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.

A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

2019 ◽  
Vol 867 ◽  
pp. 146-194 ◽  
Author(s):  
G. L. Richard ◽  
A. Duran ◽  
B. Fabrèges
Keyword(s):  
Large Scale ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Small Scale ◽  
Two Dimensional ◽  
Numerical Resolution ◽  
Wide Range ◽  
Scale Turbulence ◽  
Run Up ◽  
Averaged Model

We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.

Enhanced dissipation for quasi-geostrophic motion over small-scale topography

2000 ◽  
Vol 407 ◽  
pp. 105-122 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Additional Term ◽  
Equation Of Motion ◽  
Small Scale ◽  
Two Dimensional ◽  
Turbulent Dissipation ◽  
Dissipative Term ◽  
History Of ◽  
Large Scale Flow

The effect of a small-scale topography on large-scale, small-amplitude oceanic motion is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The topography is two-dimensional and periodic; its slope is assumed to be much larger than the ratio of the ocean depth to the Earth's radius. An averaged equation of motion is derived for flows with spatial scales that are much larger than the scale of the topography and either (i) much larger than or (ii) comparable to the radius of deformation. Compared to the standard quasi-geostrophic equation, this averaged equation contains an additional dissipative term that results from the interaction between topography and dissipation. In case (i) this term simply represents an additional Ekman friction, whereas in case (ii) it is given by an integral over the history of the large-scale flow. The properties of the additional term are studied in detail. For case (i) in particular, numerical calculations are employed to analyse the dependence of the additional Ekman friction on the structure of the topography and on the strength of the original dissipation mechanisms.

STUDY ON RELATIONSHIP BETWEEN CONDENSED PARTICLES AND STRUCTURE OF CONDENSATION JET USING 2D IMAGE AND DISCRETE WAVELETS MULTIRESOLUTION

2006 ◽  
Vol 04 (02) ◽  
pp. 227-238
Author(s):  
MOTOAKI KIMURA ◽  
MASAHIRO TAKEI ◽  
YOSHIFURU SAITO ◽  
KIYOSHI HORII
Keyword(s):  
Wavelet Transforms ◽  
Large Scale ◽  
Particle Density ◽  
Small Scale ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Two Dimensional ◽  
Condensation Zone ◽  
Two Dimensional Image ◽  
Discrete Wavelets

This paper describes the application of discrete wavelet transforms to the analysis of condensation jets in order to clarify the associated fluid and heat transfer phenomena. An experimentally-obtained, two-dimensional image of the condensation particle density around the jet was decomposed into 7 levels of resolution with their respective wavelengths. Based on the known physical characteristics of turbulent flow around the jet, levels 0 and 1 were shown to represent the large-scale components of the condensation particle density and the higher levels represent the small-scale components. From the wavelet-analyzed images, the width of the condensation zone was obtained and this compared well with the width inferred from temperature measurements. Thus, the method was verified and also provided data not available experimentally.

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.

scholarly journals The fate of random initial vorticity distributions for two-dimensional Euler equations on a sphere

2015 ◽  
Vol 786 ◽  
pp. 1-4 ◽  
Author(s):  
Paul K. Newton
Keyword(s):  
Numerical Simulations ◽  
Euler Equations ◽  
Large Scale ◽  
Initial Conditions ◽  
Infinite Family ◽  
Small Scale ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
Long Time ◽  
Initial Vorticity

The paper by Dritschel et al. (J. Fluid Mech., vol. 783, 2015, pp. 1–22) describes the long-time behaviour of inviscid two-dimensional fluid dynamics on the surface of a sphere. At issue is whether the flow settles down to an equilibrium or whether, for generic (random) initial conditions, the long-time solution is periodic, quasi-periodic or chaotic. While it might be surprising that this issue is not settled in the literature, it is important to keep in mind that the Euler equations form a dissipationless Hamiltonian system, hence the set of equations only redistributes the initial vorticity, generating smaller and smaller scales, while keeping kinetic energy, angular impulse and an infinite family of vorticity moments (Casimirs) intact. While special solutions that never settle down to an equilibrium state can be constructed using point vortices, vortex patches and other distributions, the fate of random initial conditions is a trickier problem. Previous statistical theories indicate that the long-time state should be a stationary large-scale distribution of vorticity. By carrying out careful numerical simulations using two different methods, the authors make a compelling case that the generic long-time state resembles a large-scale oscillating quadrupolar vorticity field, surrounded by persistent small-scale vortices. While numerical simulations can never conclusively settle this issue, the results might help guide future theories that seek to prove the existence of such an interesting dynamical long-time state.

scholarly journals Anisotropy of ionospheric irregularities determined from the amplitude of satellite signals at a single receiver

