A Modification to Vertical Distribution of Tidal Flow Reynolds Stress in Shallow Sea

Tidal flow is a periodic movement of unsteady and non-uniform, which has acceleration and deceleration process obviously, especially in coastal shallow waters. Many researches show that vertical distribution of tidal flow Reynolds stress deviated from linear distribution. The parabolic distribution of the tidal flow Reynolds stress was proposed by Song et al. （2009）. Although the model fills better with field observations and indoor experimental data, it has the lower truncated series expansion of tidal flow Reynolds stress, and the description of the distribution is not very comprehensive By introducing the motion equation of tidal flow and improving the parabolic distribution established by Song et al. （2009）, the cubic distribution of the tidal flow Reynolds stress is proposed. The cubic distribution is verified well by field data （Bowden and Fairbairn, 1952; Bowden et al., 1959; Rippeth et al., 2002） and experimental data （Anwar and Atkins, 1980）, is consistent with the numerical model results of Kuo et al. （1996）, and is compared with the parabolic distribution of the tidal flow Reynolds stress. It is shown that this cubic distribution is not only better than the parabolic distribution, but also can better reflect the basic features of Reynolds stress deviating from linear distribution downward with the tidal flow acceleration and upward with the tidal flow deceleration, for the foundation of further study on the velocity profile of tidal flow.

Vertical Distribution of Tidal Flow Reynolds Stress in Shallow Sea

Based on the results of the tidal flow Reynolds stresses of the field observations, indoor experiments, and numerical models, the parabolic distribution of the tidal flow Reynolds stress is proposed and its coefficients are determined theoretically in this paper. Having been well verified with the field data and experimental data, the proposed distribution of Reynolds stress is also compared with numerical model results, and a good agreement is obtained, showing that this distribution can well reflect the basic features of Reynolds stress deviating from the linear distribution that is downward when the tidal flow is of acceleration, upward when the tidal flow is of deceleration. Its dynamics cause is also discussed preliminarily and the influence of the water depth is pointed out from the definition of Reynolds stress, turbulent generation, transmission, and so on. The established expression for the vertical distribution of the tidal flow Reynolds stress is not only simple and explicit, but can also well reflect the features of the tidal flow acceleration and deceleration for further study on the velocity profile of tidal flow.

Internal solitary wave generation by the tidal flows beneath ice keel in the Arctic Ocean

A series of non-hydrostatic,non-linear numerical simulations were carried out to investigate the generation and evolution of internal solitary waves(ISWs)through the interaction of a barotropic tidal current with an ice keel in the Arctic Ocean.During the interaction process,the internal surge was generated at first,and then the wave gradually steepened due to non-linearity during its propagation away from the ice keel.The internal surge eventually disintegrated into multi-modal and rank-ordered ISW packets with the largest having an amplitude of O(10)m.Sensitivity experiments demonstrated that the ISWs’amplitudes and energy were proportional to the varying ice keel depths and barotropic tidal fl ow amplitudes,but were insensitive to the changing ice keel widths.Typical ISWs can enhance the turbulent dissipation rate of O(10^(-6))W/kg along their propagation path.Further,heat entrainment induced by the wave-ice interaction can reach O(10)MJ/m per tidal cycle.This study reveals a particular ISW generation mechanism and process in the polar ice environment,which could be important in impacting the energy transfer and heat balance in the Arctic Ocean.

Weather induced subtidal flows through multiple inlets of an arctic microtidal lagoon

