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1.
Numerical simulation of turbulent convective flow over wavy terrain   总被引：1，自引：1，他引：0  
By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude up to 0.15H and wavelength ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz o=10–4 H. The mean wind is varied between zero and 5w *, wherew * is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with /H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w *>2.  相似文献   

2.
When applied to a sea surface, shortcomings are noted for the ordinary classification of drag conditions at rigid underlying surfaces according to the Reynolds roughness number Re s . It is shown that in the case of mobile underlying surfaces, it would be more natural to use the dynamical classification of drag conditions according to the order of magnitude of the ratio ( = /) of the momentum flux toward the waves ( w) to the viscous momentum flux through the surface ( w). The relevant estimates of for the main stages of development of the wind waves indicate that the observed values of the drag coefficient of the sea surface correspond to the case of underdeveloped roughness.  相似文献   

3.
Drag and drag partition on rough surfaces   总被引：13，自引：0，他引：13  
An analytic treatment of drag and drag partition on rough surfaces is given. The aims are to provide simple predictive expressions for practical applications, and to rationalize existing laboratory and atmospheric data into a single framework. Using dimensional analysis and two physical hypotheses, theoretical predictions are developed for total stress (described by the square root of the canopy drag coefficient), stress partition (described by the ratio S/ of the stress s on the underlying ground surface to total stress ), zero-plane displacement and roughness length. The stress partition prediction is the simple equation S/= 1/(1+), where = CRCS the ratio of element and surface drag coefficients. This prediction agrees very well with data and is free of adjustable constants. Other predictions also agree well with a range of laboratory and atmospheric data.  相似文献   

4.
We have devised a partial differential equation for the prediction of dust concentration in a thin layer near the ground. In this equation, erosion (detachment), transport, deposition and source are parameterised in terms of known quantities. The interaction between a wind prediction model in the boundary layer and this equation affects the evolution of the dust concentration at the top of the surface layer. Numerical integrations are carried out for various values of source strength, ambient wind and particle size. Comparison with available data shows that the results appear very reasonable and that the model should be subjected to further development and testing.Notation (x, y, z, t) space co-ordinates and time (cm,t) - u, v components of horizontal wind speed (cm s–1) - u g, vg components of the geostrophic wind (cm s–1) - V=(u2+v2)1/2 (cm s–1) - (û v)= 1/(h – k) k h(u, v)dz(cm s–1) - V * friction velocity (cm s–1) - z 0 roughness length (cm) - k 1 von Karman constant =0.4 - V d deposition velocity (cm s–1) - V g gravitational settling velocity (cm s–1) - h height of inversion (cm) - k height of surface layer (cm) - potential temperature (°K) - gr potential temperature at ground (°K) - K potential temperature at top of surface layer (°K) - P pressure (mb) - P 0 sfc pressure (mb) - C p/Cv - (t)= /z lapse rate of potential temperature (°K cm–1) - A(z) variation of wind with height in transition layer - B(z) variation of wind with height in transition layer - Cd drag coefficient - C HO transfer coefficient for sensible heat - C dust concentration (g m–3) - C K dust concentration at top of surface layer (g m–3) - D(z) variation with height of dust concentration - u, v, w turbulent fluctuations of the three velocity components (cm s–1) - A 1 constant coefficient of proportionality for heat flux =0.2 - Ri Richardson number - g gravitational acceleration =980 cm s–2 - Re Reynolds number = - D s thickness of laminar sub-layer (cm) - v molecular kinematic viscosity of air - coefficient of proportionality in source term - dummy variable - t time step (sec) - n time index in numerical equations On sabbatical leave at University of Aberdeen, Department of Engineering, September 1989–February 1990.  相似文献   

