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1.
In wind‐driven rains, wind velocity and direction are expected to affect not only energy input of rains but also shallow ?ow hydraulics by changing roughness induced by raindrop impacts with an angle on ?ow and the unidirectional splashes in the wind direction. A wind‐tunnel study under wind‐driven rains was conducted to determine the effects of horizontal wind velocity and direction on sediment transport by the raindrop‐impacted shallow ?ow. Windless rains and the rains driven by horizontal wind velocities of 6 m s?1, 10 m s?1, and 14 m s?1 were applied to three agricultural soils packed into a 20 by 55 cm soil pan placed on both windward and leeward slopes of 7 per cent, 15 per cent, and 20 per cent. During each rainfall application, sediment and runoff samples were collected at 5‐min intervals at the bottom edge of the soil pan with wide‐mouth bottles and were determined gravimetrically. Based on the interrill erosion mechanics, kinetic energy ?ux (Ern) as a rainfall parameter and product of unit discharge and slope in the form of qbSco as a ?ow parameter were used to explain the interactions between impact and ?ow parameters and sediment transport (qs). The differential sediment transport rates occurred depending on the variation in raindrop trajectory and rain intensity with the wind velocity and direction. Flux of rain energy computed by combining the effects of wind on the velocity, frequency, and angle of raindrop impact reasonably explained the characteristics of wind‐driven rains and acceptably accounted for the differences in sediment delivery rates to the shallow ?ow transport (R2 ≥ 0·78). Further analysis of the Pearson correlation coef?cients between Ern and qSo and qs also showed that wind velocity and direction signi?cantly affected the hydraulics of the shallow ?ow. Ern had a smaller correlation coef?cient with the qs in windward slopes where not only reverse splashes but also reverse lateral raindrop stress with respect to the shallow ?ow direction occurred. However, Ern was as much effective as qSo in the sediment transport in the leeward slopes where advance splashes and advance lateral raindrop stress on the ?ow occurred. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

2.
Pan evaporation (Ep) is an important indicator of water and energy and the decline of Ep has been reported in many regions over the last decades. The climate and Ep are dependent on each other. In this study, the temporal trends of Ep and main Ep drivers, namely mean air temperature (Ta), wind speed (u), global solar radiation (Rs), net long‐wave radiation(Rnl) and vapour pressure deficit (D) from 1970 to 2012, were calculated on the basis of 26 meteorological stations on the Tibetan Plateau. The arithmetic average of Ep from 26 stations decreased with the rate of ?11.91 mm a?2; the trends of Rs, Rnl, Ta, u and D were ?1.434 w m?2 decade?1, 0.2511 w m?2 decade?1, 0.3590°C decade?1, ?0.2376 m s?1 decade?1 and 9.523 Pa decade?1, respectively. The diffuse irradiance is an essential parameter to model Ep and quantify the contribution of climatic factors to changing Ep. 60 724 observations of Rs and diffuse solar irradiance (Rd) from seven of the 26 stations were used to develop the correlation between the diffuse fraction (Rd/Rs), and the clearness index (Rs/Ro). On the basis of the estimation of the diffuse component of Rs and climatic data, we modified the PenPan model to estimate Chinese micro‐pan evaporation (Ep) and assess the attribution of Ep dynamics using partial derivatives. The results showed that there was a good agreement between the observed and calculated daily Ep values. The observed decrease in Ep was mostly due to declining wind speed (?13.7 mm a?2) with some contributions from decreasing solar irradiance (?3.1 mm a?2); and the increase of temperature had a large positive effect (4.55 mm a?2) in total whilst the increase of Rnl had insignificant effect (0.35 mm a?2) on Ep rates. The change of Ep is the net result of all the climatic variables. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