Estuarine processes in the arctic lagoons are among the least studied but important subjects, especially considering the rapid warming of arctic water which may change the length of ice-free period in the summer. In this paper, wind-driven exchange flows in the micro-tidal Elson Lagoon of northern Alaska with multiple inlets of contrasting widths and depths are studied with in situ observations, statistical analysis, numerical experiments, a regression model on the basis of dynamics, and remote sensing data. Water velocity profiles were obtained from a bottom deployed acoustic Doppler current profiler(ADCP) in the northwestern Eluitkak Pass connecting the Beaufort Sea to the Elson Lagoon during a 4.9 day ice-free period in the summer of 2013. The subtidal flow is found correlated with wind(R^2 value ～96%). Frequently occurring east, northeast and north winds from the arctic atmospheric high-and low-pressure systems push water from the Beaufort Sea into the lagoon through the wide inlets on the eastern side of the lagoon, resulting in an outward flow against the wind at the narrow northwestern inlet. The counter-wind flow is a result of an uneven wind forcing acting through the asymmetric inlets and depth,an effect of "torque" or vorticity. Under northwest wind, the exchange flow at the northwestern inlet reverses its direction, with inward flows through the upwind northwestern inlet and outward flows through the downwind eastern inlets. A regression model is established based on the momentum equations and Taylor series expansions. The model is used to predict flows in July and August of 2015 and July of 2017, supported by available Landsat satellite images. About 73%–80% of the time the flows at Eluitkak Pass are out of Elson Lagoon for the summer of 2015 and 2017. Numerical experiments are conducted to corroborate the findings and illustrate the effects under various wind conditions. A quasi-steady state balance between wind force and surface pressure gradient is confirmed.

Analytical Solution for 3D Tidal Flow with Vertically Varying Eddy Viscosity

In this study, a 3D idealized model of tidal flow, in which the tidal elevation and velocities are solved analytically, is developed. The horizontal eddy viscosity is neglected, and the vertical eddy viscosity used in the study is assumed to be independent of time and only varies as a parabolic function in the vertical direction. The analytical solution is obtained in a narrow rectangular bay, with the topography varying only across the bay. The model results are compared with the field observations in the Xiangshan Bay. The results show that the influence of varying vertical eddy viscosity mainly has two aspects. On one hand, it amplifies the magni- tude of the tidal elevation, particularly the amplitude near the head of the bay. On the other hand, it adjusts the axial velocity profile, resulting in an obvious frictional effect. Furthermore, the tidal elevation and velocities are more sensitive to the magnitude of the eddy viscosity near the bottom than the structure in the upper water layer.

NUMERICAL SOLUTION FOR TIDAL FLOW IN OPENING CHANNEL USING COMBINED MACCORMACK-FINITE ANALYSIS METHOD

A new numerical scheme for solving the tidal flow in an opening channel using the advective-diffusion shallow-water equations as the governing equations is proposed based on the combination of the MacCormack and the finite analysis methods. In the present scheme, the finite analysis method is used to discretize the momentum equation and the MacCormack technique is used to discretize the continuity equation in a single grid system. The matrix of the discretized momentum equation is characterized by predominantly main diagonal elements, which ensures favorable convergence and stability for the numerical simulation by the combined method. To verify the present method, hydraulics simulation is carried out for a section down mainstream of the Huangpu River. The computational results agree with the measured data. By use of orthogonal curvilinear coordinate system, the methods can be easily extended to the numerical simulation of the tidal flow in a tortuous channel.

A REAL-TIME MATHEMATICAL MODEL FOR TWO DIMENSIONAL TIDAL FLOW AND WATER QUALITY

A real-time mathematical model for two dimensional tidal flow and water quality is presented in this paper. The control-volume-based-finite-difference method and the 'power interpolation distribution' advocated by Patankar [4] have been employed, and new boundary condition for tidal flow is recommended. The model is un- conditionally stable and convergent, and able to deal with irregular estuarine topography and movable boundary problems. Practical application of the model is illustrated by an example for the Swatou Bay. A fair agreement be- tween the values measured and computed demonstrates the validity of the model developed.

