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1.

Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.

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2.
Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.  相似文献   

3.
Wave climate simulation for southern region of the South China Sea   总被引:2,自引:0,他引:2  
This study investigates long-term variability and wave characteristic trends in the southern region of the South China Sea (SCS). We implemented the state-of-the art WAVEWATCH III spectral wave model to simulate a 31-year wave hindcast. The simulation results were used to assess the inter-annual variability and long-term changes in the SCS wave climate for the period 1979 to 2009. The model was forced with Climate Forecast System Reanalysis winds and validated against altimeter data and limited available measurements from an Acoustic Wave and Current recorder located offshore of Terengganu, Malaysia. The mean annual significant wave height and peak wave period indicate the occurrence of higher wave heights and wave periods in the central SCS and lower in the Sunda shelf region. Consistent with wind patterns, the wave direction also shows southeasterly (northwesterly) waves during the summer (winter) monsoon. This detailed hindcast demonstrates strong inter-annual variability of wave heights, especially during the winter months in the SCS. Significant wave height correlated negatively with Niño3.4 index during winter, spring and autumn seasons but became positive in the summer monsoon. Such correlations correspond well with surface wind anomalies over the SCS during El Nino events. During El Niño Modoki, the summer time positive correlation extends northeastwards to cover the entire domain. Although significant positive trends were found at 95 % confidence levels during May, July and September, there is significant negative trend in December covering the Sunda shelf region. However, the trend appears to be largely influenced by large El Niño signals.  相似文献   

4.
Shear- and convection-driven turbulence coexists with wind-generated surface gravity waves in the upper ocean. The turbulent Reynolds stresses in the oceanic mixed layer can therefore interact with the shear of the wave-generated Stokes drift velocity to extract energy from the surface waves and inject it into turbulence, thus augmenting the mean shear-driven turbulence. Stokes production of turbulence kinetic energy (TKE) is difficult to measure in the field, since it requires simultaneous measurement of the turbulent stress and the Stokes drift profiles in the water column. However, it is readily inferred using second moment closure models of the oceanic mixed layer provided: (1) wave properties are available, along with the usual water mass properties, and radiative and air–sea fluxes needed to drive the mixed layer model and (2) the model skill can be assessed by comparing the model results against the observed dissipation rates of TKE. Comprehensive measurements made during the Reynolds 2002 campaign in the Baltic Sea have made the estimation of Stokes production possible, and in this paper, we report on the effort and the conclusions reached. Measurements of air–sea exchange parameters and water mass properties during the campaign allowed a mixed layer model to be run and the turbulent stress in the water column to be inferred. Simultaneous wave spectrum measurements enabled Stokes drift profile to be deduced and wave breaking to be included in the model run, and the Stokes production of TKE in the water column estimated. Direct measurements of the TKE dissipation rate from an upward traversing microstructure profiler were used to assure that the model could reproduce the turbulent dissipation rate in the water column. The model results indicate that the Stokes production of TKE in the mixed layer is of the same order of magnitude as the shear production and must therefore be included in mixed layer models.  相似文献   

5.
Wave climate plays an important role in the air-sea interaction over marginal seas. Extreme wave height provides fundamental information for various ocean engineering practices, such as hazard mitigation, coastal structure design, and risk assessment. In this paper, we implement a third generation wave model and conduct a high-resolution wave hindcast over the East China Sea to reconstruct a 15-year wave field from 1988 to 2002 for derivation of monthly mean wave parameters and analysis of extreme wave conditions. The numerical results of the wave field are validated through comparison with satellite altimetry measurements, low-resolution reanalysis, and the ocean wave buoy record. The monthly averaged wave height and wave period show seasonal variation and refined spatial patterns of surface waves in the East China Sea. The climatological significant wave height and mean wave period decrease from the open ocean in the southeast toward the continental area in the northwest, with the pattern generally following the bathymetry. Extreme analysis on the significant wave height at the buoy station indicates the hindcast data underestimate the extreme values relative to the observations. The spatial pattern of extreme wave height shows single peak emerges at the southwest of Ryukyu Island although a wind forcing with multi-core structure at the extreme is applied.  相似文献   

