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1.
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2.
Applications of the entrainment process to layers at the boundary, which meet the self similarity requirements of the logarithmic profile, have been studied. By accepting that turbulence has dominating scales related in scale length to the height above the surface, a layer structure is postulated wherein exchange is rapid enough to keep the layers internally uniform. The diffusion rate is then controlled by entrainment between layers. It has been shown that theoretical relationships derived on the basis of using a single layer of this type give quantitatively correct factors relating the turbulence, wind and shear stress for very rough surface conditions. For less rough surfaces, the surface boundary layer can be divided into several layers interacting by entrainment across each interface. This analysis leads to the following quantitatively correct formula compared to published measurements. 1 $$\begin{gathered} \frac{{\sigma _w }}{{u^* }} = \left( {\frac{2}{{9Aa}}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \left( {1 - 3^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \frac{a}{k}\frac{{d_n }}{z}\frac{{\sigma _w }}{{u^* }}\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ = 1.28(1 - 0.945({{\sigma _w } \mathord{\left/ {\vphantom {{\sigma _w } {u^* }}} \right. \kern-\nulldelimiterspace} {u^* }})({z \mathord{\left/ {\vphantom {z L}} \right. \kern-\nulldelimiterspace} L})^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ \end{gathered} $$ where \(u^* = \left( {{\tau \mathord{\left/ {\vphantom {\tau \rho }} \right. \kern-0em} \rho }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) , σ w is the standard deviation of the vertical velocity,z is the height andL is the Obukhov scale lenght. The constantsa, A, k andd n are the entrainment constant, the turbulence decay constant, Von Karman's constant, and the layer depth derived from the theory. Of these,a andA, are universal constants and not empirically determined for the boundary layer. Thus the turbulence needed for the plume model of convection, which resides above these layers and reaches to the inversion, is determined by the shear stress and the heat flux in the surface layers. This model applies to convection in cool air over a warm sea. The whole field is now determined except for the temperature of the air relative to the water, and the wind, which need a further parameter describing sea surface roughness. As a first stop to describing a surface where roughness elements of widely varying sizes are combined this paper shows how the surface roughness parameter,z 0, can be calculated for an ideal case of a random distribution of vertical cylinders of the same height. To treat a water surface, with various sized waves, such an approach modified to treat the surface by the superposition of various sized roughness elements, is likely to be helpful. Such a theory is particularly desirable when such a surface is changing, as the ocean does when the wind varies. The formula, 2 $$\frac{{0.118}}{{a_s C_D }}< z_0< \frac{{0.463}}{{a_s C_D (u^* )}}$$ is the result derived here. It applies to cylinders of radius,r, and number,m, per unit boundary area, wherea s =2rm, is the area of the roughness elements, per unit area perpendicular to the wind, per unit distance downwind. The drag coefficient of the cylinders isC D . The smaller value ofz o is for large Reynolds numbers where the larger scale turbulence at the surface dominates, and the drag coefficient is about constant. Here the flow between the cylinders is intermittent. When the Reynolds number is small enough then the intermittent nature of the turbulence is reduced and this results in the average velocity at each level determining the drag. In this second case the larger limit forz 0 is more appropriate.  相似文献   

3.
A new estimate of the fracture parameters of earthquakes is provided in this paper. By theMuskhelishvili method (1953) a number of basic relations among fracture-mechanics parameters are derived. A scheme is proposed to evaluate the slip weakening parameters in terms of fault dimension, average slip, and rise time, and the new results are applied to 49 events compiled in the earthquake catalogue ofPurcaru andBerckhemer (1982). The following empirical relations are found in the paper: $$\begin{gathered} \frac{{\tau _B - \tau _f }}{{\tau _\infty - \tau _f }} = 2.339 \hfill \\ {{\omega _c } \mathord{\left/ {\vphantom {{\omega _c } {W = 0.113}}} \right. \kern-\nulldelimiterspace} {W = 0.113}} \hfill \\ \log G_c \left( {{{dyne} \mathord{\left/ {\vphantom {{dyne} {cm}}} \right. \kern-\nulldelimiterspace} {cm}}} \right) = 2 \log L (km) + 6.167 \hfill \\ \log \delta _c (cm) = 2 \log L (km) - 1.652 \hfill \\ \end{gathered} $$ whereG c is the specific fracture energy,ω c the size of the slip weakening zone,δ c the slip weakening displacement,τ B ?τ f the drop in strength in the slip weakening zone,τ ∞?τ f the stress drop,L the fault length, andW the fault width. The investigation of 49 shocks shows that the range of strength dropτ B ?τ f is from several doze to several hundred bars at depthh<400 km, but it can be more than 103 bars ath>500 km; besides, the range of the sizeω c of the strength degradation zone is from a few tenths of a kilometer to several dozen kilometers, and the range of the slip weakening displacementδ c is from several to several hundred centimeters. The specific fracture energyG c is of the order of 108 to 1011 erg cm?2 when the momentM 0 is of the order of 1023 to 1029 dyne cm.  相似文献   

