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1.
A regularized version of the direct interaction approximation closure (RDIA) is compared with ensemble averaged direct numerical simulations (DNS) for decaying two-dimensional turbulence at large-scale Reynolds numbers ranging between low (≈?50) and high (≈?4000). The regularization localizes transfer by removing the interaction between large-scale and small-scale eddies depending on a specified cut-off ratio α. It thus eliminates spurious convection effects of small-scale eddies by large-scale eddies in the Eulerian direct interaction approximation (DIA) that causes the underestimation of small-scale kinetic energy by the DIA. Cumulant update versions of the RDIA closure that have comparable performance but are much more efficient computationally have also been analyzed. Both the closures and DNS use discrete wavenumber representations relevant to flows on a doubly periodic domain. This means that any differences between them are intrinsic and not partly due to using continuous wavenumber formulation for the closures.

Comparisons between the regularized closures and DNS have focused on evolved kinetic energy and palinstrophy spectra and as well on enstrophy flux spectra and on the evolution of skewness which depends sensitively on small-scale differences. All of these diagnostics compare quite well when α = 6. And this is the case for runs started from each of three initial spectra, for the range of evolved large-scale Reynolds numbers ranging from ≈?50 to ≈?4000 and for regularized DIA closures with, and particularly without, cumulant update restarts. The performance of the RDIA compared with quasi-Lagrangian closure models is discussed.  相似文献   

2.
Abstract

We describe a sequence of two-dimensional numerical simulations of inflection point instability in a stably stratified shear flow near the ground. The fastest growing Kelvin-Helmholtz modes are studied in detail; in particular we investigate the growth inhibiting effect of the ground which is predicted by linear theory and the Reynolds number dependence of the process of growth to finite amplitude. We consider flows which are both above and below the critical Reynolds number (Re = 300) which has been reported by Woods (1969) to mark the boundary between flows which have turbulent final states and those which do not. A global energy budget reveals a fundamental difference in character of the finite amplitude billows in these two Reynolds number regimes. However, for relatively high Reynolds numbers (Re = 103) we do not find any explicit evidence for secondary instability. Above the transition Reynolds number the modified mean flow induced by wave growth is characterized by a splitting of the original shear layer and of the in version in which it is embedded.  相似文献   

3.
Results from a direct numerical simulation (DNS) of the neutral and unstable turbulent Ekman layer at a Reynolds number of 1000 were used to evaluate turbulence closure models. For the neutrally stratified Ekman layer, the higher-order moments of velocity were examined and the accuracy of a kurtosis model was assessed. For the unstable Ekman layer, the analysis of higher-order moments was extended to temperature-velocity correlations. Model coefficients were optimised using DNS data and it was shown that the optimised models accurately captured the distributions of all fourth-order moments. These low-Reynolds number results can be extrapolated to higher Reynolds numbers to parameterise turbulence in other flow fields with rotational effects such as the atmospheric boundary layer.  相似文献   

4.
Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza  相似文献   

5.
Abstract

The two dimensional incompressible MHD equations describing the decay of a random initial velocity field in the presence of a uniform magnetic background field are solved numerically by a Chebyshev spectral method. The nonlinear interactions of standing Alfvén-waves of a given energy are studied for various Reynolds numbers and field strengths of the magnetic background field. Small scale structures are generated by these interactions, which increase the energy dissipation, however, the uniform background field suppresses the production of arbitrary small scales. Thus energy dissipation is found to be insignificant at sufficiently high Reynolds numbers. Anisotropies of the fluctuating field components are also studied. In the temporal evolution they appear first in the magnetic field. This is explained by the conservation of mean square vector potential in the limit of infinite conductivity.  相似文献   

6.
Abstract

Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results for convection in a shell of finite depth at substantial but not asymptotically large Taylor numbers, present nonlinear multimode calculations for similar conditions, and discuss the model and results in the context of the problem of solar convection and differential rotation. Detailed nonlinear calculations are presented for Taylor number T = 105, Prandtl number P = 1, and Rayleigh number R between 1 |MX 104 and 4 |MX 104 (which is between about 4 and 16 times critical) for a shell of depth 20% of the outer radius. Sixteen longitudinal wave numbers are usually included (all even wave numbers m between 0 and 30) the amplitudes of which are computed on a staggered grid in the meridian plane.