3.
Abstract

We have contrived a model E(αω) α μ?1ω?p+1(ω 2?ω i 2)?+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber α extending to some upper limit μ(ω) α ω r-1 (ω 2?ω i 2)½, and frequency ω extending from the inertial frequency ω i to the local Väisälä frequency n(y). The spectrum is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(α, ω) = 2παE(α1, α2, ω), with α1, α2 designating components of α. Certain moments of E(α1, α2, ω) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement η(t),…, yield the frequency spectra F (u,η,…)(ω) = ∫∫ (U 2, Z 2,…)E(α1, ∞2, ω) dα1 dα2, where U, Z,… are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber spectrum F (…)(α1) = ∫∫… dα2 dω. (iii) Moored measurements horizontally separated by X yield the coherence spectrum R(X, ω) which is related to the horizontal cosine transform ∫∫ E(α1, α2 ω) cos α1 Xdα1 dα1. (iv) Moored measurements vertically separated by Y yield R(Y, ω) and (v) towed measurements vertically separated yield R(Y, α1), and these are related to similar vertical Fourier transforms. Away from inertial frequencies, our model E(α, ω) α ω ?p-r for α ≦ μ ω ω r, yields F(ω) ∞ ω ?p, F(α1) ∞ α1 ?q, with q = (p + r ? 1)/r. The observed moored and towed spectra suggest p and q between 5/3 and 2, yielding r between 2/3 and 3/2, inconsistent with a value of r = 2 derived from Webster's measurements of moored vertical coherence. We ascribe Webster's result to the oceanic fine-structure. Our choice (p, q, r) = (2, 2, 1) is then not inconsistent with existing evidence. The spectrum is E(∞, ω) ∞ ω ?1(ω 2?ω i 2 ?1, and the α-bandwith μ ∞ (ω 2?ω i 2)+ is equivalent to about 20 modes. Finally, we consider the frequency-of-encounter spectra F([sgrave]) at any towing speed S, approaching F(ω) as S ≦ S o, and F(α1) for α1 = [sgrave]/S as S ≧ S o, where S o = 0(1 km/h) is the relevant Doppler velocity scale.  相似文献   

4.
Intergrain contact density indices for granular mixes I： Framework   总被引：2，自引：0，他引：2  
Mechanical behavior such as stress-strain response, shear strength, resistance to liquefaction, modulus, and shear wave velocity of granular mixes containing coarse and fine grains is dependent on intergrain contact density of the soil. The global void ratio e is a poor index of contact density for such soils. The contact density depends on void ratio, fine grain content （Cv）, size disparity between particles, and gradation among other factors. A simple analysis of a two-sized particle system with large size disparity is used to develop an understanding of the effects of Cv, e, and gradation of coarse and fine grained soils in the soil mix on intergrain contact density. An equivalent intergranular void ratio （ec）oq is introduced as a useful intergrain contact density for soils at fines content of less than a threshold value Crth. Beyond this value, an equivalent interfine void ratio （ef）eq is introduced as a primary intergrain contact density index. At higher values of Cv beyond a limiting value of fine grains content CVL, an interfine void ratio ef is introduced as the primary contact density index. Relevant equivalent relative density indices （Drc）eq and （Drf）eq are also presented. Experimental data show that these new indices correlate well with steady state strength, liquefaction resistance, and shear wave velocities of sands, silty sands, sandy silts, and gravelly sand mixes.  相似文献   

5.
The estimation of evapotranspiration (E) in forested areas is required for various practical purposes (e.g. evaluation of drought risks) in Japan. This study developed a model that estimates monthly forest E in Japan with the input of monthly temperature (T). The model is based on the assumptions that E equals the equilibrium evaporation rate (Eeq) and that Eeq is approximated by a function of T. The model formulates E as E (mm month−1) = 3·48 T ( °C) + 32·3. The accuracy of the model was examined using monthly E data derived using short‐term water balance (WB) and micrometeorological (M) methods for 15 forest sites in Japan. The model estimated monthly E more accurately than did the Thornthwaite and Hamon equations according to regression analysis of the estimated E and E derived using the WB and M methods. Although the model tended to overestimate monthly E, the overestimation could be reduced by considering the effect of precipitation on E. As T data are commonly available all over Japan, the model would be a useful tool to estimate forest E in Japan. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