4.
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5.
A semiempirical mathematical model of iron and manganese migration from bottom sediments into the water mass of water bodies has been proposed based on some basic regularities in the geochemistry of those elements. The entry of dissolved forms of iron and manganese under aeration conditions is assumed negligible. When dissolved-oxygen concentration is <0.5 mg/L, the elements start releasing from bottom sediments, their release rate reaching its maximum under anoxic conditions. The fluxes of dissolved iron and manganese (Me) from bottom sediments into the water mass (J Me) are governed by the gradients of their concentrations in diffusion water sublayer adjacent to sediment surface and having an average thickness of h = 0.025 cm: \({J_{Me}} = - {D_{Me}}\frac{{{C_{Me\left( {ss} \right)}} - {C_{Me\left( w \right)}}}}{h}\) (D Me ≈ 1 × 10–9 m2/s is molecular diffusion coefficient of component Me in solution; C Me(ss) and C Me(w) ≈ 0 are Me concentrations on sediment surface, i.e., on the bottom boundary of the diffusion water sublayer, and in the water mass, i.e., on the upper boundary of the diffusion water sublayer). The value of depends on water saturation with dissolved oxygen (\({\eta _{{O_2}}}\)) in accordance with the empiric relationship \({C_{Me\left( {ss} \right)}} = \frac{{C_{_{Me\left( {ss} \right)}}^{\max }}}{{1 + k{\eta _{{O_2}}}}}\) (k is a constant factor equal to 300 for iron and 100 for manganese; C Me(ss) max is the maximal concentration of Me on the bottom boundary of the diffusion water sublayer with C Fe(ss) max ≈ 200 μM (11 mg/L), and C Mn(ss) max ≈ 100 μM (5.5 mg/L).  相似文献   

6.
Calculations on the basis of the self-consistent approximation are used to study the effects of randomly distributed elliptical cracks and of non-randomly distributed circular cracks, either dry or saturated by a highly conductive material phase, on the electric conductivities of a cracked body. Analytic and numeric results are given for two special non-random distributions. In the first, the cracks are assumed randomly distributed in planes parallel to a given plane. In the second, the crack normals are randomly distributed in parallel planes. The results of the theoretical calculations indicate that the magnitudes of the crack induced variations of the dry cracked rock depend upon a crack density parameter ? rather than upon the crack porosity. Here, ? is defined as $$\varepsilon = \frac{{2N}}{\pi }< \frac{{A^2 }}{P} > $$ whereN is the average number of cracks per unit volume, andA andP are the crack area and perimeter respectively. (For circular cracks of radiusa, ?=N〈a3〉.) Although a straightforward relationship does connect ? with the porosity, it may be more meaningful for laboratory experiments to concentrate upon measuring crack-induced variations as functions of crack density rather than of porosity. For saturated cracked rocks, the results of the calculations indicate that, in addition to ?, variations in conductivity depend also upon a saturation parameter Ω, which relates crack aspect ratio α to matrix and fluid conductivities σ and σF $$\Omega = \frac{{{\sigma \mathord{\left/ {\vphantom {\sigma {\sigma _F }}} \right. \kern-\nulldelimiterspace} {\sigma _F }}}}{\alpha }.$$   相似文献   

7.
Abiogenic hydrocarbons in commercial gases from the Songliao Basin, China   总被引：3，自引：0，他引：3  
This paper discusses the kinetic fractionation, composition and distribution characteristics of carbon and hydrogen isotopes for various alkane gases formed in different environments, by different mecha- nisms and from different sources in nature. It is demonstrated that the biodegradation or thermode- gradation of complex high-molecule sedimentary organic material can form microbial gas or thermogenic gas. The δ 13C1 value ranges from -110‰ to -50‰ for microbial gases but from -50‰ to -35‰ (even heavier) f...  相似文献   

