Collapse Of Turbulence Research Articles

B112 回密度成層下にある回転一様せん断乱流のDNS(オーガナイズドセッション18 : 環境における乱流熱・物質伝達)

We have performed the direct numerical simulations (DNS) of a homogeneous shear flow to investigate how the Coriolis term affects the vertically collapsed turbulent structure under strong stable stratification. Rogallo method, i.e., a spectral method, is used for simulating a homogeneous shear flow under system rotation around the x_3 axis. Both the mean temperature gradient and the gravitational acceleration g are simultaneously imposed in the x_3 direction to include the effects of both buoyancy and rotation. The isosurfaces of the vertical vorticities become the scattered pancake-shaped vortex patch, strongly indicating the collapse of turbulence. With an increase in the rotation parameter, the effect of the wind shear becomes more intensive and the pancake structures are elongated in the streamwise direction.

Mixing and entrainment in developing stratified currents

The spatially developing region of a steady downslope current in transition from a hydraulically controlled, arrested wedge flow is examined through a set of laboratory experiments. The mixing and entrainment mechanisms at the shear interface are explored with the use of imaging techniques. The initial, unstable accelerating region, characterized by rapid development, low shear layer Richardson numbers and high entrainment rates, is limited by the effects of stratification which suppress the large-scale overturning. A subsequent high Richardson number region is characterized by weak entrainment and the collapse of turbulence from the initial region. The flow approaches a quasi-stable state as the mixed layer draws energy from the accelerating density current. Observed large-scale structure is attributed to an instability of the marginally unstable shear layer. Entrainment rates are calculated within each region for the various slopes considered and estimates for the extent of the transition regions are obtained.

Evolution of an isolated turbulent region in a stratified fluid

This paper reports an experimental study on the evolution of an isolated turbulent region in an otherwise quiescent linearly stratified fluid. A turbulent patch was generated by pulsed horizontal injection of a small volume of fluid. It was found that the turbulent blob thus produced initially grows as in a nonstratified fluid for a nondimensional time period of Nt ≈ 4–5 (with N the buoyancy frequency), attains a maximum height, and then physically collapses slowly to form a planar, quasi‐two‐dimensional dipole pattern. The timescale for the physical collapse of the blob was found to be much larger than that of the turbulence collapse. Scaling arguments are presented to explain the evolution of the turbulent region, and the experimental results are compared with the model predictions.

Instability of an Axisymmetric Vortex in a Stably Stratified, Rotating Environment

We investigate the stability of a barotropic vorticity monopole whose stream function is a Gaussian function of the radial coordinate. The model is based on the inviscid Boussinesq equations. The vortex is assumed to exist on an $f$-plane, in an environment with constant, stable density stratification. In the unstratified, nonrotating case, we find growth rates that increase monotonically with increasing vertical wave number, the so-called “ultraviolet catastrophe” characteristic of symmetric instability. This type of instability leads to rapid turbulent collapse of the vortex, possibly accompanied by wave radiation. In the limit of strong background stratification and rotation, the vortex exhibits a scale-selective instability which leads to the formation of stable lenses. The transition between these two regimes is sharp, and coincides approximately with the centrifugal stability boundary.

Mixing in Inclined Dense Jets

Experiments were performed using laser-induced fluorescence (LIF) and a microconductivity probe on turbulent dense jets inclined upwards at an angle of 60° into stationary environments. Such jets are frequently used to discharge industrial wastewaters. Time-averaged LIF images show concentration profiles that vary smoothly in space but instantaneous images show considerable patchiness. Dilution at the jet impact point was found to be higher than previously reported. Downstream from the impact point, the flow becomes predominantly horizontal with a complex additional mixing process that results in ultimate dilutions considerably higher than the impact dilution. The flow is highly turbulent in the vicinity of the falling jet with large concentration fluctuations. These fluctuations decay with distance due to turbulence collapse under the influence of density stratification. The end of the mixing zone is defined as the location where the intensity of the concentration fluctuations falls to 0.05 (i.e. 5%) of ...

