Tidal currents and residual currents at Norderney,Elbe 1, and Aussen-Eider lightships and their variation under the influence of prevailing winds

Summary Four hourly current-and wind observations during the years 1924–1927 at the German lightvessels Norderney, Elbe 1, and Aussen-Eider were subjected to harmonic analysis with emphasis on the influence of the wind on the residual as well as on the tidal current. The tidal current is strongest at Elbe 1 and weakest at Aussen-Eider. The half-monthly inequality of the current is strongly influenced by a ₂ tidal component. Wind influences the velocity, phase and duration of ebb-and flow current in a systematic way at Norderney and Elbe 1. Deviations from the mean tidal current are caused mainly by the change in wind direction rather than by wind velocity. The mean residual current is weak at the three stations. But wind driven currents have a velocity up to 5 times as great as the mean residual current and reverse their direction with the wind. The annual variation of the mean residual current, however, is caused only to a small part by the annual wind variation.Abbreviations used in this paper Gr. M. Tr. Greenwich moon transit, i.e. Greenwich civil time of the upper or lower transit of the moon through the meridian of Greenwich - C _n computed tidal current at M1/2Hn - C _n ^m computed mean tidal current at M1/2Hn - M _n Moon-half hour mean, i.e. mean of all current velocities observed during M1/2Hn - M.A. Moon age of an observation, true Greenwich time of Gr.M.Tr. directly preceeding the time of observation, expressed in 12 integral numbers, each representing M.A. falling in 12 different hourly intervals - M1/2H Moon-half hour, 1/2 of the interval between one moon transit and the next, i.e. 1/24 of 12h25m - R _n ^o ,R _n ^' ,R _n ^" residual current computed by harmonic analysis ofn M1/2H means of the mean current, the current at weak winds, and the current at strong winds respectively - d.o.f. degrees of freedom - standard deviation ofC _n fromM _n - ^* mean standard deviation ofC _n fromM _n for analysis with weighted means - A _o Standard error of the residual currentA _o - AB standard error of the harmonic coefficientsA ₁,B ₁,A ₂,B ₂,... - S ₂ Phase of the current componentS ₂     

Calculating the azimuth of mountain waves, using the effect of tilted fine-scale stable layers on VHF radar echoes

A simple method is described, based on standard VHF wind-profiler data, where imbalances of echo power between four off-vertical radar beams, caused by mountain waves, can be used to calculate the orientation of the wave pattern. It is shown that the mountain wave azimuth (direction of the horizontal component of the wavevector), is given by the vector are radar echo powers, measured in dB, in beams pointed away from vertical by the same angle towards north, south, east and west respectively, and W is the vertical wind velocity. The method is applied to Aberystwyth MST radar data, and the calculated wave vector usually, but not always, points into the low-level wind direction. The mean vertical wind at Aberystwyth, which may also be affected by tilted aspect-sensitive layers, is investigated briefly using the entire radar output 1990–1997. The mean vertical-wind profile is inconsistent with existing theories, but a new mountain-wave interpretation is proposed.     

Incoherent internal tidal currents in the deep ocean

Eleven months current meter observations from the deep Bay of Biscay were examined for the residual (incoherent internal tidal; icIT) signal, left after harmonic analysis using eight tidal constituents (large-scale barotropic or coherent baroclinic signal) within the semidiurnal band. This residual signal comprised 30% of the total tidal kinetic energy and, due to its flat spectral appearance, it was responsible for typically 5–7 days intermittency. Although icIT was part of the red noise internal wave band continuum, it was not attributable to instrumental noise. It consisted of quasi-harmonics at non-tidal harmonic frequencies having amplitudes larger than N₂, the third largest semidiurnal tidal constituent. It is suggested that the kinetic energy at these non-tidal frequencies reflects interaction between semidiurnal tidal motions and the slowly varying background conditions.Responsible Editor: Roger Proctor     

The impacts of the large-scale hydraulic structures on tidal dynamics in open-type bay: numerical study in Jakarta Bay

