Nonlinear development of phase-mixed alfvén waves     

L. Nocera  E. R. Priest  J. V. Hollweg 《地球物理与天体物理流体动力学》2013,107(1-4):111-129

Abstract

We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983).

We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude δv_y exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber k_a are damped over a timescale k_uRe ₀|δ v_y/v_A |^?2, Re ₀ being the Reynolds number corresponding to the Braginskij viscosity coefficient η₀ and v_A the Alfvén speed. Dissipation is most effective where β = (v_s /v_A) ² ≈ 1, v_s being the speed of sound.  相似文献   

Radiation damping in the context of one-dimensional wave propagation: A teaching perspective     

《Soil Dynamics and Earthquake Engineering》2013

This paper has two objectives: to connect directly radiation damping and 1D elastic wave propagation, and to create a simple teaching tool to introduce the subject to students and engineers trained in Structural Dynamics. The first objective is achieved by obtaining the equivalent radiation modal damping using time domain solutions for the fundamental mode in shear of an elastic layer (soil) on flexible rock, for the case in which the rock–soil Impedance Ratio in shear, I=(ρ_rV_r)/(ρ_sV_s)>1, where ρ=mass density and V=shear wave velocity. These time domain solutions are developed for the case of steady-state input sinusoidal shear waves propagating vertically in the rock as well as for horizontal free vibration of the layer. Both derivations result in the same approximate expression for the modal radiation damping in the first mode, ζ_r1≈2/(πI), which is in turn identical to the approximate equation obtained by Roesset and Whitman [11] using a frequency domain approach. This expression for ζ_r1 is linked to the fact that, during free vibration, the ratio between two successive positive displacement peaks u_so and u_s1 at the ground surface is u_s0/u_s1=[(1+I)/(1−I)]², associated with two wave reflections at the soil–rock interface. From this ratio, and after applying the standard expression to obtain modal damping from damped free vibration, the same expression for ζ_r1 is reached again, ζ_r1≈[1/(2π)] ln(u_s0/u_s1)≈[1/(2π)] ln[(1+I)/(1−I)]²≈2/(πI). This finding allows development of the simple teaching tool proposed at the end of the paper. While only a crude approximation lacking in rigor, this teaching tool is physically intuitive, links directly wave propagation and modal damping in a simple way and gives the correct result.  相似文献   

Tidal regime shift in Lingdingyang Bay,the Pearl River Delta: An identification and assessment of driving factors     

Heng Wang  Ping Zhang  Shuai Hu  Huayang Cai  Linxi Fu  Feng Liu  Qingshu Yang 《水文研究》2020,34(13):2878-2894

Both natural changes (e.g., tidal forcing from the ocean and global sea level rise) and human-induced changes (e.g., dredging for navigation, sand excavation, and land reclamation) exert considerable influences on the long-term evolution of tidal regimes in estuaries. Evaluating the impacts of these factors on tidal-regime shifts is particularly important for the protection and management of estuarine environments. In this study, an analytical approach is developed to investigate the impacts of estuarine morphological alterations (mean water depth and width convergence length) on tidal hydrodynamics in Lingdingyang Bay, Southeast China. Based on the observed tidal levels from two tidal gauging stations along the channel, tidal wave celerity and tidal damping/amplification rate of different tidal constituents are computed using tidal amplitude and phase of tidal constituents extracted from a standard harmonic analysis. We show that the minimum mean water depth for the whole estuary occurred in 2006, whereas a shift in tidal wave celerity for the M₂ tide component occurred in 2009. As such, the study period (1990–2016) could be separated into pre-human (1990–2009) and post-human (2010–2016) phases. Our results show that the damping/amplification rate and celerity of the M₂ tide have increased by 31% (from 7 to 9.2 m⁻¹) and 28% (from 7 to 9 m·s⁻¹) respectively, as a consequence of the substantial impacts of human interventions. The proposed analytical method is subsequently applied to analyse the historical development of tidal hydrodynamics and regime shifts induced by human interventions, thus linking the evolution of estuarine morphology to the dominant tidal hydrodynamics along the channel. The observed tidal regime shift is primarily caused by channel deepening, which substantially enlarged the estuary and reduced effective bottom friction resulting in faster celerity and stronger wave amplification. Our proposed method for quantifying the impacts of human interventions on tidal regime shifts can inform evidence-based guidelines for evaluating hydraulic responses to future engineering activities.  相似文献   

