scholarly journals On a new formulation for energy transfer between convection and fast tides with application to giant planets and solar type stars

2021 ◽  
Author(s):  
Caroline Terquem
Keyword(s):  
Shear Flow ◽  
Convective Flow ◽  
Large Scale ◽  
Dissipation Factor ◽  
Giant Planets ◽  
Small Scale ◽  
Late Type ◽  
Mean Flow ◽  
Tidal Dissipation ◽  
Tidal Period

Abstract All the studies of the interaction between tides and a convective flow assume that the large scale tides can be described as a mean shear flow which is damped by small scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover timescale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late–type binaries or the tidal dissipation factor of giant planets. Here, we argue that the above description is inconsistent, because fluctuations and mean flow should be identified based on the timescale, not on the spatial scale, on which they vary. Therefore, the standard picture should be reversed, with the fluctuations being the tidal oscillations and the mean shear flow provided by the largest convective eddies. We assume that energy is locally transferred from the tides to the convective flow. Using this assumption, we obtain values for the tidal Q factor of Jupiter and Saturn and for the circularization periods of PMS binaries in good agreement with observations. The timescales obtained with the equilibrium tide approximation are however still 40 times too large to account for the circularization periods of late–type binaries. For these systems, shear in the tachocline or at the base of the convective zone may be the main cause of tidal dissipation.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

On the irreversibility of internal-wave dynamics due to wave trapping by mean flow inhomogeneities. Part 1. Local analysis

1993 ◽  
Vol 251 ◽  
pp. 21-53 ◽  
Author(s):  
Sergei I. Badulin ◽  
Victor I. Shrira
Keyword(s):  
Shear Flow ◽  
Internal Wave ◽  
Wave Field ◽  
Large Scale ◽  
Spatial Scales ◽  
Energy Concentration ◽  
Local Analysis ◽  
Mean Flow ◽  
Wave Trapping ◽  
Wave Dynamics

The propagation of guided internal waves on non-uniform large-scale flows of arbitrary geometry is studied within the framework of linear inviscid theory in the WKB-approximation. Our study is based on a set of Hamiltonian ray equations, with the Hamiltonian being determined from the Taylor-Goldstein boundary-value problem for a stratified shear flow. Attention is focused on the fundamental fact that the generic smooth non-uniformities of the large-scale flow result in specific singularities of the Hamiltonian. Interpreting wave packets as particles with momenta equal to their wave vectors moving in a certain force field, one can consider these singularities as infinitely deep potential holes acting quite similarly to the ‘black holes’ of astrophysics. It is shown that the particles fall for infinitely long time, each into its own ‘black hole‘. In terms of a particular wave packet this falling implies infinite growth with time of the wavenumber and the amplitude, as well as wave motion focusing at a certain depth. For internal-wave-field dynamics this provides a robust mechanism of a very specific conservative and moreover Hamiltonian irreversibility.This phenomenon was previously studied for the simplest model of the flow non-uniformity, parallel shear flow (Badulin, Shrira & Tsimring 1985), where the term ‘trapping’ for it was introduced and the basic features were established. In the present paper we study the case of arbitrary flow geometry. Our main conclusion is that although the wave dynamics in the general case is incomparably more complicated, the phenomenon persists and retains its most fundamental features. Qualitatively new features appear as well, namely, the possibility of three-dimensional wave focusing and of ‘non-dispersive’ focusing. In terms of the particle analogy, the latter means that a certain group of particles fall into the same hole.These results indicate a robust tendency of the wave field towards an irreversible transformation into small spatial scales, due to the presence of large-scale flows and towards considerable wave energy concentration in narrow spatial zones.

scholarly journals Toward understanding the multiscale spatial spectrum of solar convection

2012 ◽  
Vol 8 (S294) ◽  
pp. 361-363
Author(s):  
A. V. Getling ◽  
O. S. Mazhorova ◽  
O. V. Shcheritsa
Keyword(s):  
Convective Instability ◽  
Convective Flow ◽  
Large Scale ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Spatial Spectrum ◽  
Small Scale ◽  
Two Dimensional ◽  
Solar Convection

AbstractConvection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

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.

Aerodynamic sound generation in a pipe

1968 ◽  
Vol 32 (4) ◽  
pp. 765-778 ◽  
Author(s):  
H. G. Davies ◽  
J. E. Ffowcs Williams
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Sound Field ◽  
Convective Motion ◽  
Energy Output ◽  
Small Scale ◽  
Mean Flow ◽  
Limited Region ◽  
Aerodynamic Sound ◽  
Scale Turbulence

The paper deals with the problem of estimating the sound field generated by a limited region of turbulence in an infinitely long, straight, hard-walled pipe. The field is analysed in a co-ordinate system moving with the assumed uniform mean flow, and the possibility of eddy convection relative to that reference system is considered. Large-scale turbulence is shown to induce plane acoustic waves of intensity proportional to the sixth power of flow velocity. The same is true of small-scale turbulence of low characteristic frequency. In both cases convective effects increase the acoustic output and distribute the bulk of the energy in a mode propagating upstream against the mean flow. Small-scale turbulence of higher frequency excites more modes, the sound increasing with very nearly the eighth power of velocity (U7.7) as soon as the second mode is excited. In the limit, when more than about 20 modes are excited, the energy output is unaffected by the constraint of the pipe walls, increasing with the eighth power of velocity, and being substantially amplified by convective motion.

scholarly journals Mesospheric gravity wave activity estimated via airglow imagery, multistatic meteor radar, and SABER data taken during the SIMONe–2018 campaign

