations and an approximation to cross-stream vorticity using three-dimensional single component velocity data. The striking enhancement of small-scale motion and the spatial modification of its distribution, both induced by the streamwise vortices, can be related to the onset of the mixing transition.

Buoyancy- to inertial-range transition in forced stratified turbulence

2001 ◽  
Vol 427 ◽  
pp. 205-239 ◽  
Author(s):  
GEORGE F. CARNEVALE ◽  
M. BRISCOLINI ◽  
P. ORLANDI
Keyword(s):  
Wave Breaking ◽  
Large Scale ◽  
High Strain ◽  
Inertial Range ◽  
Large Eddy Simulations ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Large Eddy ◽  
Scale Turbulence ◽  
Range Density

The buoyancy range, which represents a transition from large-scale wave-dominated motions to small-scale turbulence in the oceans and the atmosphere, is investigated through large-eddy simulations. The model presented here uses a continual forcing based on large-scale standing internal waves and has a spectral truncation in the isotropic inertial range. Evidence is presented for a break in the energy spectra from the anisotropic k−3 buoyancy range to the small-scale k−5/3 isotropic inertial range. Density structures that form during wave breaking and periods of high strain rate are analysed. Elongated vertical structures produced during periods of strong straining motion are found to collapse in the subsequent vertically compressional phase of the strain resulting in a zone or patch of mixed fluid.

A discussion on D and E region winds over Europe - Large-scale motion in the upper stratosphere and mesosphere: an evaluation of data and theories

1972 ◽  
Vol 271 (1217) ◽  
pp. 577-583 ◽  
Keyword(s):  
Energy Transfer ◽  
Large Scale ◽  
Radiative Heat ◽  
Fluid Motion ◽  
Small Scale ◽  
Meridional Plane ◽  
E Region ◽  
Scale Turbulence ◽  
Scale Motion ◽  
Evaluation Of Data

Between heights of 25 and 100 km, fluid motion is responsible for carrying energy from the radiative heat source near the summer pole to the radiative heat sink near the winter pole. The way this transfer is organized will form the theme of this contribution. All scales of motion are important: (1) The zonal-mean motion contains most of the kinetic energy but contributes to the energy transfer only through a comparatively weak circulation in the meridional plane. (2) Stationary large-scale eddies are prominent at least in the winter and carry a considerable fraction of the energy transfer. (3) Transient large-scale eddies of a variety of types are evident in the data but are likely to be feeble transporters of energy. (4) Gravity-inertial waves, generated by tidal forcing and orography and representing some aspects of small-scale turbulence, are associated mainly with the vertical transfer of energy.

scholarly journals Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 442
Author(s):  
Emmanouil G. Iliakis ◽  
Nikolaos A. Bakas
Keyword(s):  
Normal Modes ◽  
Maximum Growth ◽  
Boussinesq Approximation ◽  
High Amplitude ◽  
Small Scale ◽  
Time Interval ◽  
Transient Growth ◽  
Stratified Turbulence ◽  
Propagating Waves ◽  
Orr Mechanism

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes.

Shear and Static Instability of Inertia–Gravity Wave Packets: Short-Term Modal and Nonmodal Growth

2006 ◽  
Vol 63 (2) ◽  
pp. 397-413 ◽  
Author(s):  
Ulrich Achatz ◽  
Gerhard Schmitz
Keyword(s):  
Wind Shear ◽  
Singular Vector ◽  
Middle Atmosphere ◽  
Normal Modes ◽  
Static Stability ◽  
Small Scale ◽  
Boussinesq Model ◽  
Optimal Perturbation ◽  
Static Instability ◽  
Molecular Viscosity

Abstract The problem of nonmodal instabilities of inertia–gravity waves (IGW) in the middle atmosphere is addressed, within the framework of a Boussinesq model with realistic molecular viscosity and thermal diffusion, by singular-vector analysis of horizontally homogeneous vertical profiles of wind and buoyancy obtained from IGW packets at their statically least stable or most unstable horizontal location. Nonmodal growth is always found to be significantly stronger than that of normal modes, most notably at wave amplitudes below the static instability limit where normal-mode instability is very weak, whereas the energy gain between the optimal perturbation and singular vector after one Brunt–Väisälä period can be as large as two orders of magnitude. Among a multitude of rapidly growing singular vectors for this optimization time, small-scale (wavelengths of a few 100 m) perturbations propagating in the horizontal parallel to the IGW are most prominent. These parallel optimal perturbations are amplified by a roll mechanism, while transverse perturbations (with horizontal scales of a few kilometers) are to a large part subject to an Orr mechanism, both controlled by the transverse wind shear in the IGW at its statically least stable altitude, but further enhanced by reduced static stability. The elliptic polarization of the IGW leaves its traces in an additional impact of the roll mechanism via the parallel wind shear on the leading transverse optimal perturbation.

Similarity of dissipation and enstrophy in particle-induced small-scale turbulence

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhuo Wang ◽  
Kun Luo ◽  
Junhua Tan ◽  
Dong Li ◽  
Jianren Fan
Keyword(s):  
Small Scale ◽  
Scale Turbulence

scholarly journals Role of large-scale advection and small-scale turbulence on vertical migration of gyrotactic swimmers

2019 ◽  
Vol 4 (12) ◽  
Author(s):  
C. Marchioli ◽  
H. Bhatia ◽  
G. Sardina ◽  
L. Brandt ◽  
A. Soldati
Keyword(s):  
Vertical Migration ◽  
Large Scale ◽  
Small Scale ◽  
Scale Turbulence
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