Influence of upstream inflow on wave celerity and time to equilibrium on an overland plane     

TOMMY S. W. WONG 《水文科学杂志》2013,58(2):195-205

Abstract

Based on the kinematic wave equations, formulae for the wave celerity along an overland plane subject to uniform rainfall excess and with a constant upstream inflow together with the corresponding average wave celerity and time to equilibrium for the entire plane are derived. The formulae are further developed in terms of both the Darcy-Weisbach resistance coefficient and the Manning resistance coefficient. By comparing the wave celerities, the average wave celerities and the time to equilibrium for planes with and without upstream inflow show that the upstream inflow causes the wave celerity and the average wave celerity to be faster and the times to equilibrium to be shorter. The effect of upstream inflow is greater with increasing inflow, but the marginal effect decreases with increasing inflow. The effect is greatest for laminar flow and least for turbulent flow. For the wave celerity, the effect is also greatest at the upstream end of the plane and least at the downstream end of the plane.  相似文献   

Relationships between higher cumulants of channel response. I. Properties of the linear channel response     

W. G. STRUPCZEWSKI  J. C. I. DOOGE 《水文科学杂志》2013,58(6):675-687

Abstract

The use of dimensionless cumulants to characterize the shape of the linear response of a semi-infinite prismatic channel is extended and simplified by means of the dimensionless coefficient (γ_R) linking the Rth order shape factor to the 3rd order shape factor raised to the power of (R—2). It is shown that, for the special structure of the cumulants of the linearized St. Venant equations, the dimensionless cumulant coefficient (γ_R) of any order R > 4 is a single-valued function of γ₄. It is also shown that the value of γ_R for any Froude number F₀ combined with any shape of section and any friction law (both characterized by the parameter m) is intermediate between the values for the two limiting cases of the diffusion analogy model (F₀ = 0) and the rapid flow model (F₀ = 1). The dimensionless cumulant coefficient γ_R is related to γ₄ through a parameter p(m, F₀) by a polynomial of order [R/2]—1.  相似文献   

Relative velocities of discharge and sediment waves for the River Severn,UK     

L. J. BULL 《水文科学杂志》2013,58(5):649-660

Abstract

It is generally accepted that the celerity of a discharge wave exceeds that of a floodwave. The discharge wave is the initial wavefront (shown by an increase in stage at a particular site), whereas the floodwave refers to the body of water moving downstream. Yet, few studies have investigated the varying relationship between discharge and suspended sediment concentration as floods propagate downstream. This paper examines the relative velocities of the discharge and sediment waves for natural flood events on the River Severn, UK. Four monitoring stations were established within the upper 35 km reach of the River Severn (drainage basin area 380 km2). Discharge was monitored using fixed structures, and suspended sediment concentrations were monitored at similar locations using Partech IR40C turbidity meters. Results showed discharge wave celerity increased with flood magnitude, but relationships were more complex for sediment wave celerity. Sediment wave celerity was greater than discharge wave celerity, and is attributed to the dominant source of sediment, which is most probably bank erosion.  相似文献   