1999 ◽  
Vol 17 (4) ◽  
pp. 508-518 ◽  
Author(s):  
E. D. Tereshchenko ◽  
B. Z. Khudukon ◽  
M. O. Kozlova ◽  
T. Nygrén
Keyword(s):  
Large Scale ◽  
Ground Level ◽  
Spatial Spectrum ◽  
Ionospheric Irregularities ◽  
Small Scale ◽  
Radio Waves ◽  
Large Scale Structures ◽  
F Region ◽  
Amplitude Fluctuations ◽  
A Chain

Abstract. A new method of determining the anisotropy parameters of small-scale irregularities in the ionospheric F region is presented and experimental results are shown. The method is based on observations of amplitude fluctuations of radio waves transmitted by satellites flying above the F region. In practice, Russian navigational satellites are used and both the amplitude and the phase of the received signal is measured on the ground level. The method determines both the field-aligned anisotropy and the field-perpendicular anisotropy and orientation of the spatial spectrum of the irregularities, assuming that the contours of constant power have an elliptic shape. A possibility of applying the method to amplitude tomography is also discussed. Using a chain of receivers on the ground level, one could locate the regions of small-scale irregularities as well as determine their relative intensities. Then the large-scale background structures could be mapped simultaneously by means of ordinary ray tomography using the phase observations, and therefore the relations of small-scale and large-scale structures could be investigated.Key words. Ionosphere (auroral ionosphere; ionospheric irregularities; instruments and techniques)

scholarly journals Round table discussion of session G: MHD convection and dynamos

2006 ◽  
Vol 2 (S239) ◽  
pp. 494-495
Author(s):  
Juri Toomre
Keyword(s):  
Large Scale ◽  
Round Table ◽  
Global Scale ◽  
Magnetic Activity ◽  
Small Scale ◽  
Round Table Discussion ◽  
Dynamo Action ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
Prandtl Numbers

AbstractVigorous discussion ensued about conditions under which both small-scale and global-scale dynamo action would be realized within real stars where the flow fields are expected to be highly turbulent and the magnetic Prandtl numbers small. Our nearest star reminds us that intricate boundary-layer phenomena may have to also be considered, such as the presence of a tachocline of rotational shear at the base of the solar convection zone revealed by helioseismology, which suggests that an interface dynamo may be at work to produce the observed 22-year cycles of large-scale magnetic activity.

Dynamics of interaction of vortices in shear turbulent flows

2021 ◽  
Vol 102 (2) ◽  
pp. 56-67
Author(s):  
A.Zh. Turmukhambetov ◽  
◽  
S.B. Otegenova ◽  
K.A. Aitmanova ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Spatial Scales ◽  
Equations Of Motion ◽  
Vortex Structures ◽  
Small Scale ◽  
Two Dimensional ◽  
Practical Applications ◽  
Kinematic Effect ◽  
The One

The paper analyzes the results of a theoretical study of quasi-two-dimensional turbulence, two-dimensional equations of motion of which contain additional terms. The regularities of the dynamic interaction of vortex structures in shear turbulent flows of a viscous liquid are established. Based on the model of quasi-twodimensional turbulence, numerical values of the spatial scales of intermittency are determined as an alternation of large-scale and small-scale pulsations of dynamic characteristics. The experimentally observed alternation of vortex structures and the idea of their self-organization form the basis of the assumption of the existence of a geometric parameter determined by the size of the vortex core and the distance between their centers. Therefore, the main attention is paid to the theoretical calculation of the minimum spatial scales of the intermittency of vortex clusters. As a simplification, the vortex pairs are located in a reference frame, relative to which the centers of the vortices are stationary. Thus, the kinematic effect of the transfer of one vortex into the field of another is excluded from consideration. The symmetric and unsymmetric interactions of vortices, taking into account the one-sided and opposite directions of their rotation, are considered as realizable cases. A successful attempt is made to study the influence of the internal structure of vortex clusters on the numerical values of the minimum intermittency scales. The obtained results are satisfactorily confirmed by known theoretical and experimental data. Consequently, they can be used in all practical applications, without exception, where the structure of turbulence is taken into account, as well as for improving and expanding existing semi-empirical theories.

scholarly journals Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-Bénard Convection at Various Prandtl Number

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 582 ◽  
Author(s):  
Hui Yang ◽  
Yikun Wei ◽  
Zuchao Zhu ◽  
Huashu Dou ◽  
Yuehong Qian
Keyword(s):  
Heat Transfer ◽  
Structure Function ◽  
Dissipation Rate ◽  
Large Scale ◽  
Thermal Dissipation ◽  
Small Scale ◽  
Linear Scaling ◽  
Two Dimensional ◽  
Large Scale Circulation ◽  
Rayleigh Benard

Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for Pr=6,20,100 and 106 are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of Pr, the large scale circulation disappears with increasing Pr, and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing Pr. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate εθ already increasingly plays a dominant position in the thermal transport, εu can have no effect with increase of Pr. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing Pr. The energy spectrum significantly decreases with the increase of Pr. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing Pr, which is qualitatively consistent with the theoretical predictions.

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