6.
Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady Hartmann boundary layer control the fluid interior. It is shown how to obtain the known spin-up times for a homogeneous, nonconducting fluid (τ = E -½), a stably stratified, nonconducting fluid (τ = (σS/E, E ?1) and a homogeneous conducting fluid (τ = α?1 E -½) from the present formulation where τ = v/ωt, E = v/ωL 2, σS = vN2/κω2 and 2α2 = σB2/pω. The problem is solved in the parameter range E?α2?1, α2/E?σS using the Laplace transform and two new spin-up times are obtained. Combined into one expression, they are τ = (1 + δ)α?1E-½ where δ = σμv. The spin-up mechanism is investigated and it is found that, in contrast to the homogeneous, conducting case, torsional Alfvén waves may be instrumental in the spin-up of a stratified conducting fluid. The effects of viscous and ohmic diffusion on the torsional Alfvén wave fronts are studied and the following regimes are identified: 0 < δ ?E/α2, spin-up by meridional circulation of electric current with no Alfvén waves; E-½/α ? δ ? 1, spin-up by meridional circulation of electric current with transient Alfvén waves; α/E½ ? δ ? α2/E, spin-up by meridional circulation of current with weak Alfvén waves; 1 ? δ ? α/E½, spin-up by strong Alfvén waves; α½/E ? δ ? α2/E, spin-up by viscous diffusion with transient Alfvén waves; α/E ? δ < ∞, spin-up by viscous diffusion with no Alfvén waves.  相似文献   

7.
The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ2= 10?2-10 Sm?1), and source frequencies (f= 10?1-10?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes Hy, Hz and Ex and the phases φy and Ψx.  相似文献   

8.
A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear?α?2-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudo-spectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5× 10?3 to 5.0× 10?5, for?α?=α 0cos?θ?sin?π?(r?ri ) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of?α?0. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos.  相似文献   

9.
Using the auroral boundary index derived from DMSP electron precipitation data and the Dst index, changes in the size of the auroral belt during magnetic storms are studied. It is found that the equatorward boundary of the belt at midnight expands equatorward, reaching its lowest latitude about one hour before Dst peaks. This time lag depends very little on storm intensity. It is also shown that during magnetic storms, the energy of the ring current quantified with Dst increases in proportion to Le–3, where Le is the L-value corresponding to the equatorward boundary of the auroral belt designated by the auroral boundary index. This means that the ring current energy is proportional to the ion energy obtained from the earthward shift of the plasma sheet under the conservation of the first adiabatic invariant. The ring current energy is also pronortional to Emag, the total magnetic field energy contained in the spherical shell bounded by Le and Leq, where Leq corresponds to the quiet-time location of the auroral precipitation boundary. The ratio of the ring current energy ER to the dipole energy Emag is typically 10%. The ring current leads to magnetosphere inflation as a result of an increase in the equivalent dipole moment.  相似文献   

10.
Whether the presence of non-plastic silt in a granular mix soil impact its liquefaction potential and how to evaluate liquefaction resistance of sand containing different amounts of silt contents are both controversial issues. This paper presents the results of an experimental evaluation to address these issues. Two parameters, namely, equivalent intergranular void ratio （ec）eq and equivalent interfine void ratio （ef）eq, proposed in a companion paper （Thevanayagam, 2007） as indices of active grain contacts in a granular mix, are used to characterize liquefaction resistance of sands and silty sands. Results indicate that, at the same global void ratio （e）, liquefaction resistance of silty sand decreases with an increase in fines content （Cv） up to a threshold value （Crth）. This is due to a reduction in intergrain contact density between the coarse grains. Beyond Crth, with further addition of fines, the interfine contacts become significant while the inter-coarse grain contacts diminish and coarse grains become dispersed. At the same e, the liquefaction resistance increases and the soil becomes stronger with a fttrther increase in silt content. Beyond a limiting fines content （CrL）, the liquefaction resistance is controlled by interfine contacts only. When Cr〈Crth, at the same （e）eq, the liquefaction resistance of silty sand is comparable to that of the host clean sand at a void ratio equal to （ec）eq. When CF〉CFth, at the same （ef）eq, the cyclic strength of a sandy silt is comparable to the host silt at a void ratio equal to （ef）eq.  相似文献   

11.
Abstract

Numerical simulations of internal gravity waves-turbulence are carried out for the inviscid, viscous and forced-dissipative two-dimensional primitive equations using the spectral method. Some of the results are compared with the predictions of the eddy damped quasi-normal Markovian (EDQNM) closure for internal waves of Carnevale and Frederiksen, generalized for periodic boundary conditions and possible random forcing and dissipation. The EDQNM reduces to the Boltzman equation of resonant interaction theory in the continuum space limit and as the forcing and dissipation vanish. However, the limit is singular in the sense that as well as conserving total energy, E, and total cross-correlation between the vorticity and buoyancy fields, C, an additional conservation law, viz. z-momentum, Pz , occurs in the limit. This means that the resonant interaction equilibrium (RIE) solution of the Boltzmann equation differs from the statistical mechanical equilibrium (SME) solution of the EDQNM closure.

