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1.
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   

2.
Depth variable vertical eddy diffusion coefficients for heat (K z) were calculated from continuously measured temperature profiles in Überlinger See (western part of Lake Constance). The temperatures were averaged over vertical intervals of 10 m yielding 14 discrete values (maximum depth of Überlinger See: 147 m). A linear fit from 10 June to 29 September 1987 was used to smooth the significant temperature fluctuations caused by internal seiches of Lake Constance.Assuming horizontal homogeneity for the smoothed data the Gradient-Flux-Method was applied to compute vertical diffusion coefficientsK z at different depths using the depth variable volumes and surfaces of the 14 layers. The resulting mean diffusion coefficients for the period from June to September are 0.04 cm2/s near the thermocline and up to 0.8 cm2/s in deeper strata (accuracy: ± 50%). It is shown that horizontal mixing between Überlinger See and Obersee (main lake) alters the computation ofK z by less than 50%.A relationship betweenK z and stability (Brunt-Väisälä) frequencyN is found which corresponds well to the theory of internal wave induced turbulence.Combining the diffusion coefficients with measured phosphorus profiles, a phosphorus flux from the hypolimnion to the epilimnion of (0.7 ± 0.4) mg P m–2 d–1 was calculated, corresponding to about 20% of the average external loading per area of Lake Constance in 1986.  相似文献   

3.
A complex transfer function c (or generalized skin depth) can be derived from data for the secondary magnetic field measured by a dipole system with small coil spacing at height h above the ground. This function has a useful property: For a uniform or layered ground, the real part of c yields the‘ centroid depth’z* of the in-phase current system as a function of frequency. This parameter can be combined with the apparent resistivity ρa derived by conventional methods. The function ρa(z*), if known over a broad frequency range, yields a smoothed approximation of the true distribution ρ(z) without an initial model. The relations between ρa(z*) and ρ(z) are studied for a number of multilayer models. An example of the application of the ρa*) algorithm to data from a groundwater survey is given.  相似文献   

4.
To study the hyporheic exchange driven by a single peak flood-induced water level fluctuation (i.e., flood wave), a method combining numerical simulation with theoretical derivation was proposed based on the Inbuk Stream, Korea, where flooding occurs frequently. The hyporheic exchanges induced by different flood waves were investigated by varying amplitude (A), duration (T), wave type parameter (r), and rising duration (tp), which were adopted from the real-time stream stage fluctuations. Additionally, the idea of constant upstream flood volume (CUFV) condition for flood waves was put forward, and the effects of “Botan” (T/A) and peak number (N) on hyporheic exchange were studied. The results showed that the hyporheic exchange flux (q) was controlled by the water level h (sine-type) and its change rate v (cosine-type), and was proportional to the polynomial of them q ∝ (ω∙ h + v), where ω is the angular frequency of the flood wave. Based on this mechanism, the influence principles on hyporheic exchanges of the typical flood wave parameters (A, T, r and tp) as well as T/A and N under CUFV condition were clarified. The main characteristic variables of hyporheic exchange, which were maximum aquifer storage and residence time, were positively correlated. They also had positive relations to the integral of the flood wave over time, which increased when the wave became higher, wider, rounder and less skewed. However, when CUFV condition was imposed, the residence time was positively correlated with T/A, whereas the maximum aquifer storage was negatively correlated with T/A. With the increase in N, water exchanged more frequently and some water returned to the stream early, leading to the slight decrease in maximum aquifer storage and residence time. These findings enriched the theory of hyporheic exchange driven by surface water fluctuation and be of great significance to enhance pollutant degradation in the hyporheic zone downstream of reservoirs.  相似文献   

5.
《水文科学杂志》2013,58(4):626-641
Abstract

An analytical solution of planar flow in a sloping soil layer described by the linearized extended Boussinesq equation is presented. The solution consists of the sum of steady-state and transient-series solutions, the latter in a separation-of-variables form, and can satisfy an arbitrary initial condition via collocation; this feature reduces the number of series terms, making the solution efficient. Key parameter is the dimensionless linearization depth η o (R), R being the dimensionless recharge. The variable η o (R), not the slope, characterizes the flow as kinematic or diffusive, and R ≈ 0.2 demarcates the two regimes. The transient series converges rapidly for large η o (large R, near-diffusive flow) and slowly as η o → 0 (kinematic flow). The quasi-steady (QS) state method of Verhoest & Troch is also analysed and it is shown that the QS depth profiles approximate the transient ones well, only if Δt exceeds a system-dependent transition time between flow states (possibly >>1 day). In an application example for a 30-day recharge series, the QS solution differs from the transient one by as much as 20% (RMSE = 15%), does not track recharge changes as well and fails to conserve mass.  相似文献   

