On numerical realizability of thermal convection

Astounded at the regularity of convective structures observed in simulations of mesoscale flow past realistic topography, we investigate the computational aspects of a classical problem of flow over a heated plane. We find that the numerical solutions are sensitive to viscosity, either incorporated a priori or effectively realized in computational models. In particular, anisotropic viscosity can lead to regular convective structures that mimic naturally realizable Rayleigh–Bénard cells, which are unphysical for the specified external parameter range. Details of the viscosity appear to play a secondary role; that is, similar structures can occur for prescribed constant viscosities, explicit subgrid-scale turbulence models, ad-hoc numerical filters, or implicit dissipation of numerical schemes. This implies the need for a careful selection of numerical tools suitable for convection-resolving simulations of atmospheric circulations. The implicit large-eddy-simulation (ILES) approach using non-oscillatory schemes is especially attractive, as for under-resolved calculations it reproduces well the coarsened results of finely-resolved boundary layer convection.     

Hamiltonian description of dipoles on the plane and sphere

Poisson bracket for dipoles of ideal 2D hydrodynamics reduces to Zakharov-Faddeev-Gardner bracket by introducing new variables: coordinates of the vorticity extrema and geodesical distances from the poles to the vorticity lines. The new Hamiltonian equations include the well-known two point-vortex system and a decoupled pair of monopoles as asymptotical cases.     

Coherent Structures in Transition of a Flat-Plate Boundary Layer at Ma = 0.7

Direct numerical simulation （DNS） of a spatially evolving fiat-plate boundary layer transition process at free stream Mach number 0. 7 is performed. Tollmien-Schlichting （T-S） waves are added on the inlet boundary as the disturbances before transition. Typical coherent structures in the transition process are investigated based on the second invariant of velocity gradient tensor. The instantaneous shear stress and the mean velocity profile in the transition region are studied. In our view, the fact that the peak value of shear stress in the stress concentration area increases and exceeds a threshold value during the later stage of the trallsition process plays an important role in the laminar breakdown process.     

Late-Stage Vortical Structures and Eddy Motions in a Transitional Boundary Layer

A high-order direct numerical simulation of flow transition over a flat-plate at a free stream Mach number 0.5 is carried out. Formation and development of three-dimensional vortical structures, typically shown as λ-vortices, hairpin vortices and ring-like vortices, are observed. Numerical results show that there is a strong downdraft motion of fluid excited by every ring-like vortex in the late-stage of the transition process. At two sides of the vortical structure centerline, the downdraft motions induced by the ring-like vortex and the rotating legs superimpose. This is responsible for the appearance of a high-speed streak associated with the positive spike observed in a previous investigation and the appearance of a high-shear layer in the near wall region.     

Turbulence Modulations in the Boundary Layer of a Horizontal Particle-Laden Channel Flow

Turbulence modulations are experimentally investigated using particle image velocimetry （PIV） in the lower boundary layer of a fully developed horizontal channel flow. A simultaneous two-phase PIV measurement technique is adopted to acquire the turbulent statistics quantities and to examine the coherent structures in the near-wall region. Polythene beads with diameters of 60 μm are used as dispersed phases, and the PIV measurements have been performed at three mass loadings varying from 2.5 ×10^-4 to 5 × 10^-3. All the experiments are performed at a wall shear Reynolds number of Reτ = 430. The results show that the presence of the particles suppresses the coherent structures, with shorter streamwise extent of the quasistrearnwise structures, and then, the wall-normal velocity fluctuations and shear Reynolds stresses are both decreased in the near-core region. In addition, as a result of the particle wake, the turbulence intensity and shear Reynolds stress both increase in the vicinity of the wall. Due to the drag effects of the particles on the gas, the streamwise velocity gradients decrease in the outer region and increase in the viscous sublayer, meanwhile the thickness of the viscous sublayer also decreases. These results cause the peak values of the streamwise velocity fluctuations adjacent to the wall to increase, and the peak positions shift to the wall. This is the reason for decreasing the near-wall region and increasing the near-core region of the streamwise velocity fluctuations in appearance.     