The statistical stability of the SME and RIE spectra for the primitive equations is tested by integrating the inviscid equations using initial realizations of these spectra with random phases. It is found that E and C are accurately conserved while Pz undergoes large amplitude variations. The approach to equilibrium of initial disequilibrium spectra is monitored by examining the evolution of the entropy. The increase and asymptotic approach to a constant value corresponding to complete chaos is consistent with the behaviour predicted by the EDQNM closure.

For the viscous decay and forced-dissipative experiments, the behaviour of the entropy is also consistent with that predicted by the EDQNM closure. There is approximate equipartition of potential and total kinetic energies throughout the integrations from initial conditions having equal potential and total kinetic energies and as well equal vertical and horizontal energies, but as expected, the ratio of horizontal to vertical kinetic energy increases with time to a value greater than unity.

With Laplacian viscous dissipation and thermal diffusivity, the statistical steady states produced in the forced-dissipative experiments have k?3 power laws for k≧7. A comparison with the power laws for kinetic energy and passive scalar variance produced in a numerical simulation of the two-dimensional passive scalar problem is also presented.  相似文献   

12.
Abstract

Two fluid layers of constant density lying one over the other on top of a rigid horizontal lower boundary with either a free upper surface or a rigid upper boundary can support solitary waves. The existence of a unique branch of such waves emanating from the horizontal flow at a critical speed U ? is demonstrated in both cases by use of the Nash—Moser implicit function theorem. These results complement the global results of Amick and Turner (1986) and are analogous to the work of Friedrichs and Hyers (1954) and Beale (1977) for surface waves. It is also noted that the most obvious variational principle which characterizes these waves as constrained extremals (Benjamin, 1984) is of indefinite type, having a Hessian with infinitely many positive and infinitely many negative eigenvalues.  相似文献   

13.
Seasonal changes in the water and energy exchanges over a pine forest in eastern Siberia were investigated and compared with published data from a nearby larch forest. Continuous observations (April to August 2000) were made of the eddy‐correlation sensible heat flux and latent heat flux above the canopy. The energy balance was almost closed, although the sum of the turbulent fluxes sometimes exceeded the available energy flux (Rn ? G) when the latent heat flux was large; this was related to the wind direction. We examined the seasonal variation in energy balance components at this site. The seasonal variation and magnitude of the sensible heat flux (H) was similar to that of the latent heat flux (λE), with maximum values occurring in mid‐June. Consequently, the Bowen ratio was around 1·0 on many days during the study period. On some clear days just after rainfall, λE was very large and the sum of H and λE exceeded Rn ? G. The evapotranspiration rate above the dry canopy from May to August was 2·2 mm day?1. The contributions of understory evapotranspiration (Eu) and overstory transpiration (Eo) to the evapotranspiration of the entire ecosystem (Et) were both from 25 to 50% throughout the period analysed. These results suggest that Eu plays a very important role in the water cycle at this site. From snowmelt through the tree growth season (23 April to 19 August 2000), the total incoming water, comprised of the sum of precipitation and the water equivalent of the snow at the beginning of the melt season, was 228 mm. Total evapotranspiration from the forest, including interception loss and evaporation from the soil when the canopy was wet, was 208–254 mm. The difference between the incoming and outgoing amounts in the water balance was from +20 to ?26 mm. The water and energy exchanges of the pine and larch forest differed in that λE and H increased slowly in the pine forest, whereas λE increased rapidly in the larch forest and H decreased sharply after the melting season. Consequently, the shape of the Bowen ratio curves at the two sites differed over the period analysed, as a result of the differences in the species in each forest and in soil thawing. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