6.
For assessing earthquake hazard of metro cities, knowledge of soil amplification, thickness and properties of sedimentary layer are essential. In order to map the soil thickness using microtremor survey method, in Bangalore city, it is required to calibrate the relation between fundamental resonance frequency of the soil layer and its thickness for the region. For this purpose microtremor survey was carried out at 34 locations in the city where borehole log was available. The resonance frequency of the soil is evaluated from the microtremor recordings using the H/V ratio technique. A nonlinear regression relation between the thickness of sedimentary layer h (m), from the borehole logs, and the resonance frequency fr (Hz), was derived as h=(58.3±8.8)fr−(0.95)±0.1. Using the model of shear wave velocity increasing with depth at these locations, the derived average shear wave velocity and the corresponding soil thickness were used, to get an empirical relation between VS (m/s) and depth z(m), as Vs=(174±28)(1+z)0.16±0.07. This relation also compares reasonably with the fit obtained between simulated VS and depth from borehole logs for Bangalore city. The calibrated relations can be used at locations in Bangalore city where borehole logs are not available, for finding the thicknesses and shear wave velocities of the local soil layers at the survey locations.  相似文献   

7.
In this paper we suggest that conditional estimator/predictor of rockburst probability (and rockburst hazard, P T (t)) can be approximated with the formula P T (t) = P 1(θ 1)…P N (θ N )·P dyn T (t), where P dyn T (t) is a time-dependent probability of rockburst given only the predicted seismic energy parameters, while P i (θ i ) are amplifying coefficients due to local geologic and mining conditions, as defined by the Expert Method of (rockburst) Hazard Evaluation (MRG) known in the Polish mining industry. All the elements of the formula are (approximately) calculable (on-line) and the resulting P T value satisfies inequalities 0 ≤ P T (t) ≤ 1. As a result, the hazard space (0–1) can be always divided into smaller subspaces (e.g., 0–10−5, 10−5–10−4, 10−4–10−3, 10−3–1), possibly named with symbols (e.g., A, B, C, D, …) called “hazard states” — which saves the prediction users from worrying of probabilities. The estimator P T can be interpreted as a formal statement of (reformulated) Comprehensive Method of Rockburst State of Hazard Evaluation, well known in Polish mining industry. The estimator P T is natural, logically consistent and physically interpretable. Due to full formalization, it can be easily generalized, incorporating relevant information from other sources/methods.  相似文献   

8.
Ground total magnetic field data of Albania were used to produce estimates of the Curie point isotherm. The strategy followed was to estimate the depth to the bottom of the deepest magnetic sources. Firstly, the average depth to the top of the deepest crustal block, zt, was computed by linear fitting to the second lowest-frequency segment of the azimuthally averaged power spectrum of the total magnetic field data. Then, the depth to the centroid of the deepest crustal block, z0, was computed by linear fitting to the lowest-frequency segment of the azimuthally averaged power spectrum of a distribution of magnetic dipoles. Finally, the depth to the bottom, the inferred Curie point depth, zb, was calculated from zb=2z0−zt. Curie depth estimates for Albania vary from about 17 to 25.5 km (below sea level). These results are consistent with the depths inferred by extrapolating geothermal gradient and heat-flow values, suggesting that the Curie point depth analysis is useful to estimate the regional thermal structure. It also suggests that the approach was valid and that ground total magnetic field data can be used for this purpose.  相似文献   

9.
Magnetotelluric response is studied for an inhomogeneous medium having conductivity varying linearly with depth as σ(z) =σ1+αz. For a medium having conductivity increasing linearly with depth, the phase of the impedance approaches 60° at long periods and the apparent resistivity becomes log (ρa) = 2 log (1.36/α1/3) — 1/3 log (T'). The asymptote of log (ρa, T'→∞) when plotted against log (T') has a constant gradient —1/3 and has an intercept on the log (T') axis, which equals 6 log (1.36/α1/3). When a homogeneous layer with a moderate thickness overlies an inhomogeneous half-space, this layer does not affect the asymptote, but it affects the cut-off period and pushes this toward the long period direction. For a medium having conductivity decreasing linearly with depth, the impedance is equivalent to that of a Cagniard two-layer model; the intercept period related to the thickness is T'0=σ1(h2/2)2. Homogeneous multilayer approximations to an inhomogeneous layer are also investigated, and it is shown that the fit to the model variation depends on the number of layers and the layer parameters chosen.  相似文献   

10.
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11.
Interpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak?β, where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi‐taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.  相似文献   

12.
Abstract

In the high-amplitude wave regime, at each point in the axial plane, the temperature has a maximum, a minimum, and a time (or longitudinally) averaged value due to the propagation of the regular waves. The axial-plane profile of each of these three temperature fields was measured for 53 different combinations of ω, Δr w T and n. A few sample profiles are displayed.