AN IMPROVED EFFICIENT SEMI-IMPLICIT FINITE ELEMENT SCHEME FOR TWO-DIMENSIONAL TIDAL FLOW COMPUTATIONS

In a recent paper, an efficient semi-implicit finite element scheme for 2-dimensional tidal flow computations is proposed. In that scheme, each term of the governing equations, rather than each dependent variable, is ex- panded in terms of the unknown nodal values. Simpson's rule ix used for numerical integration to make the mass matrix diagonal. The friction terms are represented semi-implicitly to improve stability, but no additional compu- tational effort is required. The shortcomings of this scheme are that the time-stepping scheme is only first-order ae- curate and artificial smoothing is required to control the numerical noise. In this paper, the previous scheme is im- proved by including the eddy viscosity terms in the governing equations to replace artificial smoothing in noise con- trol and the time-stepping scheme is modified to make it second-order accurate. These improvements can be achieved with only a slight increase in computational effort. The test cases used previously to validate the former scheme are again employed to test the present scheme.

Numerical Simulation of Flow Field in Tidal Estuary Using Body-Fitted Coordinate System

On the basis of the physical mechanism, a body-fitted coordinate system is developed. By using this system the boundaries in simulation and in real are fitted well, and simulation with great accuracy is achieved. A computation example indicates that compared to traditional two-dimensional computation methods, the body-fitted simulation has an advantange of better coincidence with the real and can be adopted in simulating flow fields in tidal estuaries.

Numerical Investigation of Flow Motion and Performance of A Horizontal Axis Tidal Turbine Subjected to A Steady Current

Horizontal axis tidal turbines have attracted more and more attentions nowadays, because of their convenience and low expense in construction and high efficiency in extracting tidal energy. The present study numerically investigates the flow motion and performance of a horizontal axis tidal turbine with a supporting vertical cylinder under steady current. In the numerical model, the continuous equation and incompressible Reynolds-averaged Navier-Stokes equations are solved, and the volume of fluid method is employed to track free surface motion. The RNG k-ε model is adopted to calculate turbulence transport while the fractional area/volume obstacle representation method is used to describe turbine characteristics and movement. The effects of installation elevation of tidal turbine and inlet velocity on the water elevation, and current velocity, rotating speed and resultant force on turbine are discussed. Based on the comparison of the numerical results, a better understanding of flow structure around horizontal axis tidal turbine and turbine performance is achieved.

Observed characteristics of tidal currents and mean flow in the northern Yellow Sea

Several bottom-mounted Acoustic Doppler Current Profiler (ADCP) moorings were deployed in the northern Yellow Sea (NYS) during the four seasons of 2006–2007 and also the summertime of 2009. A synthesis analysis on the time-continuous records was performed to examine the characteristics and variations of tidal currents and mean flow over the observation period at these stations. Tidal currents accounted for ~75% of the total kinetic energy, with the absolute dominance of M2 constituent. Visible vertical variations of tidal flow were found on all sites, featured by the decrease of amplitude, increase of rotation rate as well as a decreasing trend of the phase for M2 component with depth. A notable exception was in the central NYS, where the maximum tidal currents occurred in the upper or middle layers (~20–40 m) instead of near the surface (<10 m). The observed mean flow was relatively weak, smaller than 15 cm/s. Velocity on the northern end of Yellow Sea Trough (YST) was characterized by low magnitude and an obvious layered structure vertically. In the Bohai Strait (BS) and the northern slope area, the currents weakened and the flow direction presented a major trend to deflect counterclockwise with depth in most observations. Summertime cyclonic circulation around the Yellow Sea Cold Water Mass (YSCWM), its intensification on the frontal zone and the Yellow Sea Warm Current (YSWC) for the winter season were all evident by our direct current measurements. However, the details of water exchange through the BS appeared partly diff erent from the traditionally-accepted pattern. The vertical diff erences of tidal and mean flow were larger in summer than that in winter, implying the influence of thermal structure to the local currents. Aff ected by the water stratification, mean flow usually reached its maximum near the thermocline in spring and summer, while showing a nearly uniform vertical distribution during winter.

NUMERICAL SIMULATION OF 2-D TIDAL FLOW AND WATER QUALITY UNDER THE CURVILINEAR COORDINATES

This paper presents a numerical method to simulate the 2-D tidal flow and water quality under the curvilinear coordinates. In order to overcome the computational difficulties in natural rivers, such as the complicated boundary figures, the great disparity between length and width of computational domain, etc. , boundary-fitted grid is used, the irregular domain in physical plane is transformed into a rectangular domain in transformed plane, and the depth-averaged momentum equations and mass equation are rewritten and discretized based on the finite volume techniques in curvilinear coordinates. Practical application of the method is illustrated by an example for the Dachangzhen Section of the Yangtze River. A fair agreement between the values measured and computed demonstrates the validity of the method developed.