5.
A previously published technique for using tethered spherical balloons as anemometers for measuring light low-level winds has been further developed. Earlier data on the relationship between the aerodynamic drag coefficient and the Reynolds number of spherical rubber balloons were combined with a large number of new data and re-analysed; and the errors in the relationship were estimated. The results allowed a more accurate calculation of wind speed from the deflection of a tethered balloon from the vertical. When combined with a new technique for calculating the effects of the tether, this enabled light to moderate low-level winds at fixed heights up to 600 m or more to be measured with simple, cheap, and readily mobile equipment; and a slight modification of the technique allowed measurement of winds in and above fog. Wind speeds measured by the ballon technique showed reasonably good agreement with measurements by an anemometer carried beneath the balloon.Glossary of Symbols a, b, c Coefficients in the relationship between lnC d and lnR - A Quantity under square root in solution for lnV whena0 - C d Wind drag coefficient for balloon - C dc Value ofC d given by calibration curve of Table I - D Dynamic wind pressure force on balloon - F Buoyant free lift of balloon with load - Re Reynold's number of balloon (sphere) - R = Re/105 - r Radius of sphere - T Tension in tether - V Wind speed - 83() =(lnC dc -lnC d ) when 83° , or 0 for other - Error in lnC d - Elevation of tether where attached to balloon - Elevation of balloon from ground tether point - Molecular viscosity of air - Ratio of circumference to diameter of circle - Density of air  相似文献   

6.
Eddy flux measurements over the ocean and related transfer coefficients   总被引：1，自引：0，他引：1  
Eddy correlation measurements of vertical turbulent fluxes made during AMTEX 1975 are used to assess the reliability of flux prediction from established bulk transfer relations, using both surface-layer and planetary boundary-layer formulations. The surface-layer formulae predict momentum and latent heat fluxes to an accuracy comparable to the direct eddy correlation method, using transfer coefficients of C DN (at 10m and in neutral conditions) increasing with wind speed, and a constant C EN - 1.5 × 10 –3 . The data suggest C CHN , for sensible heat, increases significantly with wind speed and is on average 30% lower than C CEN The boundary-layer drag coefficient, C GD , agrees within about 40% of recently published values using a vertically averaged geostrophic wind to the height of the lowest temperature inversion, corrected for trajectory curvature. Values of * / from which C CGH is derived, are in excellent agreement if the published values are modified to account for inappropriate surface temperatures used in their derivation. Preliminary values of C GE are also presented.  相似文献   

7.
A Forest SO2 Absorption Model (ForSAM) was developed to simulate (1) SO2 plume dispersion from an emission source, (2) subsequent SO2 absorption by coniferous forests growing downwind from the source. There are three modules: (1) a buoyancy module, (2) a dispersion module, and (3) a foliar absorption module. These modules were used to calculate hourly abovecanopy SO2 concentrations and in-canopy deposition velocities, as well as daily amounts of SO2 absorbed by the forest canopy for downwind distances to 42 km. Model performance testing was done with meteorological data (including ambient SO2 concentrations) collected at various locations downwind from a coal-burning power generator at Grand Lake in central New Brunswick, Canada. Annual SO2 emissions from this facility amounted to about 30,000 tonnes. Calculated SO2 concentrations were similar to those obtained in the field. Calculated SO2 deposition velocities generally agreed with published values.Notation c air parcel cooling parameter (non-dimensional) - E foliar absorption quotient (non-dimensional) - f areal fraction of foliage free from water (non-dimensional) - f w SO2 content of air parcel - h height of the surface layer (m) - H height of the convective mixing layer (m) - H stack stack height (m) - k time level - k drag coefficient of drag on the air parcel (non-dimensional) - K z eddy viscosity coefficient for SO2 (m2·s–1) - L Monin-Obukhov length scale (m) - L A single-sided leaf area index (LAI) - n degree-of-sky cloudiness (non-dimensional) - N number of parcels released with every puff (non-dimensional) - PAR photosynthetically active radiation (W m–2) - Q emission rate (kg s–2) - r b diffusive boundary-layer resistance (s m–1) - r c canopy resistance (s m–1) - r cuticle cuticular resistance (s m–1) - r m mesophyllic resistance (s m–1) - r s stomatal resistance (s m–1) - r exit smokestack exit radius (m) - R normally distributed random variable with mean of zero and variance of t (s) - u * frictional velocity scale, (m s–1) - v lateral wind vector (m s–1) - v d SO2 dry deposition velocity (m s–1) - VCD water vapour deficit (mb) - z can mean tree height (m) - Z zenith position of the sun (deg) - environmental lapse rate (°C m–1) - dry adiabatic lapse rate (0.00986°C m–1) - von Kármán's constant (0.04) - B vertical velocities initiated by buoyancy (m s–1) - canopy extinction coefficient (non-dimensional) - ()a denotes ambient conditions - ()can denotes conditions at the top of the forest canopy - ()h denotes conditions at the top of the surface layer - ()H denotes conditions at the top of the mixed layer - ()s denotes conditions at the canopy surface - ()p denotes conditions of the air parcels  相似文献   