Two Phases of Coherent Structure Motions in Turbulent Boundary Layer

Two phases of coherent structure motion are acquired after obtaining conditional phase-averaged waveforms for longitudinal velocity of coherent structures in turbulent boundary layer based on Harr wavelet transfer. The correspondences of the two phases to the two processes （i.e. ejection and sweep） during a burst are determined.     

A Conceptual Model of Somali Jet Based on the Biot--Savart Law

We study the relationship between thermal conditions on the earth bottom boundary and the formation of Somali jet based on the Biot-Savart law and the data from National Centres for Environmental Prediction （NCEP）. As the radiation from the Sun gradually moves from the southern meridian, the temperature on the surface of Somali Peninsular and Arabic Peninsular gradually increases. During the same period the surface temperature of the Northern Indian Ocean increases much slower. It is shown that this increase of the temperature difference between the land and sea is inductive to the formation and development of Rayleigh-Benard convection and leads to the increasing relative vorticity strength between positive and negative vertical vortices over the land and sea. According to the Biot-Savart law, increase of vorticity strength will correspondingly induce the horizontal velocity. A pair of positive and negative vorticity fields over the two Peninsulars and the sea surface is effective in forming and maintaining this current. This mechanism is referred to as the ＇Somali suction pump＇. It draws air continually from the Southern hemisphere and releases it at the coastal area of Somali.     

Frequency Response of Near-Wall Coherent Structures to Localized Periodic Blowing and Suction in Turbulent Boundary Layer

We experimentally investigate the frequency response of near-wall coherent structures to localized periodic blow- ing and suction through a spanwise slot in a turbulent boundary layer by changing the frequency of periodic disturbance at similar velocities of free stream. The effects of blowing and suction disturbance on energy redistri- bution, turbulent intensity U^＋ rums over y^＋ and waveforms of phase-averaged velocity during sweeping process are respectively discussed under three frequencies of periodic blowing and suction in near-wall region of turbulent boundary layer, compared with those in a standard turbulent boundary layer. The most effective disturbance frequency is figured out in this system.     

Numerical tests of a new molecule-dependent momentum transport equation

It is shown that a new incompressible fluid equation is obtained by inclusion of a new dimensionless coupling parameter in the momentum transport equation derived in [L. Jirkovsky, L. Bo-ot, Momentum transport equation for the fluids using projection-perturbation formalism and onset of turbulence, Physica A 352 (2005) 241-251] from the Boltzmann kinetic equation where the Boltzmann collision integral includes inelastic interactions of quantum origin among the particles of the fluid. Numerical results from the equation for the plane and circular Poiseuille flows are consistent with the observations. The numerical tests also manifest a difference in the onset of turbulence between the flat plates and the circular pipe flow systems. Although all obtained velocity profiles are flattened at the center-a feature of turbulence-the results demonstrate greater stability of the velocity profiles in the circular pipe flow.     

A computationally efficient scheme for the non-linear diffusion equation

This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.     

Highly directional liquid surface wave source based on resonant cavity

By placing a point source inside a resonant cavity structure, we present a method to realize a highly directional liquid surface wave source. The resonant cavity is surrounded by two slabs of different thickness, with each slab consisting of a finite square array of rigid cylinders standing vertically in the liquid. It is shown that more than 68% of the total energy is emitted out along the normal directions of the cavity within a very narrow angular range. At the resonant frequency, narrow emission pattern with half-power angular width of only several degrees is obtained.     