Modified Saint-Venant equations for flow simulation in tidal rivers

Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the Saint-Venant equations （the SVN model） are extensively used to model tidal rivers. A force-corrected term expressed as the combination of flow velocity and the change rate of the tidal fevel was developed to represent tidal effects in the SVN model. A momentum equation incorporating with the corrected term was derived based on Newton＇s second law. By combing the modified momentum equation with the continuity equation, an improved SVN model for tidal rivers （the ISVN model） was constructed. The simulation of a tidal reach of the Qiantang River shows that the ISVN model performs better than the SVN model. It indicates that the corrected force derived for tidal effects is reasonable; the ISVN model provides an appropriate enhancement of the SVN model for flow simulation of tidal rivers.

ON THE EXCHANGE FLOW IN TIDAL RIVERS AND SHALLOW ESTUARIES

An analytic model is developed to investigate the barotropic tidally driven residual exchange flow in shallow estuaries. Ebb dominated flow in deep channel and flood dominated flow on the shoals produced by the model are consistent with some observations in tidal rivers and shallow estuaries . Analysis shows that this type of exchange flow is caused by the combined effect of nonlinearity and the lateral variation of the depth. The inward flux is mainly due to the surface elevation of the wave . A seaward residual pressure gradient has to be maintained to drive the water outward for mass balance. Since the surface elevation in an estuary has only small lateral variation , the depth integrated pressure force is mainly dependent on the depth whose value in the channel is larger than that on the shoals. As a result, theretum flow in the channel is larger than that on the shoals. An ebb-flood flow spstem is thus generated.

Three-Dimensional Tidal Model and Its Application to Numerical Simulation of Water Quality in Coastal Waters

The turbulence mechanism plays an important part in the mixing process and momentum transfer of turbulence. A three-dimensional Prandtl mixing length tidal model has been developed to simulate tidal flows and water quality. The eddy viscosities and diffusivities are computed from the Prandtl mixing length model. In order to model the water quality of an estuary or coastal area many interdependent processes need to be simulated. These may be conveniently separated into three main groups: transport and mixing processes, biochemical interaction of water quality variables and the utilization and re-cycling of nutrients by living matter. The model simulates full oxygen and nutrient balance, primary productivity and the transport, reaction mechanism and fate of pollutants over tidal time-scales. The model is applied to numerical simulation of tidal flows and water quality in Dalian Bay. The model has been calibrated against a limited data set of historical water quality observations and in general demonstrates excellent agreement with all available data.

A Vertical Two-Dimensional Model to Simulate TidalHydrodynamics in A Branched Estuary

A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The governing equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are governed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations, tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.

A Study of Eddy Viscosity Coefficient in Numerical Tidal Simulation

Based on the fluid motion equations, the physical meaning of eddy viscosity coefficient and the rationality of the Boussinesq hypothesis are discussed in this paper. The effect of the coefficient on numerical stability is analyzed briefly. A semi-enclosed rectangular sea area, with an orthogonal spur dike, is applied in a 2-D numerical model to study the effect of horizontal eddy viscosity coefficient (A(H)), The computed result shows that A(H) has little influence on the tidal level and averaged flow velocity, but has obvious influence on the intensity and the range of return flow around near the spur dike. Correspondingly, a wind-driven current pool and an annular current are applied in a 3-D numerical model respectively to study the effect of vertical eddy viscosity coefficient (A(V)). The computed result shows that the absolute value of A(V) is inversely proportional to that of horizontal velocity, and the vertical gradient value of A(V) determines the vertical distribution of horizontal velocity, The distribution form of A(V) is theoretically recommended as a parabolic type, of which the maximum value appears at 0.5 H.