Analytical solution of transient flow in a sloping soil layer with recharge     

《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   

渤海海域黏性土剪切波速与抗剪强度统计关系的初步研究     

黄雅虹  吕悦军  彭艳菊  方怡 《中国地震》2020,36(3):527-538

剪切波速与地基土的抗剪强度、剪切模量和卓越周期等参数密切相关,是地震安全性评价中判定场地类别的一个主要指标和参数。鉴于海域工程中剪切波速往往难以直接由原位测得,而室内实验结果又常常与野外现场物探测试值存在较大差异,因此,如何通过其他途径有效获取满足工程需要的剪切波速参数在海域工程的地震安全性评价等方面具有迫切的实用需求。为此本文通过对渤海海域数十个石油平台项目中一系列饱和黏性土样品的剪切波速与抗剪强度实验数据的统计分析,尝试采用多种可能的函数来拟合确定二者之间的经验关系。结果表明:对于渤海海域黏性土剪切波速V_s与抗剪强度S_u之间的最佳统计经验关系为幂函数V_s=53.751S_u~(0.376)。此关系可为渤海海域工程中通过不排水抗剪强度估算剪切波速提供一种简便可行的实用性方法。  相似文献   

Fluidization of sediments in a conical basin by subterranean springs: relevance to Lake Banyoles     

Xavier Casamitjana  Jordi Colomer  Harindra J. S. Fernando 《Aquatic Sciences - Research Across Boundaries》2000,62(1):79-90

: An experimental study was carried out to investigate the resuspension of particles by a momentum jet discharging from below into a conical basin. The work was motivated by its relevance to Lake Banyoles, where sediments are suspended in different conical basins by bottom jets fed by a groundwater karstic system. Two different flow regimes were identified: a "Jet Flow" regime (JF) and a "Lutocline Flow" regime (LF). In the LF regime, the particles were resuspended, forming a well-established interface along the entire cross-sectional ara of the cone. This regime occurs when the particle Reynolds number Re_p = (u-w_s)d_p/ n {\bf Re_p = (u-w_s)d_p/ \nu} where u is the mean velocity of the flow at the jet entry, ws is the settling velocity of particles, dp is the diameter of that particles and n {\bf \nu} is the kinematic viscosity of water) is below a critical number Rec that depends on the slope of the basin. The maximum height to which particles rise in the LF regime was also determined as a function of four non-dimensional variables: D1 = ho/(Mo^1/2/ws), D2 = ho/dp, Rep and tan  b {\bf tan \, \beta} (where ho is the height of the particle bed, Mo is the kinematic momentum flux of the jet and tan  b {\bf tan \, \beta} is the slope of the basin). Application of the results to the basins of Lake Banyoles showed a good agreement provided that the aggregate properties of the suspensions are used. It is also shown that, in the LF regime, inflows to the basins can be estimated by a simple technique based on a balance between the sedimentation flux and the upward advection of sediments by the mean flow.  相似文献   

Nonlocal modons on the beta-plane     

John P. Boyd 《地球物理与天体物理流体动力学》2013,107(2-4):163-182

Abstract

The vortex pair known as a modon is a classical solitary wave in the sense that it decays exponentially with distance from the center of the wave whenever the modon's phase speed of the wave is outside the linear range. In contrast, when ?1 < c < 0, the modon “far field” is oscillatory so that the modon is “nonlocal” in the sense that it has nonzero amplitude even at arbitrarily far distances from the vortex maximum. However, Tribbia and Verkley have independently noted that the oscillatory far field may be very weak for some parameter ranges.  相似文献   

Finite-amplitude mountain waves in a compressible atmosphere including the effects of dissipation     

William Blumen 《地球物理与天体物理流体动力学》2013,107(1-3):89-104

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 z_c. The height z_c , 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 z_c. 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 &Gt; z_c 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 = z_c .  相似文献   