The kinetic energy spectrum shows a peak in the wave number range m = 12–18 at R = 104, which straddles the critical wave number m = 14 predicted by linear theory. These are modes which peak near the equator. The spectrum shows a second strong peak at m = 0, which represents the differential rotation driven by the peak convective modes. As R is increased, the amplitude of low wave numbers increases relative to high wave numbers as convection fills in in high and middle latitudes, and as the longitudinal scale of equatorial convection grows. By R = 3 |MX 104, m = 8 is the peak convective mode. There is a clear minimum in the total kinetic energy at middle latitudes relative to low and high, well into the nonlinear regime, representing the continued dominance of equatorial and polar modes found in the linear case. The kinetic energy spectrum for m > 0 is maintained primarily by buoyancy work in each mode, but with substantial nonlinear transfer of kinetic energy from the peak modes to both lower and higher wave numbers.

For R = 1 to 2 |MX 104, the differential rotation takes the form of an equatorial acceleration, with angular velocity generally decreasing with latitude away from the equator (as on the sun) and decreasing inwards. By R = 4 |MX 104, this equatorial profile has completely reversed, with angular velocity increasing with depth and latitude. Also, a polar vortex which has positive rotation relative to the reference frame (no evidence of which has been seen on the sun) builds up as soon as polar modes become important. Meridional circulation is quite weak relative to differential rotation at R = 104, but grows relative to it as R is increased. This circulation takes the farm of a single cell of large latitudinal extent in equatorial regions, with upward flow near the equator, together with a series of narrower cells in high latitudes. It is maintained primarily by axisymmetric buoyancy forces. The differential rotation is maintained at all R primarily by Reynolds stresses, rather than meridional circulation. Angular momentum transport toward the equator for R = 1–2 |MX 104 maintains the equatorial acceleration while radially inward transport maintains the opposite profile at R = 4 |MX 104.

The total heat flux out the top of the convective shell always shows two peaks for the range of R studied, one at the equator and the other near the poles (no significant variation with latitude is seen on the sun), while heat flux in at the bottom shows only a polar peak at large R. The meridional circulation and convective cells transport heat toward the equator to maintain this difference.

The helicity of the convection plus the differential rotation produced by it suggest the system may be capable of driving a field reversing dynamo, but the toroidal field may migrate with lime in each cycle toward the poles and equator, rather than just toward the equator as apparently occurs on the sun.

We finally outline additions to the physics of the model to make it more realistic for solar application.  相似文献   

7.

We are investigating numerically the nonlinear behaviour of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing from 0 to 60 and a fixed kinematic Reynolds number, small enough for the trivial solution with a zero magnetic field to be stable to velocity perturbations. At the critical magnetic Reynolds number for the onset of instability of the trivial solution the dominant eigenvalue of the kinematic dynamo problem is real. In agreement with the bifurcation theory new steady states with non-vanishing magnetic field appear in this bifurcation. Subsequent bifurcations are investigated. A regime is detected, where chaotic variations of the magnetic field orientation (analogous to magnetic field reversals) are observed in the temporal evolution of the system.  相似文献   

8.
Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B 0, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 105 have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B 0 with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.  相似文献   

9.
Abstract

We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983).

We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude δvy exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber ka are damped over a timescale kuRe 0|δ vy/vA |?2, Re 0 being the Reynolds number corresponding to the Braginskij viscosity coefficient η0 and vA the Alfvén speed. Dissipation is most effective where β = (vs /vA) 2 ≈ 1, vs being the speed of sound.  相似文献   

10.
Abstract

The long wave equations governing the flow in alluvial rivers and channels are considered. The linearized equations are re-cast in the form of a single equation of wave hierarchy type as discussed by Whitham (1974). The dynamic and kinematic waves are of third and second order respectively. Behaviour at the wave fronts is considered and a roll-wave type instability is revealed.

