Experimental study on internal waves in a stratified shear flow

This paper describes experiments on interfacial phenomena in a stratified shear flow having a sharp velocity shear at a density interface. The interface was visualized in vertical cross-section using dye, and the flow pattern was traced using aluminum powder. Two kinds of internal waves with different phase velocities and wave profiles were observed. They are here named p(positive)-waves and n(negative)-waves, respectively. By means of a two-dimensional visualization technique, the following facts have been confirmed regarding these waves. (1) The two kinds of waves propagate in the opposite direction relative to a system moving with the mean velocity at the interface, and their dispersion relations approximately agree with the two solutions of interfacial waves in a two-layer system of a linear basic shear flow. (2) The p-wave has sharp crests and flat troughs, and the n-wave has the reverse of this. This difference in wave profile is due to the finite amplitude effect. (3) Phase velocity of each wave lies within the range of the mean velocity profile, so that a critical layer exists and each wave has a “cat's eye” flow pattern in the vicinity of the critical layer, when observed in a system moving with the phase velocity. Consequently, these two waves are symmetrical with respect to the interface. The mechanisms of generation of these waves, and the entrainment process are discussed. It is inferred that when the “cat's eye” flow pattern is distorted and a stagnation point approaches the interface, entrainment in the form of a stretched wisp from the lower to the upper layer occurs for the p-wave, and from the upper to the lower layer for the n-wave.     

Shear Flow Dispersion Under Wave and Current

The longitudinal dispersion of solute in open channel flow with short period progressive waves is investigated. The waves induce second order drift velocity in the direction of propagation and enhance the mixing process in concurrent direction. The 1-D wave-period-averaged dispersion equation is derived and an expression for the wave-current induced longitudinal dispersion coefficient (WCLDC) is proposed based on Fischer's expression (1979) for dispersion in unidirectional flow. The result shows that the effect of waves on dispersion is mainly due to the cross-sectional variation of the drift velocity. Furthermore, to obtain a more practical expression of the WCLDC, the longitudinal dispersion coefficient due to Seo and Cheong (1998) is modified to incluee the effect of drift velocity. Laboratory experiments have been conducted to verify the proposed expression. The experimental results, together with dimensional analysis, show that the wave effect can be reflected by the ratio between the wave amplitude and wave period. A comparative study between the cases with and without waves demonstrates that the magnitude of the longitudinal dispersion coefficient is increased under the presence of waves.     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

生态空心块体水沙动力效应研究

生态空心块体是一种兼有调控水流与生态修复功能的工程结构物,在海堤、丁坝等近海工程中被广泛应用.通过室内水槽试验,设计多种来水来沙工况,研究生态空心块体与柔性植被共同影响下的水沙动力特性,重点探究生态空心块体内的水沙动力效应.结果 表明:生态空心块体组成的坝体结构缓流效果显著,坝体内外侧水流流速分布差异明显,坝体内部的水...     

The Effects of Vegetation on Longitudinal Dispersion

The influence of vegetation on longitudinal dispersion was studied in a laboratory flume for three flow velocities and three plant population densities. Rhodamine was injected continuously upstream of the dowel array and sampled at two positions downstream. The dispersion coefficient was estimated by fitting the concentration time series at the final downstream station. Enhanced turbulence as well as diminished vertical shear resulted in a lower dispersion coefficient when the plants were present. In addition, recirculation zones behind each stem trapped and delayed a fraction of the mass, enhancing the longitudinal dispersion and creating significant frontal delay.     

Simulation of a 3D submerged jet flow around a pile

The submerged 3D turbulent jet flow behavior around a pile on a rigid bed and on a scoured bed was studied experimentally and numerically. ADV was used to obtain the jet velocity distributions and Realizable k–ε turbulence model was used for the prediction of flow field around a pile. The jet flow area was three-dimensional and thus numerical model was a three-dimensional model. The numerical results were used to predict the velocity close to the pile and bed shear stress on the bed. In general, the results indicated that the flow field was also in agreement with the findings of previous experiments in literature and the related principles in the subject area. The experimental results demonstrated that Acoustic Doppler Velocimeter (ADV) measurements were almost identical with the Realizable k–ε turbulence model results for turbulence intensity I=10%.     

The effect of standing biomass on flow velocity and turbulence in Spartina alterniflora canopies