The construction of a Giant Sea Wall (GSW) complex in Jakarta Bay has been proposed to protect Jakarta against flood in the Master Plan for National Capital Integrated Coastal Development (NCICD). However, these large-scale hydraulic structures could significantly change the tidal dynamics in Jakarta Bay. This research investigates the potential impacts of a GSW on the tidal dynamics, including tides, currents, and residual currents in Jakarta Bay using a validated numerical model (Finite Volume Coastal Ocean Model (FVCOM)). Results show that the bay is diurnal with a maximum tidal range of ~0.9 m. The flow is mainly in an east-west direction with a maximum depth-mean current speed of up to 0.3 ms^?1. The construction of a GSW would modulate the tidal dynamics by changing the bathymetry, tidal prism, wind effect, and tidal choking effect in the bay. The maximum tidal range would be slightly increased due to the reduced tidal prism of the bay and the increased tidal choking effect. The current would penetrate into the west reservoir through the gates and channels between the artificial islands, with peak speed jets appearing at the gates (~0.3 ms^?1), due to tidal choking. A similar peak current speed appears near the right wing of the GSW due to the pressure gradient would be created by the wing of the GSW. Closing the gates would mainly affect the currents inside the west reservoir. The residual current would be slightly increased after the construction of the GSW. An eddy would be formed at the bottom level near the right wing of the GSW. The direction of the residual current is landward instead of seaward at the surface level outside the GSW. The impact of wind on surface currents would be much reduced due to the decreased water surface area. Although this study is site specific, the findings may have a wider applicability to the impacts of large-scale hydraulic structures on tidal dynamics in open-type bays.     

Modelling sand wave migration in shallow shelf seas

Sand waves form a prominent regular pattern in the offshore seabed of sandy shallow seas. The positions of sand-wave crests and troughs slowly change in time. Sand waves are usually assumed to migrate in the direction of the residual current. This paper considers the physical mechanisms that may cause sand waves to migrate and methods to quantify the associated migration rates. We carried out a theoretical study based on the assumption that sand waves evolve as free instabilities of the system. A linear stability analysis was then performed on a 2DV morphological model describing the interaction between the vertically varying water motion and an erodible bed in a shallow sea. Here, we disrupted the basic tidal symmetry by choosing a combination of a steady current (M₀) and a sinusoidal tidal motion (M₂) as the basic flow. We allowed for two different physical mechanisms to generate the steady current: a sea surface wind stress and a pressure gradient. The results show that similar sand waves develop for both flow conditions and that these sand waves migrate slowly in the direction of the residual flow. The rates of migration and wavelengths found in this work agree with theoretical and empirical values reported in the literature.     

Difference between the Lagrangian trajectories and Eulerian residual velocity fields in the southwestern Yellow Sea

The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.     

Transverse structure of tidal and residual flow and sediment concentration in estuaries

An analytical and a numerical model are used to understand the response of velocity and sediment distributions over Gaussian-shaped estuarine cross-sections to changes in tidal forcing and water depth. The estuaries considered here are characterized by strong mixing and a relatively weak along-channel density gradient. It is also examined under what conditions the fast, two-dimensional analytical flow model yields results that agree with those obtained with the more complex three-dimensional numerical model. The analytical model reproduces and explains the main velocity and sediment characteristics in large parts of the parameter space considered (average tidal velocity amplitude, 0.1–1 m s^− 1 and maximum water depth, 10–60 m). Its skills are lower for along-channel residual flows if nonlinearities are moderate to high (strong tides in deep estuaries) and for transverse flows and residual sediment concentrations if the Ekman number is small (weak tides in deep estuaries). An important new aspect of the analytical model is the incorporation of tidal variations in the across-channel density gradient, causing a double circulation pattern in the transverse flow during slack tides. The gradient also leads to a new tidally rectified residual flow component via net advection of along-channel tidal momentum by the density-induced transverse tidal flow. The component features landward currents in the channel and seaward currents over the slopes and is particularly effective in deeper water. It acts jointly with components induced by horizontal density differences, Coriolis-induced tidal rectification and Stokes discharge, resulting in different along-channel residual flow regimes. The residual across-channel density gradient is crucial for the residual transverse circulation and for the residual sediment concentration. The clockwise density-induced circulation traps sediment in the fresher water over the left slope (looking up-estuary in the northern hemisphere). Model results are largely consistent with available field data of well-mixed estuaries.     

Variations in the IMF vertical component in isolated solar wind streams

The regularities of the variations in the IMF B _z component have been studied based on the data on the solar wind streams and their solar sources. Isolated solar wind streams such as magnetic clouds and shock layers before them, undisturbed heliospheric current sheets (HCSs), leading edges and bodies of high-speed streams from coronal holes (HSSs from CHs) have been considered. It has been revealed that each type of isolated streams in the interplanetary medium has it own features in the variations in the value and direction of the B _z component related to the stream immanent properties and conditions of propagation in the interplanetary plasma. The appearance of the southward B _z component is obligatory for all these streams which are, therefore, geoeffective.     