For stable flow, the theory is used to make both qualitative and quantitative predictions in the areas of short and long term floods, tidal waves and channel dredging.

The non-uniformity in the quasi-steady theory on bedform development [see, for example, Reynolds (1985)] as the Froude number, F, approaches unity is also discussed, and appropriate scalings are obtained to derive a theory which remains valid when F ～ 1.  相似文献   

11.
The quasi-normal scale elimination (QNSE) is an analytical spectral theory of turbulence based upon a successive ensemble averaging of the velocity and temperature modes over the smallest scales of motion and calculating corresponding eddy viscosity and eddy diffusivity. By extending the process of successive ensemble averaging to the turbulence macroscale one eliminates all fluctuating scales and arrives at models analogous to the conventional Reynolds stress closures. The scale dependency embedded in the QNSE method reflects contributions from different processes on different scales. Two of the most important processes in stably stratified turbulence, internal wave propagation and flow anisotropization, are explicitly accounted for in the QNSE formalism. For relatively weak stratification, the theory becomes amenable to analytical processing revealing just how increasing stratification modifies the flow field via growing anisotropy and gravity wave radiation. The QNSE theory yields the dispersion relation for internal waves in the presence of turbulence and provides a theoretical reasoning for the Gargett et al. (J Phys Oceanogr 11:1258–1271, 1981) scaling of the vertical shear spectrum. In addition, it shows that the internal wave breaking and flow anisotropization void the notion of the critical Richardson number at which turbulence is fully suppressed. The isopycnal and diapycnal viscosities and diffusivities can be expressed in the form of the Richardson diffusion laws thus providing a theoretical framework for the Okubo dispersion diagrams. Transitions in the spectral slopes can be associated with the turbulence- and wave-dominated ranges and have direct implications for the transport processes. We show that only quasi-isotropic, turbulence-dominated scales contribute to the diapycnal diffusivity. On larger, buoyancy dominated scales, the diapycnal diffusivity becomes scale independent. This result underscores the well-known fact that waves can only transfer momentum but not a scalar and sheds a new light upon the Ellison–Britter–Osborn mixing model. It also provides a general framework for separation of the effects of turbulence and waves even if they act on the same spatial and temporal scales. The QNSE theory-based turbulence models have been tested in various applications and demonstrated reliable performance. It is suggested that these models present a viable alternative to conventional Reynolds stress closures.  相似文献   

12.
Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.  相似文献   

13.
A sea spray generation function(SSGF)for bubble-derived droplets that takes into account the impact of wave state on whitecap coverage was presented in this study.By combining the new SSGF with a previous wave-state-dependent SSGF for spume droplets,an SSGF applicable to both bubble-derived and spume droplets that includes the impacts of wave state was obtained.The produced SSGF varies with surface wind as well as with wave development.As sea surface wind increases,more sea spray droplets are produced,resulting in larger SSGFs and volume fluxes.Meanwhile,under the same wind conditions,the SSGF is mediated by wave state,with larger SSGFs corresponding to older waves and larger windsea Reynolds numbers.The impact of wave state on sea spray heat flux was then estimated by applying this SSGF while considering the thermodynamic feedback process.Under given atmospheric and oceanic conditions,the estimated sea spray heat flux increases with wind speed,wave age,and windsea Reynolds number.  相似文献   

14.
ABSTRACT

It is shown that flows in precessing cubes develop at certain parameters large axisymmetric components in the velocity field which are large enough to either generate magnetic fields by themselves, or to contribute to the dynamo effect if inertial modes are already excited and acting as a dynamo. This effect disappears at small Ekman numbers. The critical magnetic Reynolds number also increases at low Ekman numbers because of turbulence and small-scale structures.  相似文献   

