Tides off‐shore: Transition from California coastal to deep‐sea waters‡

Abstract

Tidal pressures and currents were measured with self‐contained capsules dropped to the sea floor for one month at distances of 175, 190, and 500 nautical miles from San Diego. These observations, together with a one‐week bottom pressure record by Filloux at 750 n miles, and three half‐week bottom current records by Isaacs et al, at intermediary distances, were analyzed for tidal components by cross‐correlation with a noise‐free reference time series. (For short records this method has some merit over classical tide analysis.) It was found that the tide decays seaward to e^‐1 times the coastal amplitude over a distance of order 1000 km for the semidiurnal species, slower for the diurnal species. Tidal currents turn counterclockwise, and are polarized with maximum flow parrallel to shore in the direction of tidal propagation (320°T) at local high tide. The current amplitude is roughly 2 cm/sec for the semidiurnal component, 1 cm/sec for the diurnal component. Superimposed baroclinic tidal currents lead to poor signal: noise ratios (between 1:1 and 10:1) for the barotropic currents. In contrast, the ratio is typically 1000:1 for the bottom pressures and generally exceeds that for coastal tide stations of comparable duration. Published I.H.B. tidal constants for exposed California coastal stations indicate “upshore” (towards 320°T) propagation at 140 m/sec for semidiurnal tides. 214 m/sec for diurnal tides.

To interpret these diverse observations, we have computed the dispersion laws for all possible rotationally‐gravitationally trapped waves against a straight coast with shelf. Trapped solutions are conveniently portrayed in terms of a parameter μ such that ? = sin μ = iu/v and f = ‐ cos μ = η/v define the ellipticity and impedance of the wave motion, η, u and v being off‐shelf dimensionless elevation, normal‐to‐shore and longshore components of velocity, respectively. We then attempt to fit the observations by a superposition of the possible wave classes, all of the same tidal frequency: (a) a free Kelvin‐like edge wave with small μ (mostly trapped by rotation, but somewhat slowed by the shelf); (6) a free Poincare‐like leaky wave; and (c) a forced wave (the distortion of the sea bottom by the tide producing forces plays a significant role). The mod el can account for the main features of the observed tidal heights, and gives relative amplitudes at the coast of 54:16:4 cm for components a:b:c in the case of the semidiurnal tides, 21:24:9 cm for the diurnal tides. The results place a semidiurnal amphidrome about midway between San Diego and Hawaii. Tidal currents are not well fitted by the model, and there are problems associated with the separation of barotropic and baroclinic modes, and with the benthic boundary layer. Coastal energy dissipation is small in the sea under investigation, but a “ capacitive “ phase delay appears to be associated with Northern California harbors and inland waters.     

Nonlinear development of phase-mixed alfvén waves

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.     

Resonant forcing of coastally trapped waves in a continuously stratified ocean

In a previous paper (Grimshaw, 1987) the resonant forcing of coastally trapped waves was discussed in the barotropic case. In order to extend that theory to more realistic situations, we have considered the analogous theory whereby a longshore current interacts with a longshore topographic feature, or the forcing is due to longshore wind stress, for the case of the continuously stratified ocean. As in the previous theory, near resonance, when a long-wave phase speed is close to zero (in the reference frame of the forcing), the wave motion is governed by a forced evolution equation of the KdV-type. The behaviour of the wave field is characterized by three parameters representing the bandwidth for resonance, the forcing amplitude and the dissipation. We have evaluated these parameters in various practical cases, and found that the bandwidths, which scale with ^1/2 when the forcing has dimensionless amplitude , can often be quite broad. Typically the second, third, or higher, modes may be resonant. Concurrently, the dissipation is also usually significant, leading to a steady state balance between the forcing, dissipation and nonlinear terms.     

Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small but finite inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,?v,?t), x and v being the particle position and velocity, respectively. For arbitrary inertia, position and velocity variables are coupled, with the result that p(x,?v,?t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small (but nevertheless finite) inertia, (x,?v)-variables decouple and the determination of p(x,?v,?t) is reduced to solve a system of two standard forced advection–diffusion equations in the space variables x. The latter equations are derived here from first principles, i.e., from the well-known Lagrangian evolution equations for position and particle velocity.     

A method to estimate the longshore sediment transport at ebb-tidal deltas based on their volumetric growth: Application to the Guadiana (Spain–Portugal border)

Current techniques assessing longshore sediment transport rates have large uncertainties, pleading for the development of alternative and complementary approaches. The present study proposes a method to estimate the decadal average rate of longshore transport at modern ebb-tidal deltas based on a sediment budget analysis of the outer shoal growth. This transport is obtained as the balance of the other contributions to the shoal with the total sediment input rate obtained from an inverse application of the inlet reservoir model. The method is applied to the Guadiana ebb-tidal delta, yielding an average longshore sediment transport rate (~85 000 m3 year⁻¹) in good agreement with expectations for the region. It is exemplified that this decadal averaged rate can be used to improve longshore sediment transport expressions in order to study its variability over shorter time scales. At the Guadiana, the yearly longshore sediment transport from the improved formula ranges from ~25 000 m³ (westward) to ~245 000 m³ (eastward) and is related to the North Atlantic Oscillation index. Overall, the proposed method constitutes an alternative tool to constrain the average longshore sediment transport rate over decades in the vicinity of tidal inlets. It is applicable to ebb-tidal deltas where the outer shoal growth (from an early to a mature stage) is well documented by bathymetric maps, and where the main transport pathways towards the outer shoal can be specified. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.     