8.
On mountain wave drag over complex terrain   总被引：1，自引：0，他引：1  
Summary Mountain wave drag is calculated for rotating, stratified, nonhydrostatic Boussinesq flow over a mountain ridge using linear theory for a variety of mountain profiles representing complex/irregular terrain. The inclusion of a sinusoidal corrugation to the familiar witch-of-Agnesi profile creates a stegosaurus profile. The associated drag is greatly enhanced for mesoscale mountains when the corrugation wave-number matches that for the dominant inertia-gravity wave contribution to the cross-mountain surface pressure gradient. Similarly, increasing the jaggedness (by decreasing the exponentb) increases the drag for mesoscale mountains whose topographic spectral intensity,M(k), has the form of a power law:M(k)=mk –b wherek is the zonal wavenumber.Spectral analysis of one-kilometer resolution topographic data for the Appalachian Mountains suggests that a power law profile withb=1.7 accurately represents the topographic spectral intensity and that it yields good estimates of the drag.The application of these results to the parameterization of mountain wave drag in general circulation models is discussed.With 7 Figures  相似文献   

9.
Summary Rainfall in West Africa is examined in relation to monthly mean equivalent potential temperature ( e )at the earth's surface. The study revealed that monthly mean equivalent potential temperature ( e ) and monthly rainfall (R) generally decreased northwards from the equator.A good relationship existed betweenR and e in the northern zone of West Africa (i.e., north of 7.5° N). No definite relationship existed in the southern zone. In the northern zone, the departure of e from its annual mean ( ) first became positive about a month before the onset of the rains. Positive departures from ) generally resulted in more than normal (or average) rainfall in this zone. In general, little or no rainfall occurred in West Africa whenever e was less than 320 K.
Zusammenfassung Der Niederschlag (MonatssummeR) in Westafrika wird in Zusammenhang mit der mittleren monatlichen Äquivalent-temperatur ( e ) an der Erdoberfläche untersucht. Es zeigte sich, daß die Monatswerte beider Elemente im allgemeinen vom Äquator nach Norden abnehmen.ZwischenR und e ergab sich für das nördliche Westafrika (nördlich von 7.5° N) eine gute, für die südliche Zone jedoch keine beweisbare Übereinstimmung. In der nördlichen Zone übertraf e das Jahresmittel erstmals etwa einen Monat vor Beginn der Regenzeit. Positive Abweichungen vom mittleren e hatten immer übernormalen Niederschlag in dieser Zone zur Folge. Dagegen gab es wenig oder keinen Niederschlag in Westafrika, wenn e unter 320 K lag.

With 7 Figures  相似文献   

10.
The structure of atmospheric turbulence in the surface layer over the open ocean is examined under conditions of local free convection. The raw data consist of profile and fluctuation measurements of wind and temperature as obtained from a meteorological buoy. For near neutral conditions and for waves running approximately along the wind direction, wave-induced wind fluctuations can be described by a simplified linear theory based on Miles (1957). In this case, the spectrum of wind velocity is given as the sum of two parts; for the turbulent part, the parameterization as obtained by Kaimal et al. (1972) applies, while the wave-induced part is parameterized using a simplification of Miles' linear theory. For cases of local free convection, the measurements of the vertical component of the wind velocity are well described by similarity theory; as expected, w /(-uw)1/2 is proportional to (- z/L)1/3. In order to scale the longitudinal wind velocity component, it seems to be reasonable to extend the list of relevant parameters by the height of the mixed layer z i. We obtain u /(- uw)1/2 (z/z i)1/3(- z/L)1/3 with only a poor correlation coefficient of r = 0.6. Overall, the results of local free convection scaling obtained from direct measurements show good agreement with those obtained from profile measurements. A comparison between direct and indirect determination of turbulent fluxes of momentum shows an unexplained difference of about 20%. This discrepancy is mainly due to a gap in the uw-cospectrum at the swell frequency.  相似文献   