15.
Homogeneous, nonrotating flow over a backward-facing rounded step is simulated using the 2D vertical version of two general circulation models, a z-coordinate model—the Massachusetts Institute of Technology general circulation model (MITgcm)—and a σ-coordinate model—the Bergen Ocean Model (BOM). The backward-facing step is a well-known testcase since it is geometrically simple but still embodies important flow characteristics such as separation point, reattachment length, and recirculation of the flow. The study compares the core of the two models and uses constant eddy viscosities and diffusivities. The Reynolds numbers ranges from 2·102 to 2·106. The results correspond with previously published results having a relatively stationary separation point and a fluctuating reattachment length due to downslope propagating eddies released from the reattachment zone for Reynolds numbers higher than or equal to 2 · 104. For Reynolds number within the laminar regime, the flow is stationary. The discrepancies between the models increase by enhancing Reynolds numbers. The σ-coordinate model experiences a reduction in eddy sizes with increasing resolution and Reynolds numbers in correspondence with published experiments, while the size of the eddies are independent of the Reynolds number using the MITgcm. Due to mixing generated by the staircase topography, the z-coordinate model gives a better convergence of the separation point and reattachment length compared with the BOM; however, this conclusion might change with the inclusion of a relevant turbulence scheme.  相似文献   

16.
Abstract

A new method is introduced to produce a uniform stratified flow over a stationary obstacle in an open channel. The flow is achieved by discharging the flow from the channel through a sink. The details of the sink are unimportant. The flow speed is limited only by the sink capacity. Selective withdrawal at lower densimetric Froude numbers is effectively eliminated through the use of a contraction. The standing, free-surface, long wave arising from the initiation of the flow is also eliminated by the contraction. Experiments are conducted for flow over a sphere for a range of Reynolds numbers from O(102) to O(103) and a range of Richardson numbers from O(10?1) to O(10). Dye and neutrally buoyant droplets are used for quantitative analysis of the wake structure. The wake is also probed by a hot-film anemometer. The frequency of vortex shedding is obtained. Comparison with data from towed experiments is also presented.  相似文献   

17.
Abstract

Some conflicting evidence on Reynolds' (1900) hypothesis that rain should attenuate any wave motion on the sea surface is discussed. It is concluded that rain drops ought to produce vortex rings in the sea which mix the water to a sufficient depth to affect most waves, as asserted by Reynolds. By introducing vertical and horizontal eddy viscosities to model the mixing process, an estimate is found for the rate of attenuation of wave energy by the rain. Consequently, the net effect on the wave field of attenuation by rain and generation by wind is calculated.  相似文献   

18.
随着地震物理模拟的研究目标由地质构造发展为不同类型的油气储层,明确震源指向性及介质非均质性对实验结果的影响,对提高物理模拟数据的可信性及准确性具有重要意义.利用激光测振新方法对震源指向性进行了实验测试,得到了更加精确的指向性结果,形成了模拟数据振幅补偿方法.制作了具有不同尺度特征的非均质样品,在50 kHz至1000 kHz超声频段下对纵波速度及能量进行了测试,明确了不同的波长/介质尺度比(λ/a)范围内纵波速度及干扰波与有效波能量比的变化特征.结果表明,在地震物理模拟超声频段下射线速度向散射速度的转折点出现在λ/a≈2处;散射速度向等效介质速度的转折点出现在λ/a≈100处.当满足λ/a>200条件时,干扰波与有效波能量比小于5%时,可认为满足储层模拟的等效介质条件.  相似文献   

19.
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20.
Large eddy simulations (LES) of two-dimensional turbulent convection within the anelastic approximation are presented for Rayleigh number Ra?=?109, Prandtl number Pr?=?1 with free-slip boundary conditions. Various subgrid-scale (SGS) models are investigated such as a similarity model, a dynamic similarity model, a dynamic eddy-viscosity model, a hyperdiffusion model and a hybrid model (dynamic similarity hyperdiffusion model). To study the effects of density stratification on the models, we have also carried out simulations for a Boussinesq flow. The SGS models are compared to direct numerical simulation (DNS) data on the basis of kinetic energy and entropy variance spectra, mean entropy profiles, r.m.s. entropy profiles and r.m.s. kinetic energy density profiles. The results show that for the Boussinesq flow, all the SGS models agree fairly well with the high resolution DNS data. However, for the strongly density-stratified flow, only the hyperdiffusion and the hybrid model show good performance.  相似文献   

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