An antidynamo theorem for partly symmetric flows

Abstract

It is shown that magnetic fields generated by flows v _r,(r,t)e_r+v_T where v_T is an arbitrary toroidal component (e_r˙v_T≡V≡v_T≡0), cannot be maintained indefinitely against ohmic dissipation. The poloidal field variable max |r ² B _r| is shown to decay strictly monotonically with an undetermined decay rate. A bound on the growth of the toroidal field norm ∥T∥₁ is established solely dependent on the rate of conversion of poloidal to toroidal field, so that when the poloidal field is negligible then ∥T∥₁ decays strictly monotonically. The main application of these results is to models of stellar evolution based on axisymmetric differential rotation and spherically symmetric contraction. This symmetric velocity theorem overlaps with two already known theorems, namely the toroidal velocity theorem where v _r≡0 and the radial velocity theorem where v_T≡0. The new theorem does not entirely include the already established ones, principal differences being in the rates of decay and the field variables for which the decay is proven (see Table 1).     

On temporal and spatial distribution of seismic apparent stresses in Yunnan area

Introduction In recent years the study of the digital seismology has made great progress due to the wide use of the broadband digital records. And many fine results of the focal theory have obtained. The focal theory mainly studies the physical process of the seismic fracture and production of the seismic wave, as well as its traveling process. One of the great progresses is to simulate the fracture process in the active fault. Especially a new concept of the fracture mechanics has been intro…     

Bounds on the infimum decay rate for axisymmetric incompressible dynamos

Abstract

The variational lower bound v > 0.39π² determined by Ivers (1984) for the infimum decay rate v of axisymmetric poloidal magnetic fields is corroborated numerically and an upper bound v < 0.66°² established. This is achieved by correcting and extending results for certain flows considered by Chandrasekhar (1956).     

The weak taylor state in an αω-dynamo

Abstract

A spherical αω-dynamo is studied for small values of the viscous coupling parameter ε ～ v^1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach et al. (1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ε^1/2 is independent of ε in the solutions for dynamo numbers smaller than a certain value of D _b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D _b the solution bifurcates and subsequently becomes dependent on ε. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ε = 0 become unstable and fail, while the solutions for small but non-zero ε are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context.     

Heat transfer and thermal boundary layers in high amplitude annulus waves

Abstract

The heat transfer by a rotating, differentially-heated annulus of fluid is measured throughout the high amplitude wave regime. Only Δr_w T was varied (although v(T₁₅ ).K(T₁₅ ) varied by 46%), and it is found that Nu = C₁(λ)Ra^? away from the symmetry and low amplitude to wave transition curves and this is independent of ω. (λ is the wavelength.) On the wave side of these transition curves a region exists in which Nu (symmetry) λ Nu λ C₁(λ)Ra^?. The local heat transfer rate also varies strongly with wave phase.

Using a selection of measured internal thermal fields in the steady, high amplitude wave regime, the side-wall thermal boundary layer structure is examined. It is found that Nu, = C₂·Gr₂ ^A2; both C ₂ and A ₂ are independent of ω and λ to first order. For the time mean profiles, A ₂ ≈ 0.25; in the high heat transfer portion of the wave A ₂ < ¼ and in the low heat transfer portion of the wave A ₂ > ?. These relations hold over most of the vertical extent of the side walls. The deviations of the boundary layers from the above behavior which occur on the remainder of the walls is illustrated. The average thicknesses of the wall boundary layers ∞ Ra^?¼ except in that phase of the wave in which the wall to mid-gap temperature difference is the largest.     

Study on in-situ stress measurement around coastal marginal land in Fujian

Introduction The southeast coastal margin of Chinese mainland is important to understand the mutual movement, matter exchange and energy transfer between ocean and land lithospheres, as well as their effects. The coastal area in Fujian Province is advanced in economy development but it has frequent earthquakes, or even strong earthquakes. Therefore, the current study on in-situ stress state measurement is of great significance for studying continental dynamics, marginal sea dy- namics, seismo…     

Reach-scale suspended sediment balance downstream from dams in a large Mediterranean river

Abstract

This paper presents a reach-scale sediment balance of a large impounded Mediterranean river (the lower Ebro, 1998–2008). Multi-temporal sediment storage and the influence of floods and tributaries on the sediment load were examined using continuous discharge and turbidity records. The mean annual suspended sediment load at the reach outlet (Xerta) is 0.12?×?10⁶ t, corroborating previous results. Suspended sediment concentrations were low (SSC_mean?=?13 mg L^-1), attaining a maximum of 274 mg L^-1. Erosion processes (channel-scour, bank erosion) are dominant, and net export of sediment occurs over the long term. Unexpectedly, ephemeral tributaries were found to contribute significantly: sediment delivered during torrential events attained 5% of the Ebro annual load, and was even larger than that in flushing flows. Overall, most of the suspended sediment load is transported by floods (up to 65% in some years). The results constitute basic information to underpin current management actions aiming to achieve the sustainability of the riverine and deltaic system.