Depression in the low-latitude horizontal intensity due to quiet-time ring current

Summary The external field due to plasma within the magnetosphere has been computed as a function ofA _p, which is a measure of solar wind velocity, for very quiet to slightly disturbed conditions using mean daily horizontal intensity from 1932 to 1968 at Alibag. The intensity, corrected for secular change and reduced to a common epoch, showed initially a small increase withA _p followed by a steady depression with further increase in the index. ForA _p7.5, which is representative of conditions over the 33-hour interval during which data relating to low-energy protons were acquired and used byHoffman andBracken [4]²) to compute current distributions, the decrease, computed here from surface data, is 6 . This is in goodagreement with the southward directed field of the quiet-time proton belt 9±5 obtained byHoffman andBracken.     

Migrating sand waves

A simple mathematical model is described, which reproduces the major features of sand waves' appearance and growth and in particular predicts their migration speed. The model is based on the linear stability analysis of the flat configuration of the sea bottom subject to tidal currents. Attention is focused on the prediction of the complex growth rate that bottom perturbations undergo because of both oscillatory fluid motions and residual currents. While the real part _r of controls the amplification or decay of the amplitude of the bedforms, the imaginary part _i is related to their migration speed. Previous works on the migration of the sand waves (Németh etal. 2002) consider a forcing tide made up by the M2 constituent (oscillatory period equal to 12 h) plus the residual current Z0 and predict always a downcurrent migration of the bedforms. However, field cases exist of upcurrent-migrating sand waves (downcurrent/upcurrent-migrating sand waves mean bedforms moving in the direction of the steady residual tidal current or in the opposite direction, respectively). The inclusion of a tide constituent characterized by a period of 6 h (M4) is the main novelty of the present work, which allows for the prediction of the migration of sand waves against the residual current Z0. Indeed, the M4 tide constituent, as does also the residual current Z0, breaks the symmetry of the problem forced only by the M2 tide constituent, and induces sand-wave migration. The model proposed by Besio etal. (2003a) forms the basis for the present analysis. Previous works on the subject (Gerkema 2000; Hulscher 1996a,b; Komarova and Hulscher 2000) are thus improved by using a new solution procedure (Besio etal. 2003a) which allows for a more accurate evaluation of the growth rate for arbitrary values of the parameter r, which is the ratio between the horizontal tidal excursion and the perturbation wavelength. Responsible Editor: Jens Kappenberg     

Atmosphere and Earth's rotation

The theoretical aspects of the transfer of angular momentum between atmosphere and Earth are treated with particular emphasis on analytical solutions. This is made possible by the consequent usage of spherical harmonics of low degree and by the development of large-scale atmospheric dynamics in terms of orthogonal wave modes as solutions of Laplace's tidal equations.An outline of the theory of atmospheric ultralong planetary waves is given leading to analytical expressions for the meridional and height structure of such waves. The properties of the atmospheric boundary layer, where the exchange of atmospheric angular momentum with the solid Earth takes place, are briefly reviewed. The characteristic coupling time is the Ekman spin-down time of about one week.The axial component of the atmospheric angular momentum (AAM), consisting of a pressure loading component and a zonal wind component, can be described by only two spherical functions of latitude : the zonal harmonicP ₂ ⁰ (), responsible for pressure loading, and the spherical functionP ₁ ¹ () simulating supperrotation of the zonal wind. All other wind and pressure components merely redistributeAAM internally such that their contributions toAAM disappear if averaged over the globe. It is shown that both spherical harmonics belong to the meridional structure functions of the gravest symmetric Rossby-Haurwitz wave (0, –1)^*. This wave describes retrograde rotation of the atmosphere within the tropics (the tropical easterlies), while the gravest symmetric external wave mode (0, –2) is responsible for the westerlies at midlatitudes. Applying appropriate lower boundary conditions and assuming that secular angular momentum exchange between solid Earth and atmosphere disappears, the sum of both waves leads to an analytical solution of the zonal mean flow which roughly simulates the observed zonal wind structure as a function of latitude and height. This formalism is used as a basis for a quantitative discussion of the seasonal variations of theAAM within the troposphere and middle atmosphere.Atmospheric excitation of polar motion is due to pressure loading configurations, which contain the antisymmetric functionP ₂ ¹ () exp(i) of zonal wavenumberm=1, while the winds must have a superrotation component in a coordinate system with the polar axis within the equator. The Rossby-Haurwitz wave (1, –3)^* can simulate well the atmospheric excitation of the observed polar motion of all periods from the Chandler wobble down to normal modes with periods of about 10 days. Its superrotation component disappears so that only pressure loading contributes to polar motion.The solar gravitational semidiurnal tidal force acting on the thermally driven atmospheric solar semidiurnal tidal wave can accelerate the rotation rat of the Earth by about 0.2 ms per century. It is speculated that the viscous-like friction of the geomagnetic field at the boundary between magnetosphere and solar wind may be responsible for the westward drift of the dipole component of the internal geomagnetic field. Electromagnetic or mechanical coupling between outer core and mantle may then contribute to a decrease of the Earth's rotation rate.     