Plant-flow interactions on the surface of tidal wetlands result in flow characteristics that are profoundly different from non-vegetated flows. Reductions in mean flow velocity and turbulence, especially the vertical components, limit vertical mixing and may impact a wide range of processes including geochemical exchanges at the sediment water interface, larval recruitment and dispersion, and sediment deposition and retention. The goal of this paper is to quantify horizontal and vertical components of velocity, turbulence intensity and total turbulent kinetic energy in Spartina alterniflora canopies in southeastern North Carolina and to relate flow characteristics to particulate transport on the marsh surface. Another aim of this paper is to assess the extent to which the distribution of standing biomass affects mean flow and turbulence by comparing S. alterniflora data to other canopy types and through a series of canopy manipulations which altered canopy height and stem densities.The results of this study indicate that flow velocity, turbulence intensity, and total turbulent kinetic energy (TKE) are significantly reduced within the vegetated canopy and that this reduction is inversely related to the amount of biomass present in the water column. Within the canopy, approximately 50% of the initial mean velocity and TKE is reduced within 5 m of the canopy edge. Within the canopy, mean velocity and TKE_horiz usually exceeded vertical velocity or TKE_vert and the vertical components of flow were attenuated more strongly than the horizontal. These results suggest that within the vegetation, turbulence contributes more to lateral advection than to vertical mixing. As a result, total suspended solid concentrations were shown to decrease logarithmically with distance from the canopy edge and to decrease at a faster rate in more densely vegetated regions of the canopy (i.e. lower TKE_vert) as compared to areas of sparser vegetation (i.e. higher TKE_vert).     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅰ. Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models, i. e. , the problem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal waters at high radar frequency bands （ X-band and C-band）, the impact of the ocean surface mixed layer turbulence and the significance of strat- ified oceanic model on SAR remote sensing of internal solitary waves are proposed. In the north of the South China Sea by utilizing some observed data of background field the nonlinearity coefficient, the dispersion coefficient, the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately. Through simulations of internal tide transfor- mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of internal wave field are obtained. The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m, but the maximum current speeds take place at depth 20 m in this area of the sea （about 20°30＇N, 114°E） in August. It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation. The obtained results provide the possibility for the simulation of SAR signatures of internal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

The effect of oscillations on the flow patterns near a simulated bed

This work investigates the effect of oscillations on the flow near a simulated bed and their impact on erosion. Those oscillations were generated by using wavy lids at the top of a small toroidal channel. Particular attention is dedicated to their influence on the velocity field and turbulence near the bed. The experiments were made in a mini circular flume using a 2D LDA system. It was concluded that such oscillations induce non negligible shear stresses in the flow main stream, becoming more important to the dispersion of entrained matter into the flow than to the initiation of the erosion process.     

Investigation of the Dependence of the Space Structure and Phase Characteristics of the First-Mode Internal Waves in the Atlantic Ocean on the Hydrological Conditions

By using the linear theory of internal waves in a continuously stratified ideal incompressible liquid of finite depth and hydrological data, we study the dispersion properties and space structure of the vertical velocity of the first mode of free internal waves in the Atlantic Ocean. The dependence of the characteristics of waves on the hydrological structure of waters is analyzed. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 3–10, July–August, 2005.     

Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part II: Cnoidal waves

Vortex generation and evolution due to flow separation around a submerged rectangular obstacle under incoming cnoidal waves is investigated both experimentally and numerically. The Particle Image Velocimetry (PIV) technique is used in the measurement. Based on the PIV data, a characteristic velocity, phrased in terms of incoming wave height, phase speed, dimension of the obstacle, and a local Reynolds number are proposed to describe the intensity of vortex. The numerical model, which solves the two dimensional Reynolds Averaged Navier Stokes (RANS) equations, is used to further study the effects of wave period on the vortex intensity. Measurements for the mean and turbulent velocity fields further indicate that the time history of the intensity of fluid turbulence is closely related to that of the vortex intensity.     

Effect of vertically logarithmic steady currents on shallow surface waves

The combined wave-current flow has been solved by researchers by assuming wave over either depthwise constant or linear current profile. Some complicated nonlinear current profiles have also been considered to simulate various shear currents. We consider a nonlinear current vertically logarithmic in nature and examine its interaction with a periodic surface wave. The Navier-Stokes equations for incompressible flow are solved for the current part and by using periodic boundary conditions. The effect of logarithmic current on wave components is assessed. The corresponding celerity and dispersion equation yields a close-form solution for the shallow-wave approximation. Several comparative trends between wave-only, wave with log current, and wave with constant current for the wave following/opposing these currents have been discussed. The flow properties of the first order are presented which can be applicable to the real inland and coastal flows, where progressive waves are ubiquitous over a depthwise logarithmic current. The work is further extended to the second-order semiempirical wave component by using past experimental data on the wave spectrum of combined flow. Published in Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 20–40, May–June, 2008.     

Observations of a Kelvin-Helmholtz Billow in the Ocean

We identified a Kelvin-Helmholtz billow from vertical turbulence velocity and instantaneous heat flux signals obtained from airfoil shear probes and thermistors mounted on a research submarine. The vertical turbulence velocity indicates that the horizontal scale of the billow was about 3.5 m. The spectral slope of the vertical turbulence velocity component is close to −2, revealing the flow is two-dimensional. We show a remarkable agreement between the length scales of the observed billow and those computed from direct numerical simulations based on similar conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stationary waves in the flow of a homogeneous fluid with vertical shear of the velocity

A plane problem of free stationary gravitational waves in a horizontal current with vertical shear of the velocity is studied in the linear statement. The determination of the parameters of waves is reduced to the solution of the Sturm–Liouville boundary-value problem. For some vertical distributions of current velocity, we obtain analytic solutions. We propose a numerical algorithm for finding the parameters of waves. On the basis of the performed analysis, we establish the possibility of existence of stationary surface waves in currents for certain ranges of the Froude number. As the Froude number decreases, the waves become shorter, which leads to a faster attenuation of waves disturbances with depth. Under the actual conditions, the waves are short and suffer the influence of shear currents only in the subsurface layer of the ocean.     

