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1.
The numerical analysis of the stationary field of current velocity on the upper boundary of the bottom boundary layer in the Barents Sea is performed on the basis of a simplified model taking into account the fields of wind velocity and density of water for the principal periods of the seasonal cycle and the bottom topography. The analysis is based on the climatic BarKode database and the data on the wind velocity over the Barents Sea for the last 50 yr. The numerical results demonstrate that the field of bottom currents is fairly nonuniform and the current velocities vary from several fractions of 1 cm/sec to 5 cm/sec in the zones with noticeable slopes of the bottom. The estimates of the thickness of the bottom boundary layer are obtained for the constant coefficient of bottom friction C f = 0.04. In the major part of the water area of the Barents Sea, the thickness of the bottom boundary layer is close to 1 m. In the regions with significant slopes of the bottom, it increases to 2–2.5 m and, in the two zones of intensification of the bottom currents, becomes as large as 5 m. The maximum estimate of the coefficient of turbulent viscosity is close to 5 cm2/sec. The mean value of the coefficient of vertical density diffusion K S is equal to 2.34 cm2/sec and its standard deviation is equal to 1.52 cm2/sec. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 31–49, September–October, 2007.  相似文献   

2.
In the Boussinesq approximation, for topographic waves entrapped by a sloping bottom, we determine mean currents induced by a wave due to nonlinearity with regard for turbulent viscosity and diffusion. We determine the thickness of the bottom boundary layer, the vertical turbulent exchange coefficients, and turbulent stresses on the upper boundary of the boundary layer depending on the parameters of the wave. In the diffusion approximation, we find the vertical distribution of the concentration of sediments suspended by the wave and the flow rates of sediments along and perpendicular to the isobaths. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 13–24, September–October, 2005.  相似文献   

3.
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.  相似文献   

4.
The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion (A wb) at the top of the boundary layer. A wb, in turn, is normally derived from linear wave theory by \fracU\textwbT\textw2p \frac{{{U_{\text{wb}}}{T_{\text{w}}}}}{{2\pi }} , where U wb is the maximum water particle velocity measured at the top of the boundary layer and T w is the wave period. However, it is shown here that A wb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of U wb, T w, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549–560, (2010).  相似文献   

5.
An analytical theory which describes the motion in a turbulent wave boundary layer near a rough sea bottom by using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the sea bottom. In the outer layer the eddy viscosity is taken as a constant. The mean velocity and shear stress profiles, the bottom shear stress and the bottom friction coefficient are presented, and comparisons are made with experimental results.  相似文献   

6.
In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary,and to discretize the Green’s integral expression based on Laplace equation.The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface.The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step.In m-time iteration within the computational process of time step(n-1)Δt to nΔt,the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration.Thus,an improved tracking mode of nonlinear wave surface is established,and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.  相似文献   

7.
A large number of studies have been done dealing with sinusoidal wave boundary layers in the past. However, ocean waves often have a strong asymmetric shape especially in shallow water, and net of sediment movement occurs. It is envisaged that bottom shear stress and sediment transport behaviors influenced by the effect of asymmetry are different from those in sinusoidal waves. Characteristics of the turbulent boundary layer under breaking waves (saw-tooth) are investigated and described through both laboratory and numerical experiments. A new calculation method for bottom shear stress based on velocity and acceleration terms, theoretical phase difference, φ and the acceleration coefficient, ac expressing the wave skew-ness effect for saw-tooth waves is proposed. The acceleration coefficient was determined empirically from both experimental and baseline k–ω model results. The new calculation has shown better agreement with the experimental data along a wave cycle for all saw-tooth wave cases compared by other existing methods. It was further applied into sediment transport rate calculation induced by skew waves. Sediment transport rate was formulated by using the existing sheet flow sediment transport rate data under skew waves by Watanabe and Sato [Watanabe, A. and Sato, S., 2004. A sheet-flow transport rate formula for asymmetric, forward-leaning waves and currents. Proc. of 29th ICCE, ASCE, pp. 1703–1714.]. Moreover, the characteristics of the net sediment transport were also examined and a good agreement between the proposed method and experimental data has been found.  相似文献   

8.
A simple numerical model, based on the Reynolds stress equations and k–ε turbulence closure scheme, is developed for the coastal wave and current bottom boundary layer. The current friction velocity is introduced to account for the effect of currents on waves. The implicit Crank–Nicolson finite difference method discretizes the governing equations. Vertical changing step grids with the constant ratio for two adjacent spatial steps are used together with the equal time steps in the modeling. Vertical profiles of mean current velocity and wave velocity amplitude are obtained. These modeled results are compared with the laboratory experimental data of Van Doorn [1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands]. It has been shown that modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands) mean velocity profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands) wave velocity amplitude profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled wave velocity amplitudes are in good agreement with the laboratory experimental data of Van Doorn [1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands].  相似文献   