Simulation of the Lagrangian tide-induced residual velocity in a tide-dominated coastal system: a case study of Jiaozhou Bay,China

The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M ₂ tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection.

     

Simulation of the Lagrangian tide-induced residual velocity in a tide-dominated coastal system: a case study of Jiaozhou Bay, China

The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M ₂ tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection.     

EISCAT measurements of the solar wind

EISCAT observations of interplanetary scintillation have been used to measure the velocity of the solar wind at distances between 15 and 130R (solar radii) from the Sun. The results show that the solar wind consists of two distinct components, a fast stream with a velocity of 800 km s^–1 and a slow stream at 400 kms^–1. The fast stream appears to reach its final velocity much closer to the Sun than expected. The results presented here suggest that this is also true for the slow solar wind. Away from interaction regions the flow vector of the solar wind is purely radial to the Sun. Observations have been made of fast wind/slow wind interactions which show enhanced levels of scintillation in compression regions.     

Residual circulation and stratification in the Liverpool Bay region of freshwater influence

Wind and tidal straining are proposed as key mechanisms influencing the magnitude and timing of the horizontal flux of freshwater across regions of freshwater influence (ROFIs). Evidence for this hypothesis is presented in estimates of the tidally averaged residual current profile, obtained from 5 years of continuous acoustic doppler current profiler measurements in the Liverpool Bay ROFI. The modified horizontal Richardson number (R_x^wtR_{x}^{wt}), which includes both the tidal and the wind forcing, was assessed as a measure of stratification. R_x^wtR_{x}^{wt} was found to be a good indicator of the timing of the evolution and destruction of stratification, but was not as successful as an indicator of the magnitude of stratification, both enduring and periodic. The observed mean residual velocities are compared to those predicted by a classical solution, and the eddy viscosity (N _z ) is shown to be a control on differences between the observed and predicted circulation. Principal component analysis is used to show that the strongest residual currents occur when the water column periodically alternates between a well-mixed and stratified state, a consequence of straining, rather than simply related to the density gradient. Evidence of wind straining was found in the correspondence between the wind direction and the near surface and near bed residual current direction.     

Modeling studies of tidal dynamics and the associated responses to coastline changes in the Bohai Sea,China

Over the past 30 years, reclamation projects and related changes have impacted the hydrodynamics and sediment transport in the Bohai Sea. Three-dimensional tidal current models of the Bohai Sea and the Yellow Sea were constructed using the MIKE 3 model. We used a refined grid to simulate and analyze the effects of changes in coastline, depth, topography, reclamation, the Yellow River estuary, and coastal erosion on tidal systems, tide levels, tidal currents, residual currents, and tidal fluxes. The simulation results show that the relative change in the amplitude of the half-day tide is greater than that of the full-day tide. The changes in the tidal amplitudes of M₂, S₂, K₁, and O₁ caused by coastline changes accounted for 27.76–99.07% of the overall change in amplitude from 1987 to 2016, and water depth changes accounted for 0.93–72.24% of the overall change. The dominant factor driving coastline changes is reclamation, accounting for 99.55–99.91% of the amplitude changes in tidal waves, followed by coastal erosion, accounting for 0.05–0.40% of the tidal wave amplitude changes. The contribution of changes in the Yellow River estuary to tidal wave amplitude changes is small, accounting for 0.01–0.12% of the amplitude change factor. The change in the highest tide level (HTL) is mainly related to the amplitude change, and the correlation with the phase change is small. The dominant factor responsible for the change in the HTL is the tide amplitude change in M2, followed by S2, whereas the influence of the K1 and O1 tides on the change in the HTL is small. Reclamation resulted in a decrease in the vertical average maximum flow velocity (V_VAM) in the Bohai Sea. Shallower water depths have led to an increase in the V_VAM; deeper water depths have led to a decrease in the maximum flow velocity. The absolute value of the maximum flow velocity gradually decreases from the surface to the bottom, but the relative change value is basically constant. The changes in the tidal dynamics of the Bohai Sea are proportional to the degree of change in the coastline. The maximum and minimum changes in the tidal flux appear in Laizhou Bay (P-LZB) and Liaodong Bay (P-LDB), respectively. The changes in the tidal flux are related to the change in the area of the bay. Due to the reduced tidal flux, the water exchange capacity of the Bohai Sea has decreased, impacting the ecological environment of the Bohai Sea. Strictly controlling the scale of reclamation are important measures for reducing the decline in the water exchange capacity of the Bohai Sea and the deterioration of its ecological environment.     