14.
In this study, we examined the year 2011 characteristics of energy flux partitioning and evapotranspiration of a sub‐alpine spruce forest underlain by permafrost on the Qinghai–Tibet Plateau (QPT). Energy balance closure on a half‐hourly basis was H + λE = 0.81 × (Rn ? G ? S) + 3.48 (W m?2) (r2 = 0.83, n = 14938), where H, λE, Rn, G and S are the sensible heat, latent heat, net radiation, soil heat and air‐column heat storage fluxes, respectively. Maximum H was higher than maximum λE, and H dominated the energy budget at midday during the whole year, even in summer time. However, the rainfall events significantly affected energy flux partitioning and evapotranspiration. The mean value of evaporative fraction (Λ = λE/(λE + H)) during the growth period on zero precipitation days and non‐zero precipitation days was 0.40 and 0.61, respectively. The mean daily evapotranspiration of this sub‐alpine forest during summer time was 2.56 mm day?1. The annual evapotranspiration and sublimation was 417 ± 8 mm year?1, which was very similar to the annual precipitation of 428 mm. Sublimation accounted for 7.1% (30 ± 2 mm year?1) of annual evapotranspiration and sublimation, indicating that the sublimation is not negligible in the annual water balance in sub‐alpine forests on the QPT. The low values of the Priestley–Taylor coefficient (α) and the very low value of the decoupling coefficient (Ω) during most of the growing season suggested low soil water content and conservative water loss in this sub‐alpine forest. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

15.
Abstract

Chandrasekhar (1961) has summarized the stability results of Bénard convection in a rotating fluid for the cases where the boundary surfaces are both rigid and free, and for both exchange of stabilities and overstability. His analysis provides very accurate results for a limited range of Taylor number J. Bisshopp and Niiler (1965) presented an asymptotic analysis of the rigid boundary problem for exchange of stabilities which is valid for very large Taylor number. The present paper makes use of modern rotating fluid theory to develop an approximate scheme for evaluating the Rayleigh number and other parameters and variables. Known asymptotic results for the free boundary problem at large J are used and an expansion in powers of E1/6 (the Ekman number, E = 2J ?½) yields a sequence of equations and appropriate boundary conditions for the rigid boundary problem. After the algorithm for the calculation is developed, results are given for the problem to second order in the expansion parameter for the case of exchange of stabilities and to first order in the expansion parameters for the overstable case. Ekman boundary layers are important in the development as one might expect. However, an additional, diffusive boundary layer of thickness E? is necessary to provide the details of the temperature field. This boundary layer is the thermal response in the vertical direction to the horizontal spacing of the cells which is also order E?. The horizontal spacing of the cells is essentially a series of contiguous, Stewartson (1957) layers of thickness E?.  相似文献   

16.
Samples of water from poor to very rich fens in the Schefferville region of subarctic Quebec revealed strong spatial and temporal variations in dissolved organic carbon (DOC), ranging from 2 to 40 mg 1?1. Concentrations of DOC tend to increase during the summer and decrease in the autumn, at most sites, which probably reflects increased plant tissue decomposition and higher rates of evapotranspiration. Principal components analysis revealed that DOC is strongly associated with Fe, NO?3-N and NO?2-N, but essentially independent of other chemical properties of the peat water, such as pH, Ca, Mg, K, P, and NH+4-N. Based on observed concentrations of DOC and estimates of summer runoff (June to September), export of DOC from four peatlands ranges from 1·1 to 4·9 gCm?2, with the lowest values for peatlands underlain by dolomite. Molecular weight fractionation of four samples revealed significant differences in the dissolved organic matter (DOM), with the largest fractions (GF/C to 10 000 nmw) being dominant in the more acid samples. The ratio of absorbance at 400 and 600 nm wavelengths (E4:E6) has been used as a simple indicator of differences in DOM type, ranging from 3 to 15. There is a strong seasonal pattern of increasing E4:E6 ratio during the summer at many sites, though this ratio is essentially independent of other chemical properties of peat waters.  相似文献   