Variations in tidal currents and suspended sediment concentration of the upper part of the North Channel of Changjiang Estuary over the past 10 years

The tidal current duration （TCD） and velocity （TCV） and suspended sediment concentration （SSC） were measured in the dry season in December, 2011 and in the flood season in June, 2012 at the upper part of the North Channel of Changjiang Estuary. They were assimilated with the measured data in 2003, 2004, 2006 and 2007, using the tidal range＇s proportion conversion. Variations in TCD and TCV, preferential flow and SSC have been calculated. Influences of typical engineering projects such as Qingcaosha fresh water reservoir, Yangtze River Bridge, and land reclamation on the ebb and flood TCD, TCV and SSC in the North Channel for the last 10 years are discussed. The results show that： （1） currently, in the upper part of North Channel, the ebb tide dominates; after the construction of the typical projects, ebb TCD and TCV tends to be larger and the vertical average ebb and flood SSC decrease during the flood season while SSC increases during the dry season; （2） changes in the vertical average TCV are mainly contributed by seasonal runoff variation during the flood season, which is larger in the flood season than that in the dry season; the controlling parameters of increasing ebb TCD and TCV are those large-scale engineering projects in the North Channel; variation in SSC may result mainly from the reduction of basin annual sediment loads, large-scale nearshore projects and so on.

A New Wetting and Drying Method for Moving Boundary in Shallow Water Flow Models

To deal with the moving boundary hydrodynamic problems of the tidal flats in shallow water flow models, a new wetting and drying （WD） method is proposed. In the new method, a ＂predicted water depth＂ is evaluated explicitly based on the simplified shallow water equations and used to determine the status （wet or dry） together with the direction of flow. Compared with previous WD method, besides the water elevation, more factors, such as the flow velocity and the surface shear stress, are taken into account in the new method to determine the moving boundary. In addition, a formula is deduced to determine the threshold, as critical water depth, which needs to be preset before simulations. The new WD method is tested with five cases including three 1D ones and two 2D ones. The results show that the new WD method can simulate the wetting and drying process, in beth typical and practical cases, with smooth manner and achieves effective estimation of the retention volume at shallow water body.

Expiratory Flow Limitation and Its Relation to Dyspnea and Lung Hyperinflation in Patients with Chronic Obstructive Pulmonary Disease: Analysis Using the Forced Expiratory Flow-Volume Curve and Critique

Background: Tidal expiratory flow limitation (tEFL) is defined as absence of increase in air flow during forced expiration compared to tidal breathing and is related to dyspnea at rest and minimal exertion in patients with chronic airflow limitation (CAL). Tidal EFL has not been expressed as a continuous variable (0% - 100%) in previous analyses. Objective: To relate the magnitude of tEFL to spirometric values and Modified Medical Research Council (MMRC) score and Asthma Control Test (ACT). Methods: Tidal EFL was computed as percent of the tidal volume (0% - 100%) spanned (intersected) by the forced expiratory-volume curve. Results: Of 353 patients screened, 192 (114 M, 78 F) patients (136 with COPD, 56 with asthma) had CAL. Overall characteristics: (mean ± SD) age 59 ± 11 years, BMI 28 ± 7, FVC (% pred) 85 ± 20, FEV1 (% pred) 66 ± 21, FEV1/FVC 55% ± 10%, RV (% pred) 147 ± 42. Tidal EFL in patients with tEFL was 53% ± 39%. Using univariate analysis, strongest correlations were between tEFL and FVC and between tEFL and RV in patients with BMI < 30 kg/m2. In patients with nonreversible CAL, tEFL was positively associated with increasing MMRC, negatively with spirometric measurements, and positively with RV/TLC. In asthmatics, ACT scores were higher in patients with mean BMI ≥ 28 kg/m2 (p < 0.00014) and RV/TLC values > 40% (p < 0.03). Conclusions: Dyspnea is strongly associated with tEFL and lung function, particularly in patients with nonreversible CAL. Air trapping and BMI contribute to tEFL.