11.
Equilibrium evaporation beneath a growing convective boundary layer   总被引：1，自引：1，他引：0  
Expressions for the equilibrium surface Bowen ratio ( s ) and equilibrium evaporation are derived for a growing convective boundary layer (CBL) in terms of the Bowen ratio at the top of the mixed layer i and the entrainment parameter A R . If AR is put equal to zero, the solution for s becomes-that previously obtained for the zero entrainment or closed box model. The Priestley-Taylor parameter is also calculated and plotted in terms ofA R and i . Realistic combinations of the atmospheric parameters give values of in the range 1.1 to 1.4.  相似文献   

12.
The effect of changes in zonal and meridional atmospheric moisture transports on Atlantic overturning is investigated. Zonal transports are considered in terms of net moisture export from the Atlantic sector. Meridional transports are related to the vigour of the global hydrological cycle. The equilibrium thermohaline circulation (THC) simulated with an efficient climate model is strongly dependent on two key parameters that control these transports: an anomaly in the specified Atlantic–Pacific moisture flux (Fa) and atmospheric moisture diffusivity (Kq). In a large ensemble of spinup experiments, the values of Fa and Kq are varied by small increments across wide ranges, to identify sharp transitions of equilibrium THC strength in a 2-parameter space (between Conveyor On and Off states). Final states from this ensemble of simulations are then used as the initial states for further such ensembles. Large differences in THC strength between ensembles, for identical combinations of Fa and Kq, reveal the co-existence of two stable THC states (Conveyor On and Off)—i.e. a bistable regime. In further sensitivity experiments, the model is forced with small, temporary freshwater perturbations to the mid-latitude North Atlantic, to establish the minimum perturbation necessary for irreversible THC collapse in this bistable regime. A threshold is identified in terms of the forcing duration required. The model THC, in a Conveyor On state, irreversibly collapses to a Conveyor Off state under additional freshwater forcing of just 0.1 Sv applied for around 100 years. The irreversible collapse is primarily due to a positive feedback associated with suppressed convection and reduced surface heat loss in the sinking region. Increased atmosphere-to-ocean freshwater flux, under a collapsed Conveyor, plays a secondary role.  相似文献   

13.
A Comparative Analysis of Transpiration and Bare Soil Evaporation   总被引：4，自引：0，他引：4  
Transpiration Ev and bare soil evaporation Eb processes are comparatively analysed assuming homogeneous and inhomogeneous areal distributions of volumetric soil moisture content . For a homogeneous areal distribution of we use a deterministic model, while for inhomogeneous distributions a statistical-deterministic diagnostic surface energy balance model is applied. The areal variations of are simulated by Monte-Carlo runs assuming normal distributions of .The numerical experiments are performed for loam. In the experiments we used different parameterizations for vegetation and bare soil surface resistances and strong atmospheric forcing. According to the results theEv()-Eb() differences are great, especially in dry conditions. In spite of this, the available energy flux curves of vegetation Av() and bare soil Ab() surfaces differ much less than the Ev() and Eb() curves. The results suggest that Ev is much more non-linearly related to environmental conditions than Eb. Both Ev and Eb depend on the distribution of , the wetness regime and the parameterization used. With the parameterizations, Eb showed greater variations than Ev. These results are valid when there are no advective effects or mesoscale circulation patterns and the stratification is unstable.  相似文献   

14.
It is shown that K-theory has to be modified for chemical systems that react with time scales similar to the turbulence time scale. In such systems, the value of the exchange coefficient depends not only on the turbulence parameters, but also on the chemical reaction rates. As an example, the NO-O3-NO2 chemical system is studied. Using second-moment equations, new flux-gradient relationships for the neutral atmospheric surface layer are obtained which depend on the time scale ratios of turbulence ( t ) and chemical reactions ( ch), i.e., reactive K-theory. Within the framework of this reactive K-theory, the flux of a chemical species is both a function of the concentration gradients of the three chemical species involved and of the ratio of the time scale of turbulence to the time scale of chemistry. In the special case of slow chemistry ( t ch) inert K-theory is applicable.The reactive exchange coefficients are implemented in a surface-layer model that calculates the flux and concentration profiles of the three chemical species. The results of the calculations of the effective exchange coefficients are different for reactive K-theory and inert K-theory; the differences are largest for nitric oxide, but smaller for ozone and nitrogen dioxide.  相似文献   