Three dimensionalization of the stratified mixing layer

A theoretical analysis of the stability of a stratified, two-dimensional Kelvin–Helmholtz billow against three-dimensional perturbations is presented. This predicts the three-dimensional spectrum to be dominated by a shear aligned convective instability, which is localized in the region surrounding the billow core. The results of a direct numerical simulation of the evolution of the three-dimensional stratified mixing layer fully verify the dominance of this convective mode in the mixing transition. The origin of the streamwise streaks of vorticity, which precede turbulent collapse in a stratified shear layer, is thereby explained.

Application of a new second-moment closure to turbulent channel flow rotating in orthogonal mode

Computations are reported and compared with direct numerical simulations of turbulent flow in a plane channel rotating in orthogonal mode, an arrangement that is highly relevant to flow in axial turbomachinery. The new second-moment closure adopted achieves a level of agreement similar to that for the non-rotating case; in particular it accurately captures the augmentation and attenuation of mixing near the pressure and suction surfaces respectively. Attempts at increasing the rotation number Ro beyond 0.05 led to the unstable collapse of turbulence near the suction surface, a behavior which is consistent with experimental data but not with the direct simulations.

Particle acceleration in lower-hybrid cavitons

In this paper we investigate particle acceleration resulting from the relaxation of unstable ion ring distributions, producing strong wave activity at the lower hybrid frequency. It is shown that strong lower hybrid wave turbulence collapses in configuration space producing density cavities containing intense electrostatic lower hybrid wave activity. The collapse of these intense nonlinear wavepackets saturate by particle acceleration producing energetic electron and ion tails. There are several mechanisms whereby unstable ion distributions could be formed in plasmas, including reflection at perpendicular shocks, tearing modes, and loss cone depletion.Numerical simulations of ion ring relaxation processes, obtained using a 2½-D fully electromagnetic, relativistic particle in cell code are discussed. We apply the results to the problem of explaining energetic particle production in solar flares. The results show the simultaneous acceleration of both electrons and ions to very high energies: electrons are accelerated to energies in the range 10-500 keV, while ions are accelerated to energies of the order of MeV's. Our simulations also show wave generation at the electron cyclotron frequency. The strong turbulence collapse process leads to a highly filamented plasma producing many localized regions for particle acceleration of width ≃ 10λDe.

Langmuir wave decay and collapse in the Jovian foreshock

Langmuir waves are known to be created upstream of planetary bow shocks by the two-stream instability driven by sunward-streaming particles. In this paper we examine Langmuir waves detected by Ulysses' Unified Radio and Plasma wave experiment (URAP) upstream of Jupiter. Wave envelopes qualitatively consistent with collapsed Langmuir waves are common in the Ulysses dataset, and while a few events have amplitudes exceeding the published theoretical thresholds for turbulent Langmuir wave collapse, the majority of events are too weak. Langmuir wave decay via backscattering within preexisting density fluctuations in the solar wind is examined as a mechanism capable of localizing Langmuir waves. Langmuir decay is found to be a viable process which may play a role in preparing plasma conditions for collapse, but cannot alone account for the observed data.

Measurements of turbulence and fossil turbulence near ampere seamount

Abstract Measurements of temperature and velocity microstructure near and downstream of a shallow seamount are used to compare fossil turbulence versus non-fossil turbulence models for the evolution of turbulence microstructure patches in the stratified ocean. According to non-fossil oceanic turbulence models, all overturn length scales LT of the microstructure grow and collapse in constant proportion to each other and to the turbulence energy (Oboukov) scale LO and the inertial buoyancy (Ozmidov) scale L R ≡(ϵ/N 3 ) 1 2 of the patches; that is, with LTrms ≈1.2LR and viscous dissipation rate ϵ ≈ ϵ 0 ∗ . According to the Gibson fossil turbulence model, all microstructure originates from completely active turbulence with ϵ ⩾ ϵ 0 ≈ 3L T 2 N 3 (≈ 28ϵ 0 ∗ ) and L T /√6 ≈ L Trms , but this rapidly decays into a more persistent active-fossil state with ϵ0⩾ϵ⩾ϵF ≈ 30vN2, where N is the buoyancy frequency and v is the kinematic viscosity and, without further energy supply, finally reaches a completely fossil turbulence hydrodynamic state of internal wave motions, with ϵ ⩽ ϵF. The last turbulence eddies, with ϵ ≈ ϵF, vanish at a buoyant-inertial-viscous (fossil Kolmogorov) scale LKF that is much smaller than the remnant overturn scales LT for large ϵ0/ϵF ratios. These density, temperature, and salinity overturns with LT ≈ 0.6 LR0 ⪢ 0.6 LR persist as turbulence fossils (by retaining the memory of ϵo) and collapse very slowly. In the near wake below the summit depth of Ampere seamount, a much larger proportion of completely active turbulence patches was found than is usually found in the ocean interior away from sources. Dissipation rates ϵ and turbulence activity coefficients A T ≡ (ϵ/ϵ 0 ) 1 2 of microstructure patches were found to decrease downstream, suggesting that the active turbulence indicated by the patches with AT ⩾ 1 was caused by the presence of the seamount as a turbulence source. Therefore, the turbulence and mixing processes of ocean layers far away from turbulence sources probably have been undersampled by microstructure data sets lacking any AT ⩾ 1 patches. This is because large fractions of the mixing and viscous dissipation of the patches occur in short-lived active turbulence regimes that are too brief to be detected. Consequently, large underestimates of the true space-time average turbulence fluxes and turbulence and scalar dissipation rates may result if non-fossil turbulence models are assumed in ocean microstructure data interpretation.