9.
A coupled wave–tide–surge model has been developed in this study in order to investigate the effect of the interactions among tides, storm surges, and wind waves. The coupled model is based on the synchronous dynamic coupling of a third-generation wave model, WAM cycle 4, and the two-dimensional tide–surge model. The surface stress, which is generated by interactions between wind and wave, is calculated by using the WAM model directly based on an analytical approximation of the results using the quasi-linear theory of wave generation. The changes in bottom friction are created by the interactions between waves and currents and calculated by using simplified bottom boundary layer model. In consequence, the combined wave–current-induced bottom velocity and effective bottom drag coefficient were increased in the shallow waters during the strong storm conditions.  相似文献   

10.
As known fromin situ observations, inhomogeneities of flows and of the atmospheric boundary layer produce variations of the intensity of wind wave breaking. A relevant phenomenological model is suggested here, describingin situ data on the breaking of waves in the presence of internal waves. The response of the wave breaking to the flow's inhomogeneity enhances with the growth of its spatial or temporal scale. For the mesoscale (10–100 km) inhomogeneities, the model is essentially simplified—wave breakings depict the local energy inputs to wind waves. The model allows us to compute currents of various type in the wave breaking intensity field. The results may have practical implications, in terms of remote sensing of the ocean. Translated by Vladimir A. Puchkin.  相似文献   

11.
The vertical structure of the M2 tidal current in the Yellow Sea is analyzed from data acquired using an acoustic Doppler current profiler. The observed vertical profiles of the M2 tidal current are decomposed into two rotating components of counter-clockwise and clockwise, and restructured using a simple one-point model with a constant vertical eddy viscosity. The analyzed results show that the internal fictional effect dominates the vertical structure of the tidal current in the bottom boundary layer. In the Yellow Sea, the effect of the bottom friction reduces the current speed by about 20–40% and induces the bottom phase advance by about 15–50 minutes. In the shallower coastal regions, the effects of bottom topography are more prominent on the vertical structure of tidal currents. The vertical profile of the tidal current in summer, when the water column is strongly stratified, is disturbed near the pycnocline layer. The stratification significantly influences the vertical shear and distinct seasonal variation of the tidal current.  相似文献   

12.
A coupled wave–tide–surge model has been established in this study in order to investigate the effect of tides, storm surges, and wind waves interactions during a winter monsoon on November 1983 in the Yellow Sea. The coupled model is based on the synchronous dynamic coupling of a third-generation wave model, WAM-Cycle 4, and the two-dimensional tide–surge model. The surface stress generated by interactions between wind and waves is calculated using the WAM-Cycle 4 directly based on an analytical approximation of the results obtained from the quasi-linear theory of wave generation. The changes of bottom friction factor generated by waves and current interactions are calculated by using simplified bottom boundary layer model. The model simulations showed that bottom velocity and effective bottom drag coefficient induced by combination of wave and current were increased in shallow waters of up to 50 m in the Yellow Sea during the wintertime strong storm conditions.  相似文献   

13.
We perform the experimental verification of the applicability of the theory of similarity to the wave boundary layer and the assessment of wave-induced perturbations of the air flow depending on various conditions of stratification of the atmosphere and the state of the sea. The measurements were carried out from a stationary platform located in the coastal part of the Black Sea. The experimental procedure is based on the simultaneous measurements of the profile and fluctuations of the wind speed at 5–6 levels in the 1.3–21-m layer, the elevations of the sea surface, the directions of waves and winds, and the mean gradients of temperature and humidity of air. The structure of the boundary layer in the region of measurements depends on the direction of the wind. For weak and moderate onshore winds (< 9 m/sec), the approximate balance is preserved between the production and dissipation of turbulent energy in the cases of unstable and neutral stratification. On the average, the estimates of friction velocity according to the profiles are higher than the dissipative estimates by 10% mainly due to the deficiency of dissipation near the surface. For the offshore wind, the structure of the boundary layer abruptly changes and is determined not by the local parameters but by strong turbulent eddies formed over the dry land. The intensity of low-frequency turbulent fluctuations and the gradient of wind velocity near the surface in the coastal zone are 1.5–2 times higher than for the open sea. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 42–61, May–June, 2007.  相似文献   

14.
The results of direct numerical simulations of the boundary layer generated at the bottom of a solitary wave are described. The numerical results, which agree with the laboratory measurements of Sumer et al. (2010) show that the flow regime in the boundary layer can be laminar, laminar with coherent vortices and turbulent. The average velocity and bottom shear stress are computed and the results obtained show that the logarithmic law can approximate the velocity profile only in a restricted range of the parameters and at particular phases of the wave cycle. Moreover, the maximum value of the bottom shear stress is found to depend on the dimensionless wave height only, while the minimum (negative) value depends also on the dimensionless boundary layer thickness. Diagrams and simple formulae are proposed to evaluate the minimum and maximum bottom shear stresses and their phase shift with respect to the wave crest.  相似文献   