15.
Summary A radiative transfer model has been used to determine the large scale effective 6.6 GHz and 37 GHz optical depths of the vegetation cover. Knowledge of the vegetation optical depth is important for satellite-based large scale soil moisture monitoring using microwave radiometry. The study is based on actual observed large scale surface soil moisture data and observed dual polarization 6.6 and 37 GHz Nimbus/SMMR brightness temperatures over a 3-year period. The derived optical depths have been compared with microwave polarization differences and polarization ratios in both frequencies and with Normalized Difference Vegetation Index (NDVI) values from NOAA/AVHRR. A synergistic approach to derive surface soil emissivity from satellite observed brightness temperatures by inverse modelling is described. This approach improves the relationship between satellite derived surface emissivity and large scale top soil moisture fromR 2=0.45 (no correction for vegetation) toR 2=0.72 (after correction for vegetation). This study also confirms the relationship between the microwave-based MPDI and NDVI earlier described and explained in the literature.List of Symbols f frequency [Hz] - f i(p) fractional absorption at polarizationp - h surface roughness - h h cos2 - H horizontal polarization - n i complex index of refraction - p polarization (H orV) - R s microwave surface reflectivity - T B(p) brightness temperature at polarizationp - T * normalized brightness temperature - T polarization difference (T v-T H) - T s temperature of soil surface - T c temperature of canopy - T max daily maximum air temperature - T min daily minimum air temperature - V vertical polarization - soil moisture distribution factor; also used for the constant to partition the influence of bound and free water components to the dielectric constant of the mixture - empirical complex constant related to soil texture - microwave transmissivity of vegetation (=e –) - * effective transmissivity of vegetation (assuming =0) - microwave emissivity - s emissivity of smooth soil surface - rs emissivity of rough soil surface - vs emissivity of vegetated surface - soil moisture content (% vol.) - K dielectric constant [F·m–1] - K fw dielectric constant of free water [F·m–1] - K ss dielectric constant of soil solids [F·m–1] - K m dielectric constant of mixture [F·m–1] - K o permittivity of free space [8.854·10–12 F·m–1] - high frequency limit ofK wf [F·m–1] - wavelength [m] - incidence angle [degrees from nadir] - polarization ratio (T H/T V) - b soil bulk density [gr·cm–3] - s soil particle density [gr·cm–3] - R surface reflectivity in red portion of spectrum - NIR surface reflectivity in near infrared portion of spectrum - eff effective conductivity of soil extract [mS·cm–1] - vegetation optical depth - 6.6 vegetation optical depth at 6.6 GHz - 37 vegetation optical depth at 37 GHz - * effective vegetation optical depth (assuming =0) - single scattering albedo of vegetation With 12 Figures  相似文献   

16.
In-water and remote measurements of ocean color   总被引：2，自引：0，他引：2  
Spectral measurements of downwelling irradiance, E d(), above the surface, and of upwelling irradiance just below the surface, E u(), allow computation of spectral values of the diffuse reflectance R() = E u()/E d(); this yields full information about the true color and brightness of the ocean. Typical results are presented and interpreted for waters very different in turbidity and phytoplankton content. Conversely, the possibility of infering the water content from R() data at selected wavelengths is examined in terms of the respective number of equations and unknowns. The necessary use of assumptions and of empirical laws is emphasized.The magnitude of the useful signal emerging from the water, and the magnitude of the additional signals due to specular reflexion at the interface and to atmospheric scattering, are compared on the basis of spectroradiometric measurements performed within and above the sea, from different altitudes. These unwanted signals are dominant, causing a drastic change in the spectral composition of the light received by a remote sensor. The evaluation of the atmospheric effect must be very precise in order to recover the marine signal with a sufficient accuracy for a meaningful application of any kind of algorithm.This work was supported in part by the Centre National d'Exploitation des Océans (under contract CNEXO 77/1695) and in part by the Centre National de la Recherche Scientifique (RCP 247 & ERA 278).  相似文献   