TWO-AND-ONE-HALF DIMENSIONAL IN-PLANE WAVE PROPAGATION*     

N. BLEISTEIN 《Geophysical Prospecting》1986,34(5):686-703

This paper collects certain results concerning wave propagation in two-and-one-half dimensions, i.e., three-dimensional (3-D) wave propagation in a medium that has variations in two dimensions only. The results of interest are for sources and receivers in the plane determined by the two directions of parameter variation. The objective of this work is to reduce the analysis of the in-plane propagation to 2-D analysis while retaining–at least asymptotically–the proper 3-D geometrical spreading. We do this for the free space Green's function and for the Kirchhoff approximate upward scattered field from a single reflector. In both cases the derivation is carried out under the assumption of a background velocity c(x, z) with the special cases c = c₀ and c = c(z).  相似文献   

旋转地球流体的一个非线性奇异孤立波精确解     

李春雁 《地球物理学报》1990,33(3):336-342

本文求出了旋转地球流体的f平面浅水波方程组的一个非线性精确解.这是一个处处连续、分片光滑的凹形孤立波,在波谷处为一尖点（奇异点）,其移速比长波速度gh^1/2略小,为（1+a/h）（gh（1+a/h））^1/2,其中a<0.其水平尺度与水深几乎无关.  相似文献   

The effects of alongshore variation in bottom topography on a boundary current—(topographically induced upwelling)     

Gerald S. Janowitz  Leonard J. Pietrafesa 《Continental Shelf Research》1982,1(2):123-141

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 (L_D/L)² ≤ Ro 1, where L_D 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 q_o = V_u(h,z)|Vh|/α, where V_u(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(V_u/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   

On conditions for the unique inversion of seismic travel-time curves     

V. S. Geyko 《Pure and Applied Geophysics》1980,119(4):880-887

It is shown that when the travel-time curve of a refracted wave from a surface source is known and at least one of the following conditions is satisfied, i.e. when

1. the travel-time curve of a wave reflected from a horizontal interface lying below the deepest low velocity layer is known, or
2. the travel-time curve of a wave from a deep source situated below the deepest low velocity layer is known, or
3. the measureH(u)=mes {z∶z≥0,v ^?1 (z)≥u} is analytical in some segment [c, d], where \(0< c< d< \infty , c< a_n , H(a_n ) = \bar z_n ,\bar z_n\) is the depth of the lower end of the deepest low velocity layer and in the interval [c, ∞) an analytical functionH(u)) exists which providesH(u)≡H(u)) ifu∈[c, d], then (1) velocityv(z) outside the low velocity layers and (2) the measureH _k (u)=mes {z∶z∈L _k,v ^?1 (z)≥u} for each low velocity layerL _k,k=1, 2, ..., n, are defined unambiguously.

  相似文献   

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows on infiltrating surfaces     

V. P. Singh 《水文研究》1995,9(1):1-18

Error equations for the kinematic wave and diffusion wave approximations were derived under simplified conditions for space-independent flows occurring on infiltrating planes or channels. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions were parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness, lateral inflow and infiltration when the initial condition is vanishing. The error equations were found to be the Riccati equation.  相似文献   

Quantifying the impact of climate variables on reference evapotranspiration in Pearl River Basin,China     

Tao Zhang  Kyaw Tha Paw U 《水文科学杂志》2019,64(16):1944-1956

ABSTRACT

The impact of climate variables on monthly reference evapotranspiration (ET_o) is a critical issue in water resources management and irrigation planning. The spatio-temporal contribution of climate variables to ET_o in the Pearl River Basin (PRB), China, from 1960 to 2016 were calculated based on sensitivity and relative change of each climatic variable. The results show that annual ET_o total decreased by 1.64% and diminished in magnitude from the southeast to the northwest. Sunshine duration, wind speed and relative humidity decreased by 15.5%, 7.4%, and 4.0%, respectively, while average temperature increased by 4.25%. The ET_o showed a positive sensitivity to all variables except relative humidity, which showed a negative sensitivity. Sunshine duration had the highest contribution of ?4.26%, and the overall decrease in ET_o was mainly caused by the declines in sunshine duration and wind speed, which offset the positive impact of rises in average temperature and reduction in relative humidity.  相似文献