8.
A new approach to the theory of electromagnetic induction is developed that is applicable to moving as well as stationary sources. The source field is considered to be a standing wave generated by two waves travelling in opposite directions along the surface of the earth. For a stationary source the incident waves have velocities of the same magnitude, however for a moving source the velocities of the two incident waves are respectively increased and decreased by the velocity of the source. Electromagnetic induction in the earth is then considered as refraction of these waves and gives, for both stationary and moving sources, the magnetotelluric relation: $$\frac{{ - E_y }}{{H_x }} = \left( {\frac{{i\omega \mu }}{\sigma }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - i\frac{{v^2 }}{{\omega \mu \sigma }}} \right)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $$ where ν is the wavenumber of the source, μ is the permeability (4π·10?7) and σ is the conductivity of the earth. ω is the angular frequency of the variation observed on the earth. For a stationary source the observed frequency is the same as the source frequency, however the effect of moving a time-varying source is to make the observed frequency different from the frequency of the source. Failure to recognise this in previous studies led to some erroneous conclusions. This study shows that a moving source isnot “electromagnetically broader” than a stationary source as had been suggested.  相似文献   

9.
Investigation of the time-dependent seismicity in 274 seismogenic regions of the entire continental fracture system indicates that strong shallow earthquakes in each region exhibit short as well as intermediate term time clustering (duration extending to several years) which follow a power-law time distribution. Mainshocks, however (interevent times of the order of decades), show a quasiperiodic behaviour and follow the ‘regional time and magnitude predictable seismicity model’. This model is expressed by the following formulas $$\begin{gathered} \log T_t = 0.19 M_{\min } + 0.33 M_p - 0.39 \log m_0 + q \hfill \\ M_f = 0.73 M_{\min } - 0.28 M_p + 0.40 \log m_0 + m \hfill \\ \end{gathered} $$ which relate the interevent time,T t (in years), and the surface wave magnitude,M f , of the following mainshock: with the magnitude,M min, of the smallest mainshock considered, the magnitude,M p , of the preceded mainshock and the moment rate,m 0 (in dyn.cm.yr?1), in a seismogenic region. The values of the parametersq andm vary from area to area. The basic properties of this model are described and problems related to its physical significance are discussed. The first of these relations, in combination with the hypothesis that the ratioT/T t , whereT is the observed interevent time, follows a lognormal distribution, has been used to calculate the probability for the occurrence of the next very large mainshock (M s ≥7.0) during the decade 1993–2002 in each of the 141 seismogenic regions in which the circum-Pacific convergent belt has been separated. The second of these relations has been used to estimate the magnitude of the expected mainshock in each of the regions.  相似文献   

10.
Summary If the condition R(A)=k(n), whereA is the design matrix of the type n × k and k the number of parameters to be determined, is not satisfied, or if the covariance matrixH is singular, it is possible to determine the adjusted value of the unbiased estimable function of the parameters f(), its dispersion D( (x)) and 2 as the unbiased estimate of the value of 2 by means of an arbitrary g-inversion of the matrix . The matrix , because of its remarkable properties, is called the Pandora Box matrix. The paper gives the proofs of these properties and the manner in which they can be employed in the calculus of observations.  相似文献   

11.
The following Poisson’s equation with the Stokes’ boundary condition is dealt with $$\left\{ \begin{gathered} \nabla ^2 T = - 4\pi Gp outside S, \hfill \\ \left. {\frac{{\partial T}}{{\partial h}} = \frac{1}{\gamma }\frac{{\partial y}}{{\partial h}}T} \right|_s = - \Delta g, \hfill \\ T = O\left( {r^{ - 3} } \right) at infinity, \hfill \\ \end{gathered} \right.$$ whereS is reference ellipsord. Under spherical approximation transformation, the ellipsoidal correction terms about the boundary condition, the equation and the density in the above BVP are respectively given. Therefore, the disturbing potentialT can he obtained if the magnitudes aboveO(ε4) are neglected.  相似文献   

12.
Summary Seven optimal networks consisting of 4 to 10 stations are compared for a given region, where velocity-depth profiles and the distribution of seismic intensity are known. Assuming that the standard error of arrival time is t =0.05 s and the standard errors of the parameters of velocity-depth profiles are equal to 5% of their values, the average standard errors of the origin time and focus coordinates are estimated. The application of optimum methods to the planning of seismic networks in the Lublin Coal Basin is presented, and maps of standard errors of origin time , depth and epicenter ( xy ) for the case of an optimum network of 6 seismic stations are given.  相似文献   