17.
The parameters commonly considered to define climate are the mean annual precipitation and mean annual potential evapotranspiration. In this study an attempt has been made to develop a relationship between average drought frequency and the evapotranspiration/precipitation ratio for the arid, semi‐arid and subhumid climatic regions of India. The climatic regions are delineated using two climatic indices: namely (i) the ratio of mean annual precipitation (Pa) to global terrestrial mean annual precipitation (Pg), and (ii) the ratio of mean annual potential evapotranspiration (Ep) to mean annual precipitation (Pa). It was noted that the average drought frequency (i e., year?1.) decreases gradually from dry to wet regions. The return period varies from 2 to 3 years in the arid regions (12>Ep&sol;Pa≥5), 3 to 5 years in semi‐arid regions (5>Ep&sol;Pa≥2), and 5 to 8 years in sub‐humid regions (2>Ep&sol;Pa≥3&sol;4). Another relationship was developed between the average frequency of drought occurrence and the ratio of mean annual deficit to mean annual precipitation, (Ep?Pa)&sol;Pa. The results have been compared with the drought experiences documented for other regions of the world. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

18.
Evaporation from the forest floor (EFF) in a deciduous broadleaf forest was measured using microlysimeter and closed‐chamber systems. The microlysimeter was used at six points in the experimental basin, and measurements gave different EFF values at different points. This could be attributed to the local photoenvironment of each sampling point, rather than to litter conditions, if the spatial variation in air temperature (Ta) or vapour pressure deficit (VPD) at the forest floor was small within this basin. A detachable microlysimeter measured condensation in the litter layer during the night, indicating that the litter layer, as well as the mulch layer, played a role in preventing evaporation from the soil layer. The closed‐chamber system made it possible to continuously measure long‐term EFF. EFF was closely related to VPD; even during the night, when solar radiation was zero, EFF amounted to 14·0% of the daily EFF. The daily EFF was 0·20 ± 0·13 mm day?1 during the study period, with two seasonal peaks: in late spring (0·31 mm day?1 in April) and early fall (0·22 mm day?1 in September). The former peak has been reported from two deciduous forests in Japan and is strongly related to the solar radiation reaching the forest floor when the trees are dormant. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

19.
Abstract

An exceptional case to the model-independent theory of Knobloch (1995) is presented, by investigating a rotating cylindrical annulus of height H and side wall radii r o and r i, with non-slip, perfectly thermally conducting side walls and thermally insulating stress-free ends. Radial heating permits the possibility of either two- or three-dimensional convective solutions being the preferred mode. An analytical solution is obtained for the two-dimensional case and a numerical solution for the three-dimensional solution, which is also applied to the two-dimensional solution. It is shown that both two- and three-dimensional solutions can be realized depending on the aspect ratio, γ = H/d, where d = r o-r i is the thickness of the annulus, the radii ratio λ = r i/r o and the rotation rate of the model. For γ = O(1) and λ = 0.4, the preferred convective solution is three-dimensional when the Taylor number, T < 102 and two-dimensional for T > 102. For small aspect ratios, γ ? 1, the preferred mode is two-dimensional for all rotation rates.  相似文献   

20.
Three-dimensional (3-D) numerical simulations of single turbulent thermal plumes in the Boussinesq approximation are used to understand more deeply the interaction of a plume with itself and its environment. In order to do so, we varied the Rayleigh and Prandtl numbers from Ra?～?105 to Ra?～?108 and from Pr?～?0.025 to Pr?～?70. We found that thermal dissipation takes place mostly on the border of the plume. Moreover, the rate of energy dissipation per unit mass ε T has a critical point around Pr?～?0.7. The reason is that at Pr greater than ～0.7, buoyancy dominates inertia and thermal advection dominates wave formation whereas this trend is reversed at Pr less than ～0.7. We also found that for large enough Prandtl number (Pr?～?70), the velocity field is mostly poloidal although this result was known for Rayleigh–Bénard convection (see Schmalzl et al. [On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 2004, 67, 390--396]). On the other hand, at small Prandtl numbers, the plume has a large helicity at large scale and a non-negligible toroidal part. Finally, as observed recently in details in weakly compressible turbulent thermal plume at Pr?=?0.7 (see Plourde et al. [Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 2008, 604, 99--123]), we also noticed a two-time cycle in which there is entrainment of some of the external fluid to the plume, this process being most pronounced at the base of the plume. We explain this as a consequence of calculated Richardson number being unity at Pr?=?0.7 when buoyancy balance inertia.  相似文献   

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