Correlations of several internal thermal parameters (especially Ro g,t ) with the externally imposed parameters, are given along with the spatial variation of the thermal fields. Ro g,t is always less than the value which would occur if the symmetrical regime existed, while the variation of Sz g,t with the imposed parameters is about the same as for the symmetrical regime. The parametric variation of the wave amplitude is the only quantity dependent on n. Based on the parametric variation of the fields, the wave regime diagram can be subdivided into several different regions : a quasi-conductive, a conductive-convective zone, and a region at large rotation rates and temperature differences characterized by Ro g,t = Ro g,w 2, Sz o,l = Ro g,w , and ΔT′ = (z′)0.6.

The Ro g, l fields are compared to existing theory and some of the experimental stability diagrams of Fultz et al. (1964) are reconstructed using the internal instead of the externally imposed Rossby number. The transition from three to four waves via a “minor wave” is illustrated.  相似文献   

13.
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14.
Stochastic modelling is applied to the analysis of local earthquake recordings, which are usually extremely rich in random incident-wave trains that are chaotically superimposed because of scattering effects in the Earth's crust. The presence in the seismic signal of effects connected with the scale of inhomogeneity in the lithosphere cannot be deterministically described in detail. The application of a stochastic second-order autoregressive model to accelerometric records for the higher magnitude (ML ? 6) Friuli earthquakes and to short-period seismometric records for the aftershocks of the strong earthquake of 6 May 1976 has allowed inferences to be drawn about the spectral properties of seismic signals and the propagation mechanisms of seismic waves. These inferences are based on an extremely small number of parameters of a mathematical model suitable for simultaneously describing the random sequence of scattered wave trains in the time and frequency domains. Useful physical information has been obtained about the dynamic characteristic correlation times and the predominant frequency of the seismic signals; moreover, the strength, σ2e(t), of the innovation of the stochastic process fitting the real digital data set has been estimated. From the envelopes of σ2e(t), the quantity heuristically used in the stochastic approach to describe seismic excitation, the·mean free-path between successive scatterings (l), or the equivalent diffusivity coefficient (d) and turbidity (g), and their dependence on seismic wave frequency have been investigated. For Friuli, using seismometric data at an epicentral distance of ～ 20 km and earthquakes with a magnitude just under 2, mean free-path estimates obtained by means of autoregressive parameters vary from ～ 5 km for the strong interaction model to ～ 30 km for the single scattering model. Furthermore, by means of accelerometric records for the strongest earthquakes in Friuli during May and September 1976, the dependence for the maximum of the seismic excitation on the epicentral distance R was estimated as (σ2e)max ～ R?ν (with ν 1.94 ± 0.13), which is in good agreement with results obtained for the same region using standard methods by means of acceleration peaks versus R. Lastly, stochastic modelling provides a method of estimating change versus time for the predominant frequency and characteristic correlation time of narrow band digital recordings. These two parameters were computed by means of autoregressive parameters in different physical situations and were found to be functions of the earthquake source, the instrumentation frequency response, and the Earth's filtering effects.  相似文献   

15.
Abstract

Measurements have been made of the net horizontal force F acting on a sphere moving with horizontal velocity U (Reynolds numbers in the range 102-104) through a stratified fluid rotating about a vertical axis with uniform angular velocity Ω. In both homogeneous and stratified rotating fluids with small Rossby number R(R = U/Ωa ? 1 where a is the radius of the sphere) the force F is of magnitude 2ΩρUV (where ρ is the density of the fluid and V is the volume of the sphere). In a homogeneous fluid the relative directions of F and U were found to depend on the quantity F = 8Ωa 2/UD (where D is the depth of the fluid in which the object is placed (Mason, 1975)). In a rotating stratified fluid the relative directions of F and U are found to depend on the inverse Froude number k(k = Na/U where N 2 = (g/δ)?ρ/?z) provided D > 4aΩ/N. In a homogeneous fluid with F ? 1 the force F is mainly in the U direction (a drag force due to inertial wave radiation) and is ～ ?0.4 |MX 2ΩρUV For F ? 1 a “Taylor column” occurs and the force, in correspondence with theoretical expectations, is ～ - 2Ω |MX UρV In a rotating stratified fluid with N ～2Ω and k ? 1 the force F is mainly in the U direction but is roughly one half of that occurring in the homogeneous situation with F ? 1 (tentatively explained as due to the evanescence of inertia-gravity disturbances). In a rotating stratified fluid with k ? 1 the flow should have no vertical motion (as with F ? 1) and again in correspondence with theoretical expectations the drag is ～ ?2 Ω |MX UρV. In a non-rotating stratified fluid the drag coefficient C D(C D = F U/½?ρU 2) was measured in the range k = 0.1 to 10 and had a maximum value ～ 1.2 for k ～ 3.  相似文献   

16.
Abstract

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height zc. The height zc , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above zc. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere.