13.
A modified formula of the cumulative frequency-magnitude relation has been formulated and tested in a previous paper by the authors of this study. Based on the modified relationship, the following reoccurrence formulas have been obtained.
  1. For the ‘T-years period’ larger earthquake magnitude,M T $$M_T = \frac{1}{{A_3 }}ln\frac{{A_2 }}{{(1/T) + A_1 }}.$$
  2. For the value of the maximum earthquake magnitude, which is exceeded with probabilityP inT-years period,M PT $$M_{PT} = \frac{{ln(A_2 .T)}}{{A_3 }} - \frac{{ln[A_1 .T - ln(1 - P)]}}{{A_3 }}.$$
  3. For the probability of occurrence of an earthquake of magnitudeM in aT-years period,P MT $$P_{MT} = 1 - \exp [ - T[ - A_1 + A_2 \exp ( - A_3 M)]].$$
The above formulas provide estimates of the probability of reoccurrence of the largest earthquake events which are significantly more realistic than those based on the Gutenberg-Richter relationships; at least for numerous tested earthquake samples from the major area of Greece.  相似文献   

14.
Strombolian-type volcanic activity is characterized by a series of gas bubbles bursting at the top of a magma column and leading to the ejection of lava clots and gas emission at the surface. The quantitative analysis of physical parameters (e.g., velocity, size, and mass fluxes) controlling the emission dynamics of these volcanic products is very important for the understanding of eruption source mechanisms but remains difficult to obtain in a systematic fashion. Ground-based Doppler radar is found to be a very effective tool for measuring ejecta velocities at a high acquisition rate and close to the emission source. We present here a series of measurements carried out at Mt. Etna’s Southeast crater, using an L-band volcanological Doppler radar, during the 4 July 2001 Strombolian eruptions. Doppler radar data are supplemented by the analysis of video snapshots recorded simultaneously. We provide here a set of physical parameters systematically retrieved from 247 Strombolian explosions spanning 15 min and occurring during the paroxysm of the eruption from 21:30 to 21:45 UT. The time-average values give a maximum particle velocity of Vmaxp = 94.7±24 \textm/s V_{{\max }}^p = {94}.{7}\pm {24} {\text{m/s}} , a bulk lava jet velocity of V\textPW - rad = 37.6±1.9 \textm/s {V_{{{\text{PW - rad}}}}} = {37}.{6}\pm {1}.{9} {\text{m/s}} , and an initial gas velocity at the source vent of V0g = 118.4±36 \textm/s V_0^g = {118}.{4}\pm {36} {\text{m/s}} . The time-averaged particle diameter is found to be about D\textPW - rad = 4.2±2.1 \textcm {D_{{{\text{PW - rad}}}}} = {4}.{2}\pm {2}.{1} {\text{cm}} . The volume and mass gas fluxes are estimated from time-averaged source gas velocities over the sequence duration at Qvg = 3 - 11 ×103\textm3\text/s Q_v^g = {3} - {11} \times {1}{0^{{3}}}{{\text{m}}^{{3}}}{\text{/s}} and Qmg = 0.5 - 2 ×103\textkg/s Q_m^g = 0.{5} - {2} \times {1}{0^{{3}}}{\text{kg/s}} , respectively.  相似文献   

15.
Generous statistical tests   总被引：1，自引：1，他引：0  
A common statistical problem is deciding which of two possible sources, A and B, of a contaminant is most likely the actual source. The situation considered here, based on an actual problem of polychlorinated biphenyl contamination discussed below, is one in which the data strongly supports the hypothesis that source A is responsible. The problem approach here is twofold: One, accurately estimating this extreme probability. Two, since the statistics involved will be used in a legal setting, estimating the extreme probability in such a way as to be as generous as is possible toward the defendant’s claim that the other site B could be responsible; thereby leaving little room for argument when this assertion is shown to be highly unlikely. The statistical testing for this problem is modeled by random variables {X i } and the corresponding sample mean the problem considered is providing a bound ɛ for which for a given number a 0. Under the hypothesis that the random variables {X i } satisfy E(X i ) ≤ μ, for some 0  < μ < 1, statistical tests are given, described as “generous”, because ɛ is maximized. The intent is to be able to reject the hypothesis that a 0 is a value of the sample mean while eliminating any possible objections to the model distributions chosen for the {X i } by choosing those distributions which maximize the value of ɛ for the test used.  相似文献   