Strong Langmuir turbulence at Jupiter?

Langmuir wave packets with short scale lengths l ≲ 100λe have been observed in Jupiter's foreshock. We assess whether the observations are consistent with the relatively new nucleation mechanism for nonlinear collapse of Langmuir waves. Theoretical constraints on the electric fields and scale sizes of collapsing wave packets are summarized, extended and placed in a form suitable for easy comparison with Voyager and Ulysses data. The published data are reviewed and possible instrumental underestimation of fields discussed. New upper limits for the fields of the published wave packets are estimated. Our results are: (1) Wave packets formed at the nucleation scale from the observed large‐scale fields cannot collapse because they are disrupted before collapse occurs. (2) The published wave packets are quantitatively inconsistent with strong turbulence collapse. (3) Strict constraints exist for more intense wave packets to be able to collapse: E ≳ 1 – 8 mV m−1 for scales l ≲ 1000λe. Means for testing these conclusions using Voyager and Ulysses data are suggested.

Mixing across a lutocline

The results of a laboratory experiment showed that mixing across a lutocline (the interface between clear water on top and a fluid‐mud mixture underneath) is controlled not only by mud‐induced buoyancy effects through a Richardson‐number dependence, but also by the sediment‐induced collapse of turbulence in the fluid‐mud layer. The dependence of particle settling velocity on the concentration of suspended sediment can limit the height of resuspension of sediments and stop lutocline erosion after an initial period of active mixing.

Ocean Outfalls. II: Spatial Evolution of Submerged Wastefield

Some of the basic features of submerged wastefield formation in stratified currents are reported in this paper. Dilution increased with distance from the diffuser in the initial mixing region until it attained a maximum value, which is the initial dilution, after which it remained constant. By assuming a model of buoyancy‐induced turbulence collapse, expressions for the observed dependency on current speed in the forced entrainment regime of initial dilution, rise height, and mixing region length were obtained. An expression for lateral spreading in parallel currents was derived which was found to be of the same form as for unstratified currents, except that the rate of spreading in stratified currents is much slower. An expression for the rate of spreading in perpendicular currents was derived by applying results from mixed‐region collapse. An applications example shows that the initial mixing region can extend for several hundred meters downstream from the discharge. Because of gravitational spreading, a line diffuser will produce a wastefield width comparable to the diffuser length for most oceanic conditions, suggesting that Y or similarly complex diffuser configurations are not necessary to produce a widely dispersed wastefield.

Three-dimensional strong Langmuir turbulence and wave collapse.

Results from the first fully three-dimensional simulations of driven damped strong Langmuir turbulence and wave collapse are presented. Key results are that turbulence is maintained at least in part by nucleation, the cores of most collapsing objects are pancake shaped in form, and the power spectrum falls off approximately as the product of a power law and an exponential at large wave number.