The Fourier spectrum of the solution for z ≫ zc is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n ?-8/3 characterizes the marginal state of the wave at z = zc .  相似文献   

17.
FollowingDmitriev (1960) a rigorous theoretical solution for the problem of scattering by a perfectly conducting inclined half-plane buried in a uniform conductive half-space has been obtained for plane wave excitation. The resultant integral equation for the Laplace transform of scattering current in the half-plane is solved numerically by the method of successive approximation. The scattered fields at the surface of the half-space are found by integrating the half-space Green's function over the transform of the scattering current.The effects of depth of burial and inclination, of the half-plane on the scattered fields are studied in detail. An increase in the depth of burial leads to attenuation of the fields. Inclination introduces asymmetry in the field profiles beside affecting its magnitude. Depth of exploration is greater for quadrature component. An interpretation scheme based on a phasor diagram is presented for the VLF-EM method of exploration for rich vein deposits in a conductive terrain.List of symbols x, y, z Space co-ordinates - Half-space conductivity - 0 Free-space permeability - Excitation frequency (angular) - T Time - h Depth of the half-plane - a Inclination of the half-plane - E x x-Directed total electric field - E x p x-Directed primary electric field - E xo p x-Directed primary electric field atz=0 directly over the half-plane - H y y-Component of total magnetic field - H y p y-Component of primary magnetic field - H y0 p y-Component of primary magnetic field atz=0 directly over the half-plane - H z z-Component of total magnetic field - H z p z-Component of primary magnetic field - J x Surface density ofx-directed scattering current - G Green's function - k 0,K Wave numbers - u,u 0,u 1,u 2 Functions - Space co-ordinate - s Variable in transform domain - Variable of integration - Normalized scattering current - Laplace transform of - N Normalized - , 0, 1, 2 Functions - t Variable of integration - Skin depth - H Total magnetic field - H p Primary magnetic field - H 0 p Primary magnetic field atz=0 directly over the half-plane - M,Q,R,S,U,V Functions - N 1,N 2 Functions  相似文献   

18.
In the dimict lake Arend (5.1 km2, 146 hm3, 49.5 m zmax), nitrogen is production-limiting with concentrations below the detection limit during the production period. Phytoplankton achieves biomasses of up to 18 mg/l fresh matter, essential contributions being made by Aphanizomenon with 2 mg/l and Anabaena with up to 10 mg/l. Nitrogen fixation was measured by the ethine reduction technique (acetylene reduction) during periods of the occurrence of heterocystforming Cyanophyceae and achieved peak values up to 6.59 μg N2 · h?1 · l?1 or 14.87 m?2 · h?1 g N2 · m?2 · h?1. The rates of fixation show a safe correlation with the biomass of heterocyst-containing Cyanophyceae (r = 0.88), their development beginning at values below the N : P-ratio of 2.66.  相似文献   

19.
A theory which describes the constant f-plane flow of a steady inviscid baroclinic boundary current over a continental margin with a bathymetry that varies slowly in the alongshore but rapidly in the offshore directions is developed in the parameter regime (LD/L)2 ≤ Ro 1, where LD is the internal deformation radius, L the horizontal length scale, and Ro the Rossby number. To lowest order in the Rossby number the flow is along isobaths with speed qo = Vu(h,z)|Vh|/α, where Vu(h,z) is the upstream speed, α the upstream bottom slope at depth h, and Vh the bottom slope downstream at depth h. The lowest order flow produces a variation in the vertical component of relative vorticity along the isobath as the magnitude and direction of Vh vary in the downstream direction. The variation of vorticity requires a vertical as well as a cross-isobath flow at first order in the Rossby number. The first order vertical velocity is computed from the vorticity equation in terms of upstream conditions and downstream variations of the bathymetry. The density, pressure, and cross-isobath flow at first order in the Rossby number are then calculated. It is shown that in the cyclonic region of current (d/dh(Vu/α) > 0), if the isobaths diverge in the downstream direction ((∂/∂s)|Vh| < 0), then upwelling and onshore flow occur. The theory is applied to the northeastern Florida shelf to explain bottom temperature observations.  相似文献   

20.
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