16.
Theoretical constraints on the stress-dilation relation for a deforming Coulomb material requirev ifC=0 andv sin-1( m / m ) always, wherev is the dilation angle, is the friction angle,C is cohesion, m is the maximum shear stress, and m is the mean effective stress. Recent laboratory measurements of friction and dilatancy of simulated fault gouge show that small amplitude shear-load cycling causes compaction and consolidation. Comparison of the data with theory indicates that such load cycling produces: (1) increased coefficient of friction (or friction angle), (2) increased cohesion, and (3) increased dilatancy rate (or dilation angle). Under certain conditions of load cycling without significant plastic shear strain accumulation ( p <0.005) we find thatv exceeds both and, in contrast to theory, sin-1( m / m ). This result is interpreted in terms of enhanced cohesion and overconsolidation, which lead to residual stresses within the gouge. An analogy is drawn between these special loading conditions and those extant on natural faults. In particular, our results imply that jostling and minor stress variations associated with microearthquakes may produce strengthening of fault gouge and changes in the fault zone's stress-dilatancy relation. Hence, compaction associated with microseismicity may lead to subsequent dilation of fault gouge, even for faults with large displacement rates and large net offsets (e.g., San Andreas). In regions where such dilation persists over sufficient displacements (on the order of the critical slip distance for seismic faulting) it may tend to inhibit unstable slip.  相似文献   

17.
Analysis of data, covering four rainy seasons, of rain current, point-discharge current and potential gradient reveal novel relations in the form (i) $$Q_{r + } /Q_{r - } = k_1 (T_{r + } /T_{r - } )^{1.1} $$ for rain charge and duration ratios; and (ii) $$Q_{p - } /Q_{p + } = k_2 (T_{p - } /T_{p + } )^{1.1} $$ for point charge and duration ratios, where thek's are constants; and (iii) $$i_r = - \alpha (i_p - c)$$ for rain and point-discharge current densities, where α has the same value for all types of rain andc is a constant controlled by the rainfall intensityR. For rain not associated with point discharge the relation takes the familiar form $$i_r = - AR(E - \bar E)$$ Theoretical values are obtained for \ga andA on the basis of the Wilson ion-capture theory as worked out in detail by Whipple and Chalmers.  相似文献   

18.
The TKE dissipation rate in the northern South China Sea   总被引：1，自引：0，他引：1  
The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε p〉 of the deep basin and on the shelf. Linear correlation between 〈ε p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ reaches 17–19 mW/m2, dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{p}} $ was mostly ～10–30 % of $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ . A weak dependence of bin-averaged dissipation $ \overline{\varepsilon} $ on the Richardson number was noted, according to $ \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} $ , where ε 0 + ε m is the background value of $ \overline{\varepsilon} $ for weak stratification and Ri cr?=?0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.  相似文献   

19.
The experimental flow data for rocks and minerals are reviewed and found to fit a law of the form $$\dot \varepsilon = A'\left[ {sinh (\alpha \sigma )} \right]^n \exp \left[ {{{ - (E * + PV * )} \mathord{\left/ {\vphantom {{ - (E * + PV * )} {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \right]$$ where \(\dot \varepsilon \) This law reduces to the familiar power-law stress dependency at low stress and to an exponential stress dependency at high stress. Using the material flow law parameters for olivine, stress profiles with depth and strain rate are computed for a representative range of temperature distributions in the lithosphere. The results show that the upper 15 to 25 km of the oceanic lithosphere must behave elastically or fail by fracture and that the remainder deforms by exponential law flow at intermediate depths and by power-law flow in the rest. A model computation of the gravitational sliding of a lithospheric plate using olivine rheology exhibits a very sharp decoupling zone which is a consequence of the combined effects of increasing stress and temperature on the flow law, which is a very sensitive function of both.  相似文献   

20.
Sediment-induced buoyancy destruction and drag reduction in estuaries   总被引：2，自引：2，他引：0  
This paper presents an analysis of drag reduction by buoyancy destruction in sediment-laden open channel flow. We start from the log-linear profile proposed by Barenblatt (Prikladnaja Matematika i Mekhanika, 17:261–274, 1953), extended with a second length scale to account for free surface effects. Upon analytical integration over the water depth, an expression for sediment-induced drag reduction is found in terms of an effective Chézy number, water depth, bulk Richardson number, and Rouse number. This relation contains one empirical/experimental coefficient, which was obtained from a large series of numerical experiments with a 1DV point model. Upon calibration of this model against field and laboratory observations, we tuned the turbulent Prandtl–Schmidt number and found an optimal value of σ T?=?2, consistent to observations by Cellino and Graf (ASCE, J Hydraulic Engineering, 125:456–462, 1999). All numerical results could be correlated with the simple relation \( C_{\text{eff}} = C_0 + 4\sqrt {g} hRi_{*} \beta \), which is valid for fine sediment suspensions under conditions typical in open channel flow.  相似文献   

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