Editor D. Koutsoyiannis; Associate editor D. Hughes

Citation Tena, A., Batalla, R.J. and Vericat, D., 2012. Reach-scale suspended sediment balance downstream from dams in a large Mediterranean river. Hydrological Sciences Journal, 57 (5), 831–849.     

Note on the scalar dynamo model

Abstract

Bayly (1993) introduced and investigated the equation (? _t + v·▽-η ▽²)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.     

The geodynamo as a bistable oscillator

Abstract

Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating α reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ∝(1 ? a ²)², subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2?3) × 10⁵ year, is shown to imply a secular variation of the axial dipole moment of ～ 15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data.     

Instability of flows near the onset of convection in a rotating layer with stress-free horizontal boundaries

We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε² being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε^8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k _c . For waves, the largest growth rate is of the order ε^4/3. In the case of Eckhaus instability the growth rate is of the order of α².     

A source-Sink laboratory model of the ocean circulation

Abstract

A two gyre circulation and inertial western boundary currents have been observed in a sloping bottom laboratory model of a barotropic ocean circulation. Water of viscosity v is contained in a rotating (angular velocity ω), square basin of side L (30 cm) with a flat top and a bottom slope (tan θ) such that the depth (H) varies from 12 to 15 cm. The flow is driven by a distributed source and sink at the upper surface, a plate drilled with 342 holes. The hole distribution and size is arranged so that the average imposed vertical velocity, w = w ₀ sin (2πy′/30), models the Ekman divergence from a two gyre zonal wind stress. Fluid flow is observed with the thymol blue technique over the ranges of Rossby numbers (w ₀/2ωL tan θ) from 1.44 × 10^?3 to 1.41 × 10^?2 and Ekman numbers (v/2ωH ²) from 2.13 × 10^?5 to 2.10 × 10^?3. At the largest Rossby numbers the flow pattern changes markedly, but the non-uniformity of the imposed vertical velocity also penetrates deep into the fluid in this regime.     

Experimental examination on the heterogeneity parameter C v of earthquake precursors

Two rock samples with different structures and materials were deformed under a biaxial loading system, and multipoint strain measurements were performed for each sample. The distribution of strain anomalies during the deformation and the instability process were analyzed by using C _v value put forward by WANG Xiao-qing and CHEN Xue-zhong, et al, a parameter to describe the heterogeneous distribution of earthquake precursors, so as to examine the method of C _v value and to explore its physical meaning experimentally. The result shows that the change of C _v value is correlated to the change of deformation characteristics and is an effective parameter to describe the heterogeneity of precursor distribution. C _v value increases firstly and then decreases before the instability, and the instability occurs when C _v value decreases to the level before increasing. This indicates that C _v value may be a useful parameter for earthquake prediction. Foundation item: Chinese Joint Earthquake Sciences Foundation (9507435).     

Estimating water balance components of tropical wetland lakes in the Pantanal dry season,Brazil

Abstract

Water balance studies with stable water isotopes have rarely been conducted in remote and tropical wetland areas. As such, little is known regarding the water balance and groundwater–surface water interaction in the Pantanal, one of the largest and most pristine wetlands in the world. We applied MINA TrêS, a water balance model utilizing stable water isotopes (δ¹⁸O, δ²H) and chloride (Cl^-) to assess the dry-season hydrological processes controlling groundwater–surface water interactions and the water balance of six floodplain lakes in the northern Pantanal, Brazil. Qualitatively, all lakes exhibited similarity in hydrological controls. Quantitatively, they differed significantly due to morphological differences in controlling groundwater inflow and lake volume. Our approach is readily transferable to other remote and tropical wetland systems with minimal data input requirements, which is useful in regions with sparse hydrometric monitoring.

Editor Z.W. Kundzewicz     

On the spin-up of a stably stratified,electrically conducting fluid. Part 1: Spin-up controlled by the hartmann layer

Abstract

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

On the propagation of topographically trapped waves

Abstract

In the context of ageostrophic theory in a homogeneous ocean, a nondimensional number is determined which corresponds to the Ursell number for long gravity waves. It is defined as Q = NL ²/h ³, where N is the amplitude of the wave travelling along the long length-scale direction, L is its length and h (which for gravity waves is the water depth) is given by h=(l ⁴ f ²/g)^1/3. where l is the short length-scale, f the Coriolis parameter and g the acceleration due to gravity. The physical meaning of Q is as follows: if Q? O(1) the free evolution of the wave is linear and weakly dispersive, if Q = O(1) nonlinear and dispersive effects balance out and finally if Q ?O(1) the evolution is nonlinear and non-dispersive. Expressions for the time scales for the development of dispersive and nonlinear effects are also determined. These results apply to topographically trapped waves, namely barotropic continental shelf and double Kelvin waves travelling along a rectilinear topographic variation.