Turbulence in stratified fluids: A review

Buoyancy length scale and internal disturbance Froude number criteria for turbulence collapse in stratified fluid are examined in the light of recent laboratory experiments, oceanographie observations, and numerical simulations. From these it emerges that the onset of collapse occurs when the turbulence integral length scale is of the order of the buoyancy length scale, giving a disturbance Froude number close to 1. Complete collapse of three‐dimensional turbulence, characterized by nearly zero vertical mass flux, occurs at a lower value of the disturbance Froude number. In particular, a spatially inhomogeneous turbulence undergoes a drastic change in structure at a value of the disturbance Froude number of 0.2–0.3. In the collapsed state, internal wave motion and quasi two‐dimensional turbulence coexist on different time scales, results supported also by the rotating turbulence analogy. Vertical diffusion coefficients and mixing efficiency, which are of direct practical importance, are also examined.

The Turbulence Field Generated by a Linear Gravity Wave

Abstract An approximate but standard turbulence closure—the so-called “1½ order closure”—is employed to calculate the turbulence field generated by a stationary, large amplitude gravity wave in the middle atmosphere. Turbulence is generated within the superadiabatic phases of the gravity wave and is damped within other phases of the wave. Turbulence collapse is accounted for in the damping region. Determined are the intensity (rms turbulence velocity) and the local turbulence diffusivity as a function of wave amplitude, frequency, wavelength and position in space. Also calculated is an a priori, although approximate, prediction of the wave amplitude required to saturate the gravity wave, and the degree of superdiabaticity at saturation. Simplifying approximations limit the calculations to 2HkzUk≫ 1. The results are approximate because of the nature of the turbulence model but the qualitative results have simple explanations.

Evolution of Finite Amplitude Kelvin–Helmholtz Billows in Two Spatial Dimensions

Abstract A two-dimensional numerical model is used to calculate the nonlinear evolution of Kelvin-Helmholtz (KH) billows for various Reynolds numbers in the range where the turbulent collapse of the waves is expected. The onset of disordered motions is not observed in these numerical experiments, presumably because the transition requires the third spatial degree of freedom. Although we have shown elsewhere that these two-dimensional KH wave states are unstable with respect to three-dimensional perturbations, the spanwise coherent large-scale structure is observed to persist in presence of the small-scale fluctuations. Thus the two-dimensional wave structure is of importance in itself and the present paper is devoted to a detailed study of the laminar evolution of the dominant large-scale vortices. An analysis of the transfer of energy between the wave and the mean flow firmly establishes that the wave does not enter a steady state upon achieving maximum amplitude. Rather, it begins an almost periodic exc...

Structure of molecular clouds. V - Detailed models and observational characteristics

A detailed model of centrally condensed clouds containing regions of active star formation is derived from observations. The model has nearly equal turbulent and systematic collapse velocities and indicates that such clouds are not clumpy. Alfvenic waves can explain the turbulent velocities if the magnetic field varies as n2./sup 1/2/

Observations of Pressure Jump Lines in the Midwest, 10–12 August 1976

Abstract Strong thunderstorm activity over Iowa on two successive afternoons was the apparent source of pressure-jump lines (PJL's) which moved SSE at 50 km h−1 through the nocturnal boundary layer and were detected by National Weather Service (NWS) stations as far away as Paducah, Kentucky. Rainshowers and thunder were reported at many NWS stations as the PJL's passed. The Regional Air Monitoring System (RAMS) network at St. Louis provided detailed information on the PJL'S. Arrival there was indicated by an abrupt pressure rise of 1.5 mb, a near reversal of the surface flow, and a vertical displacement of 750 m extending through the lower 4 km of the atmosphere. The passage of each PJL was coincident with the turbulent collapse of the nocturnal jet. The observations of the PJL events seem indicative of an internal bore and are similar to those of the Morning Glory seen in northern Australia. We speculate that the bore originates from a late afternoon convergence produced by thunderstorm outflow and oppos...

Open Channel Flow with Suspended Sediments

Characteristics of open channel flow with suspended sediments were theoretically investigated introducing a theory based on the Monin-Obukhov length. First, a velocity distribution equation based on the theory showed a good agreement with the measured velocity distribution. Second, the hydraulic resistance and the distribution of suspended sediment concentration observed in experiments were explained theoretically. Third, a transport rate formula for suspended sediments, in which classical equations were included as a particular case, was obtained; and this formula, in cooperation with a reference concentration derived in the present study, showed agreement with experimental results. Finally, the critical condition for deposition of suspended particles and the collapse of turbulence were derived and verified by experiments.