15.
On the basis of the data of field measurements, we present the results of numerical analysis of the intensity of vertical turbulent exchange in stratified layers of the Black Sea in the region of the shelf–continental-slope boundary depending on the local stratification. The experiments were carried out within the framework of the GEF/BSERP and Black Sea-2004 international projects. The data were obtained by using a probing version of the Sigma-1 measuring complex. In processing the data of measurements, we apply a procedure of evaluation of the coefficient of vertical turbulent diffusion depending on the external conditions based on the analysis of the spectra of the gradient of temperature fluctuations. For the two studied regions of the shelf, the coefficients of turbulent exchange turn out to be much higher (by about an order of magnitude) than for the open sea under similar conditions. This can be explained by the specific features of the bottom topography affecting the dynamics of quasiinertial waves playing to role of the main causes of small-scale mixing and vertical diffusion. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 14–24, November–December, 2008.  相似文献   

16.
To find variations in the dynamics of the surface M 2 tide in the White Sea induced by the spatially inhomogeneity of the resistance coefficient, we use a modified version of the QUODDY-4 three-dimensional finite-element hydrostatic model. This version differs from the original version in that it has a module introduced to calculate the resistance coefficient in the bottom boundary layer (BBL). The resistance coefficient is found from resistance laws for an oscillating rotating turbulent BBL over hydrodynamically rough and partially rough (smoothly rough) underlying surfaces describing the dependence of the resistance coefficient and other integral characteristics of resistance on dimensionless similarity parameters: the sea-bottom Rossby number Ro, the streaming Reynolds number Re, and the relative (normalized to tidal frequency) inertial frequency f/σ. The use of spatial inhomogeneity of the resistance coefficient was shown not to lead to considerable changes in tidal characteristics. The values of these characteristics are several times larger than the instrumental measurement errors for the level and velocity but less than the errors in their calculation.  相似文献   

17.
The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.  相似文献   

18.
Using the micro-structure profiler, TurboMAP, large values for the turbulent energy dissipation rate ε were found just above the bottom of the shelf and around the thermocline near the continental shelf break in the East China Sea. The values found above the bottom are produced by the bottom stress due to tidal currents, resulting in a distinct bottom mixed layer where the vertical eddy diffusivity Kz is also large. Distinct maxima in the values of ε detected around the thermocline are located at the depth of the fine-scale shear maxima detected with the moored ADCP. The vertical profiles of ε were compared with those of the current velocity, and it was found that the maxima in ε appear to correspond to those of the shear with fine scale. The magnitude of the observed ε coincided approximately with the ε calculated from the fine-scale shear and the buoyancy frequency according to the parameterization proposed by Gregg (1989), if the large-scale mean shear caused by the Kuroshio is subtracted. However, it is not clear whether the parameterization for the internal wave fields in the open ocean is applicable to the estimation of ε in the shelf break. Whereas the most predominant value of ε was found just above the bottom and around the thermocline, the maxima of ε could be found in the internal area. They could have been caused by the propagation of the vertically high wave number internal tides along the characteristic ray.  相似文献   

19.
To describe the phenomenon of cold surges in the Black Sea in winter, we study the problem of atmospheric response to a local heat source on the surface in two simple formulations. In the shallow-water model, the planetary boundary layer of the atmosphere is homogeneous with variable upper bound. In the second model, the boundary layer has a constant thickness and its stratification is homogeneous. In the one-dimensional problem, for a constant wind blowing perpendicularly to the sea coast, the atmospheric response is determined by a single dimensionless parameter called the Froude number. Depending on its value, there are two possible different modes of the response. The range Fr < 1 (subcritical mode) corresponds to gentle winds, strong stratifications, thick boundary layers, and high velocities of inertial gravitational waves. The range Fr > 1 (supercritical mode) corresponds to strong winds, weak stratifications, thin boundary layers, and low wave velocities. In the two-dimensional problem for a round sea, there are four qualitatively different types of response depending on the combination of two dimensionless parameters: the Froude number and the ratio of the radius of the sea to the radius of deformation. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 3–22, September–October, 2008.  相似文献   

20.
Hydrographic data show that the meridional deep current at 47°N is weak and southward in northeastern North Pacific; the strong northward current expected for an upwelling in a flat-bottom ocean is absent. This may imply that the eastward-rising bottom slope in the Northeast Pacific Basin contributes to the overturning circulation. After analysis of observational data, we examine the bottom-slope effect using models in which deep water enters the lower deep layer, upwells to the upper deep layer, and exits laterally. The analytical model is based on geostrophic hydrostatic balance, Sverdrup relation, and vertical advection–diffusion balance of density, and incorporates a small bottom slope and an eastward-increasing upwelling. Due to the sloping bottom, current in the lower deep layer intensifies bottomward, and the intensification is weaker for larger vertical eddy diffusivity (K V), weaker stratification, and smaller eastward increase in upwelling. Varying the value of K V changes the vertical structure and direction of the current; the current is more barotropic and flows further eastward as K V increases. The eastward current is reproduced with the numerical model that incorporates the realistic bottom-slope gradient and includes boundary currents. The interior current flows eastward primarily, runs up the bottom slope, and produces an upwelling. The eastward current has a realistic volume transport that is similar to the net inflow, unlike the large northward current for a flat bottom. The upwelling water in the upper deep layer flows southward and then westward in the southern region, although it may partly upwell further into the intermediate layer.  相似文献   

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