The relations between the linear and bilinear atmospheric tidal fields in geometric height and in log-pressure coordinates

The relationships between the linearized meteorological variables as expressed in geometric height and in log-pressure coordinates are derived from the assumptions of classical atmospheric tidal theory. While the horizontal velocity components are the same to first-order in the two coordinate systems, a linearized vertical velocity differencew-H ₀ occurs because of the periodic vertical displacement of the constant pressure surfaces due to time-dependent, hydrostatic density perturbations; a linearized temperature differenceT- also results when these displacements occur in the presence of a zero-order vertical gradient of temperature. Both of these differences can be expressed in terms of the tidal geopotential field. For a given tidal mode, both differences are generally proportional to the square root of the ratio of the tidal mode's equivalent depth and the atmospheric scale height; the temperature difference is also proportional to the background temperature lapse rate. It is further shown that the two classical tidal vertical structure equations commonly derived in their respective geometric height and log-pressure coordinate systems are in fact identical to first-orderas long as the same thermotidal forcing function is used. Expressions for the zonal-mean components of the tidal bilinear fluxes, formed by zonally averaging the product of two longitudinally varying, linearized tidal fields, are also derived for the two coordinate systems. For the bilinear fields the largest relative differences (a few tens of percent) are for the tidal zonal-mean forcing per unit mass of the zonal wind. For Earth and Mars, differences between the tidal vertical velocity fields are generally less than 25% but may be significantly larger in the Martian atmosphere during one of its episodic planetary-scale dust storms. Tidal temperature differences are generally smaller.     

Seismic anisotropy of shales

Shales are a major component of sedimentary basins, and they play a decisive role in fluid flow and seismic‐wave propagation because of their low permeability and anisotropic microstructure. Shale anisotropy needs to be quantified to obtain reliable information on reservoir fluid, lithology and pore pressure from seismic data, and to understand time‐to‐depth conversion errors and non‐hyperbolic moveout. A single anisotropy parameter, Thomsen's δ parameter, is sufficient to explain the difference between the small‐offset normal‐moveout velocity and vertical velocity, and to interpret the small‐offset AVO response. The sign of this parameter is poorly understood, with both positive and negative values having been reported in the literature. δ is sensitive to the compliance of the contact regions between clay particles and to the degree of disorder in the orientation of clay particles. If the ratio of the normal to shear compliance of the contact regions exceeds a critical value, the presence of these regions acts to increase δ, and a change in the sign of δ, from the negative values characteristic of clay minerals to the positive values commonly reported for shales, may occur. Misalignment of the clay particles can also lead to a positive value of δ. For transverse isotropy, the elastic anisotropy parameters can be written in terms of the coefficients W₂₀₀ and W₄₀₀ in an expansion of the clay‐particle orientation distribution function in generalized Legendre functions. For a given value of W₂₀₀, decreasing W₄₀₀ leads to an increase in δ, while for fixed W₄₀₀, δ increases with increasing W₂₀₀. Perfect alignment of clay particles with normals along the symmetry axis corresponds to the maximum values of W₂₀₀ and W₄₀₀, given by and . A comparison of the predictions of the theory with laboratory measurements shows that most shales lie in a region of the (W₂₀₀, W₄₀₀)‐plane defined by W₄₀₀/W₂₀₀≤W^max₄₀₀/W^max₂₀₀ .