About bursty behaviour, coherent structures, wide scrape-off layer and large parallel flows in the edge of the Tore Supra tokamak

We present the measurements of plasma characteristics in the scrape-off layer (SOL) of the Tore Supra tokamak performed by means of reciprocating Langmuir probe. The probe is inserted into the machine from top. As the radial distance from last closed flux surface (LCFS) increases, ion saturation current exhibits stronger bursty character and its probability density function becomes increasingly skewed towards positive values. At the same time, burst duration and inter-burst time increase dramatically. We explain this phenomenon by radial propagation and dynamics of the ensemble of coherent turbulent structures of different size. The results of two-dimensional fluid modelling based of flux-driven interchange instability mechanism are in excellent agreement with experimental results. We obtained clear experimental evidence that most of the coherent structures are formed in poloidally localized region of the SOL around the outboard midplane. If the probe is magnetically connected to this region, the SOL is very wide and we detect bursty behaviour in the far SOL. On the other hand, if the probe is not magnetically connected to the outboard midplane region (magnetic field lines are intercepted by the outboard limiter), then the SOL is very thin and bursty behaviour is much less prominent. Detection of bursty behaviour in the far SOL is correlated with existence of wide SOL pointing on important role of bursty transport by means of coherent turbulent structures in establishing the width of the SOL in tokamaks. The measurements of parallel flow in the SOL shows that plasma particle radial flux coming from confinement region to the SOL is mostly poloidally localized around the outboard midplane. Our estimations show that more than 80% of plasma particle radial flux is coming from confinement region to the SOL in poloidally localized region — approximately ±15° — around the outboard midplane. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Roma, Italy, June 26–27, 2006.     

PIV Measurements and Mechanisms of Adjacent Synthetic Jets Interactions

Interactions of adjacent synthetic jet actuators with varying relative amplitude and the relative phase of driving voltage are measured using a particle image velocimetry （PIV）. Varying relative amplitude or relative phase of driving voltage of the adjacent actuators vectors the direction of the ensuing merged jet of the adjacent synthetic jets. The vectoring mechanism of the adjacent vortex pairs, attract-impact causing deflection （AICD）, is provided to explain why the merged jet is generally vectored to the side of the phase-leading synthetic jet or the synthetic jet with higher driving voltage.     

Painleve Property and New Analytic Solutions for a Variable-Coefficient Kadomtsev--Petviashvili Equation with Symbolic Computation

A variable-coemcient Kadomtsev-Petviashvili equation is investigated. The Painlev6 analysis leads to its explicit Painlevd-integrable conditions. An auto-Backlund transformation and the bilinear form are presented via the truncated Painlev6 expansion and symbolic computation. Several families of new analytic solutions arepresented, including the soliton-like and periodic solutions.     

On the use of SODAR data to estimate mixing height

Estimation of the mixing height is one of the most common applications of SODAR data for more than twenty years and SODAR has been shown to provide reliable results under a great variety of meteorological and site conditions. Nevertheless there are still some unsolved questions. The paper gives a brief review of results obtained during the last two decades. Additionally some of the open problems are discussed in more detail. These are the determination of the stable boundary layer height from digitized SODAR data, its relation to other common height scales, its parameterization, and finally the estimation of the height of a deep convective boundary layer, exceeding the SODAR probing range.     

Global Structures and Multi-Temporal Variabilities of MLT Migrating Diurnal Tide

Migrating diurnal tide in the MLT region is examined by the application of Hough mode decomposition with the tide delineated from the SABER/TIMED temperatures over 2002-2006. The decomposition results show that in the height range 60-100km, the （1, 1） mode is the most predominant among eight leading Hough modes including four propagating and four trapped modes. It exhibits a sustained maximum at 97 km and significant semi-annual oscillation. Additionally, a novel feature of inter-annual variation with period of about two years is clearly seen in the （1, 1） mode, e.g., repeated maxima are seen at the March equinox of 2002, 2004 and 2006, respectively. This feature is further manifested by the tidal amplitudes in the height range 70-100km in the height-time cross-section at the equator. It is likely of the QBO as the height range just coincides to where the zonal mean zonal winds derived by using the UARS data exhibiting the QBO. The other results show that the （1, 2） mode is important at 〈 80 km exhibiting comparable amplitude to that of the （1, 1） mode, and in particular the nearly anti-correlation with the （1, 1） mode. The tide at about 85 km is suggested of rather complex as the four trapped modes exhibit maximum at these heights, which indicates the presence of local excitations or sources at below.     