17.
Using synchronous multi-level high frequency velocity measurements, the turbulence spectra within the trunk space of an alpine hardwood forest were analysed. The spectral short-circuiting of the energy cascade for each velocity component was well reproduced by a simplified spectral model that retained return-to-isotropy and component-wise work done by turbulence against the drag and wake production. However, the use of an anisotropic drag coefficient was necessary to reproduce these measured component-wise spectra. The degree of anisotropy in the vertical drag was shown to vary with the element Reynolds number. The wake production frequency in the measured spectra was shown to be consistent with the vortex shedding frequency at constant Strouhal number given by f vs = 0.21ū/d, where d can be related to the stem diameter at breast height (dbh) and ū is the local mean velocity. The energetic scales, determined from the inflection point instability at the canopy–atmosphere interface, appear to persist into the trunk space when , where C du is the longitudinal drag coefficient, a cr is the crown-layer leaf area density, h c is the canopy height, and β is the dimensionless momentum absorption at the canopy top.  相似文献   

18.
Summary In this study the trend of the time sequence of the integral aerosol optical depth (k a), as proposed by Unsworth and Monteith, was determined for clear days in summer for the period 1962–1988 in Athens. The trend was found by fitting a third degree polynomial curve and it was concluded that (k a) showed a considerable increase (i.e. from the value of 0.18 to 0.31) in the period 1962–1976 and remained approximately constant until 1979, after which it started decreasing again slowly until 1988. The increase of (k a) in the period 1962–1976 is likely attributable to the rapid development of the city in this period, while the decrease of (k a) after 1979 probably reflects the efficiency of some restrictions which were imposed on the pollutant emissions during this period. In addition, an analysis of the percentage frequency distribution found that while 95% of the values of (k a) ranged from 0.100 to 0.400 in the beginning of the period (1964–1967), in recent years (1984–1987) the same percentage of the values of (k a) ranged from 0.100 to 0.500.With 3 Figures  相似文献   

19.
A random-walk model for dispersion of heavy particles in turbulent air flow   总被引：1，自引：0，他引：1  
A random-walk model is presented for calculating the dispersion of heavy particles in a turbulent air flow when only air turbulence statistics and the drag characteristics of the particle are known. Algebraic expressions for the modification of air velocity variance 2 and Lagrangian autocorrelation tune-scale T L,due to particle inertia effects, are derived. These expressions introduce only a very small computational overhead on the random-walk models for inertia-less particles of Wilson et al. (1983). Measurements of T Land by Snyder and Lumley (1971) for four different particles are used to determine constants in the heavy-particle model. It is shown that the agreement between the model, for a single set of constants, and the dispersion measurements is good for the 47 m hollow glass, 87 m glass, and 47 m copper particles. The predictions for the 87 m corn pollen particles show less satisfactory agreement by underestimating dispersion measurements by 15% after 0.4s. Finally, some aspects of the model's application to spray dispersion in and above a crop canopy are considered.  相似文献   

20.
We analyze the checkerboard problem of many alternating surfaces with different properties, on scales up to (say) 3,000 m. Power-law representations of the vertical profiles of mean wind speed and eddy diffusivity lead to solutions in terms of Kelvin and trigonometric functions.These solutions are used to determine blending heights (*), where deviations from the mean of concentration, or of vertical flux density, fall to some small fraction, , of their value at the surface. Values of *are important for regional and larger-scale meteorological models. In smaller scale micrometeorological studies, they may serve also as the top levels of surface boundary layers.An important result for both theoretical and experimental contexts is that deviations of flux persist with elevation much more strongly than those of concentration, so that, in general, * should be based on flux rather than concentration. Representative values of *, for = 0.05, are of order 5 and 30 m for surface pattern wavelengths of 102 and 103 m, respectively. Values of * are robust to changes in adopted power-law indices, and are independent of wind speed. Surface roughness has a mild but calculable effect.  相似文献   

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