2020 ◽  
Author(s):  
Fabio Vargas ◽  
Jorge L. Chau ◽  
Harikrishnan Charuvil Asokan ◽  
Michael Gerding
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Large Scale ◽  
Lower Thermosphere ◽  
Small Scale ◽  
Meteor Radar ◽  
Mean Flow ◽  
Horizontal Scale ◽  
Momentum Fluxes ◽  
Mesosphere And Lower Thermosphere

Abstract. We describe in this study the analysis of small and large horizontal scale gravity waves from datasets composed of images from multiple mesospheric nightglow emissions as well as multistatic specular meteor radar (MSMR) winds collected in early November 2018, during the SIMONe–2018 campaign. These ground-based measurements are supported by temperature and neutral density profiles from TIMED/SABER satellite in orbits near Kühlungsborn, northern Germany (54.1° N, 11.8° E). The scientific goals here include the characterization of gravity waves and their interaction with the mean flow in the mesosphere and lower thermosphere and their relationship to dynamical conditions in the lower and upper atmosphere. We obtain intrinsic parameters of small and large horizontal scale gravity waves and characterize their impact in the mesosphere region via momentum flux and flux divergence estimations. We have verified that a small percent of the detected wave events are responsible for most of the momentum flux measured during the campaign from oscillations seen in the airglow brightness and MSMR winds. From the analysis of small-scale gravity waves in airglow images, we have found wave momentum fluxes ranging from 0.38 to 24.74 m2/s2 (0.88 ± 0.73 m2/s2 on average), with a total of 586.96 m2/s2 (sum over all 362 detected waves). However, small horizontal scale waves with flux > 3 m2/s2 (11 % of the events) transport 50 % of the total measured flux. Likewise, wave events having flux > 10 m2/s2 (2 % of the events) transport 20 % of the total flux. The examination of two large-scale waves seen simultaneously in airglow keograms and MSMR winds revealed relative amplitudes > 35 %, which translates into momentum fluxes of 21.2–29.6 m/s. In terms of gravity wave–mean flow interactions, these high momentum flux waves could cause decelerations of 22–41 m/s/day (small-scale waves) and 38–43 m/s/day (large-scale waves) if breaking or dissipating within short distances in the mesosphere and lower thermosphere region. The dominant large-scale waves might be the result of secondary gravity excited from imbalanced flow in the stratosphere caused by primary wave breaking.

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

scholarly journals Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170388 ◽  
Author(s):  
C. J. Cotter ◽  
G. A. Gottwald ◽  
D. D. Holm
Keyword(s):  
Large Scale ◽  
Particle Dynamics ◽  
Homogenization Theory ◽  
Small Scale ◽  
Mean Flow ◽  
Time Dynamics ◽  
Fluid Equations ◽  
Diffusive Limit ◽  
The Mean ◽  
Stochastic Fluid

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. ( doi:10.1098/rspa.2014.0963 )), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

scholarly journals Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence

2016 ◽  
Vol 73 (5) ◽  
pp. 2229-2253 ◽  
Author(s):  
Navid C. Constantinou ◽  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Large Scale ◽  
Cooperative Interaction ◽  
Small Scale ◽  
Mean Flow ◽  
Theoretical Understanding ◽  
Laminar Jet ◽  
Planetary Scale ◽  
Statistical State ◽  
Beta Plane ◽  
Scale Turbulence

Abstract Jets coexist with planetary-scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary-scale waves requires adopting the perspective of statistical state dynamics (SSD), which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work, the stochastic structural stability theory (S3T) implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet–wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller-scale motions that constitute the incoherent component. It is found that mean flow–turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner. Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small-scale turbulence, which results in a change in the mode structure, allowing the mode to tap the energy of the mean jet. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with the energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet–wave coexistence regime in planetary turbulence.

On the vorticity transport due to dissipating or breaking waves in shallow-water flow

2000 ◽  
Vol 407 ◽  
pp. 235-263 ◽  
Author(s):  
OLIVER BÜHLER
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Small Scale ◽  
Practical Consideration ◽  
Mean Flow ◽  
Vorticity Transport

Theoretical and numerical results are presented on the transport of vorticity (or potential vorticity) due to dissipating gravity waves in a shallow-water system with background rotation and bottom topography. The results are obtained under the assumption that the flow can be decomposed into small-scale gravity waves and a large-scale mean flow. The particle-following formalism of ‘generalized Lagrangian-mean’ theory is then used to derive an ‘effective mean force’ that captures the vorticity transport due to the dissipating waves. This can be achieved without neglecting other, non-dissipative, effects which is an important practical consideration. It is then shown that the effective mean force obeys the so-called ‘pseudomomentum rule’, i.e. the force is approximately equal to minus the local dissipation rate of the wave's pseudomomentum. However, it is also shown that this holds only if the underlying dissipation mechanism is momentum-conserving. This requirement has important implications for numerical simulations, and these are discussed.The novelty of the results presented here is that they have been derived within a uniform theoretical framework, that they are not restricted to small wave amplitude, ray-tracing or JWKB-type approximations, and that they also include wave dissipation by breaking, or shock formation. The theory is tested carefully against shock-capturing nonlinear numerical simulations, which includes the detailed study of a wavetrain subject to slowly varying bottom topography. The theory is also cross-checked in the appropriate asymptotic limit against recently formulated weakly nonlinear theories. In addition to the general finite-amplitude theory, detailed small-amplitude expressions for the main results are provided in which the explicit appearance of Lagrangian fields can be avoided. The motivation for this work stems partly from an on-going study of high-altitude breaking of internal gravity waves in the atmosphere, and some preliminary remarks on atmospheric applications and on three-dimensional stratified versions of these results are given.

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