Effect of open gap in coastal forest on tsunami run-up—investigations by experiment and numerical simulation

The objective of this study is to investigate the effects of an open gap, such as a road, in a coastal forest on tsunami run-up. A numerical model based on two-dimensional nonlinear long-wave equations was developed to account for the effects of drag and turbulence induced shear forces due to the presence of vegetation. Experiments were conducted on a forest simulated with vertical cylinders by changing the gap width. The numerical model was validated in good agreement with the experimental results. The numerical model was then applied to a wide forest of Pandanus odoratissimus, a tree species that is a dominant coastal vegetation on a sand dune in South and Southeast Asia. The effect of vertical stand characteristics of P. odoratissimus with aerial roots was considered on the drag resistance. A straight open gap perpendicular to the shoreline was used to investigate the effect of gap width. As the gap width increases, the flow velocity at the end of the open gap first increases, reaches a maximum, and then decreases, while the run-up height increases monotonously. The maximum velocity in the present condition is 1.7 times the maximum velocity without a coastal forest. The effects of different gap arrangements in the forest on tsunami run-up were also investigated in this paper. The flow velocity at the end of an open gap can be reduced by a staggered arrangement.     

Study on dynamics of shear waves——Ⅰ. Scale analysis and dispersion relation

- Starting from satellite remote sensing data, the dynamical processes of shear waves occurring at the boundary between the western boundary current and the shelf slope water are studied and dynamically analyzed in this study. The average wavelength is 75 km, and the average amplitude (from crest to trough )17 km. the average phase speed 100 cms-1 for the shear waves along the north wall of the Gulf Stream to the east of Cape Hatteras measured from NOAA satellite IR (infrared ) images. The average wavelength of shear waves along the north wall of the Kuroshio Current is 57 km, and the average amplitude 17 km. For the shear waves occurring along the west wall of the Gulf Stream to the south of Cape Hatteras, the average wavelength is 131 km, and the average amplitude 33 km measured from Seasat SAR (synthetic aperture radar )images. The time for one cycle of shear wave event is about one week.In order to explore the dynamical mechanisms of shear waves, we solved the vorticity equation for a stratified flu     

Turbulent perturbations of velocity in the conwy estuary

Field measurements of the vertical and horizontal components of fluid velocity 0·43 m above the bed have been made with an electromagnetic flowmeter in a partially mixed reach of the Conwy estuary for parts of a flood and an ebb tide. The turbulent mean velocity and density fields showed different effects for flood and ebb tides caused by the interaction of shear and the longitudinal density gradient. The turbulent velocity parameters were generally dominated by bed-generated turbulence effects, but significant longer period contributions attributed to the shear-density interactions were detected. The shear-stress measurements made by two independent methods showed good agreement. The results generally show good agreement with previous less complete data. The use of the Richardson number to quantify vertical stability needs further consideration for partially mixed estuarine flows.     

A note on flow structure in the Great Ouse estuary

Field measurements of vertical profiles of velocity and salinity along with turbulence measurements have been used to examine the effect of density gradients on the flow structure in the Great Ouse estuary. During the flood tide shear and longitudinal density gradients cause well mixed conditions in the lower part of the water column. In the upper part of the water column secondary flow effects induced by transverse density gradients, and acceleration effects can contribute to the formation of stable vertical density gradients. On the ebb tide the vertical density gradient appears to be the dominant factor which determines the structure of the flow. The velocity and shear stress data show the evidence of large scale motions which are consistent with the postulated flood and ebb flow structures.     

Effect of the kelp Laminaria hyperborea upon sand dune erosion and water particle velocities

This paper presents a set of results from a laboratory study on water wave propagation above submerged vegetation growing in the surf zone and the effect of submerged vegetation on dune erosion. The study has focused on the kelp Laminaria hyperborea. The reason is that this kelp is commercially harvested along the Norwegian coast and there is a need to obtain better knowledge on the possible consequences of this harvesting. Experiments were run with irregular waves over a sloping bottom, and a kelp field was simulated by 5000 artificial kelp plants in a 1:10 scale. The experiments primarily focused on the effect of kelp upon erosion of a sand dune, wave damping and water velocities. It was found that the water level is a very important factor to the degree of dune erosion, while the kelp has only a minor effect. The kelp does, however, cause significant wave damping and the degree of wave breaking is reduced. It was also found that the kelp modifies the water velocity profile. In a region above the kelp canopy layer, the time-averaged water velocity was shoreward, while the seaward undertow was confined to a region higher up in the water column.