Actual Tropical Waves Identified by the Wavenumber-Frequency Spectrum Analysis during Boreal Summer

Based on daily satellite-observed outgoing longwave radiation （OLR） data, the tropical intraseasonal oscillation （ISO） associated with the Asian summer monsoon is found to be dominant during the 2005 summer. Such an ISO along with other tropical waves are identified using a wavenumber-frequency spectrum analysis. Some of Significant spectral peaks coincide well with the dispersion curves of the equatorially trapped wave modes from shallow＇water theory, with various equivalent depths of 12-200 m, suggesting that actual tropical waves can be detected from observational data. Although the formation mechanism of the ISO is more complicated than those of other tropical waves with higher frequencies, significant spectral peaks that correspond to the ISO with a period of 30-60 days distinctly appear in the OLR spectra. The selective wavenumber-frequency filtering of OLR data is thus performed to isolate the ISO, Kelvin and equatoriai Rossby waves, and the properties and signatures of such tropical waves that control tropical atmospheric variability for the 2005 summer are clearly identified.     

On the lower bound of net driving power in controlled duct flows

We examine mathematically the lower bound of the net driving power (i.e., the summation of pumping and actuation powers) of a controlled duct flow under a constant flow rate. The net power in a duct with arbitrary cross-section in the presence of the inertial term, blowing/suction from the wall, and arbitrary body forces can be decomposed into four terms: (1) dissipation due to the velocity profile of the Stokes flow (in other words, pumping power for the Stokes flow); (2) dissipation due to deviation of the mean velocity from the Stokes flow profile; (3) dissipation due to velocity fluctuations; and (4) correlation between the wall-pressure of the Stokes flow and the time-averaged blowing/suction velocity. Of these, the first three terms are shown to be non-negative, while the sign of the fourth term is indefinite. The fourth term vanishes in cases where the duct has a constant-shape cross-section, such as cylindrical pipes and plane channels. Namely, in such cases, the lower bound of net power is exactly given by the dissipation rate (pumping power) of the Stokes flow at the same flow rate.     

Improving the description of sunglint for accurate prediction of remotely sensed radiances

The bidirectional reflection distribution function (BRDF) of the ocean is a critical boundary condition for radiative transfer calculations in the coupled atmosphere-ocean system. Existing models express the extent of the glint-contaminated region and its contribution to the radiance essentially as a function of the wind speed. An accurate treatment of the glint contribution and its propagation in the atmosphere would improve current correction schemes and hence rescue a significant portion of data presently discarded as “glint contaminated”. In current satellite imagery, a correction to the sensor-measured radiances is limited to the region at the edge of the glint, where the contribution is below a certain threshold. This correction assumes the sunglint radiance to be directly transmitted through the atmosphere. To quantify the error introduced by this approximation we employ a radiative transfer code that allows for a user-specified BRDF at the atmosphere-ocean interface and rigorously accounts for multiple scattering. We show that the errors incurred by ignoring multiple scattering are very significant and typically lie in the range 10-90%. Multiple reflections and shadowing at the surface can also be accounted for, and we illustrate the importance of such processes at grazing geometries.     

The Rossby wave extra invariant in the physical space

It was found out in 1991 that the Fourier space dynamics of Rossby waves possesses an extra positive-definite quadratic invariant, in addition to the energy and enstrophy. This invariant is similar to the adiabatic invariants in the theory of dynamical systems. For many years, it was unclear if this invariant—known only in the Fourier representation—is physically meaningful at all, and if it is, in what sense it is conserved. Does the extra conservation hold only for a class of solutions satisfying certain constraints (like the conservation in the Kadomtsev-Petviashvili equation)? The extra invariant is especially important because this invariant (provided it is meaningful) has been connected to the formation of zonal jets (like Jupiter’s stripes).In the present paper, we find an explicit expression of the extra invariant in the physical (or coordinate) space and show that the invariant is indeed physically meaningful for any fluid flow. In particular, no constraints are needed. The explicit form also enables us to note several properties of the extra invariant.