6.
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.  相似文献   

7.
A mesoscale model has been applied to calculate climatological means of the surface wind. A reliable average requires more than 40 model runs, which are differentiated by the direction and speed of the geostrophic wind under the assumption of neutral stratification. The frequency distributions of the geostrophic wind have been taken from observations of the 850-hPa winds at the radiosonde station in Prague for a 10-year period. The simulation results have been averaged over all sectors and speed classes of the geostrophic wind according to their frequencies. A comparison of the calculated mean wind speeds with observed ones shows deviations of about 0.4 ms−1 outside the mountains. The representation of steep topography and isolated mountains on the basis of a 3-km horizontal resolution of the simulations needs special treatment in order to reduce the gap of up to 4 ms−1 between observed and simulated mean wind speeds over mountains. Therefore, an empiric speed-up formula has been applied to the isolated mountains that otherwise would fall through the 3-km meshes. The corresponding deviations have been reduced to 1.5 ms−1.  相似文献   

8.
Modelling of water levels in the Baltic Sea, aimed at evaluating the influence of the trajectories and propagation speeds of a deep idealized cyclone on sea-level extremes in the Gulf of Finland, is done using the hydrodynamic model BSM6. An analytical expression for determination of the atmospheric pressure in this cyclone takes into account the existence of the cold front and the time evolution of the cyclone intensity. The empirical parameters in this relation are based on those of the deep cyclone ‘Erwin’ which passed over the Baltic Sea region in 2005.  相似文献   

9.
Climate models are increasingly being used to force dynamical wind wave models in order to assess the potential climate change-driven variations in wave climate. In this study, an ensemble of wave model simulations have been used to assess the ability of climate model winds to reproduce the present-day (1981–2000) mean wave climate and its seasonal variability for the southeast coast of Australia. Surface wind forcing was obtained from three dynamically downscaled Coupled Model Intercomparison Project (CMIP-3) global climate model (GCM) simulations (CSIRO Mk3.5, GFDLcm2.0 and GFDLcm2.1). The downscaling was performed using CSIRO’s cubic conformal atmospheric model (CCAM) over the Australian region at approximately 60-km resolution. The wind climates derived from the CCAM downscaled GCMs were assessed against observations (QuikSCAT and NCEP Re-analysis 2 (NRA-2) reanalyses) over the 1981–2000 period and were found to exhibit both bias in mean wind conditions (climate bias) as well as bias in the variance of wind conditions (variability bias). Comparison of the modelled wave climate with over 20 years of wave data from six wave buoys in the study area indicates that direct forcing of the wave models with uncorrected CCAM winds result in suboptimal wave hindcast. CCAM winds were subsequently adjusted for climate and variability bias using a bivariate quantile adjustment which corrects both directional wind components to align in distribution to the NRA-2 winds. Forcing of the wave models with bias-adjusted winds leads to a significant improvement of the hindcast mean annual wave climate and its seasonal variability. However, bias adjustment of the CCAM winds does not improve the ability of the model to reproduce the storm wave climate. This is likely due to a combination of storm systems tracking too quickly through the wave generation zone and the performance of the NRA-2 winds used as a benchmark in this study.  相似文献   

10.
Severe sea states in the North Sea present a challenge to wave forecasting systems and a threat to offshore installations such as oil and gas platforms and offshore wind farms. Here, we study the ability of a third-generation spectral wave model to reproduce winter sea states in the North Sea. Measured and modeled time series of integral wave parameters and directional wave spectra are compared for a 12-day period in the winter of 2013–2014 when successive severe storms moved across the North Atlantic and the North Sea. Records were obtained from a Doppler radar and wave buoys. The hindcast was performed with the WAVEWATCH III model (Tolman 2014) with high spectral resolution both in frequency and direction. A good general agreement was obtained for integrated parameters, but discrepancies were found to occur in spectral shapes.  相似文献   

11.
Loading by atmosphere and by the Baltic Sea cause gravity change at Metsähovi, located 15 km from the open sea. Gravity is changed by both the Newtonian attraction of the loading mass and by the crustal deformation. We have performed loading calculations using appropriate Green's function for both gravity and deformation, for both atmospheric and Baltic loading. The loading by atmosphere has been computed using a detailed surface pressure field from high resolution limited area model (HIRLAM) for north Europe up to 10° distances. Baltic Sea level is modelled using tide gauge records. Calculations show that 1 m of uniform layer of water corresponds to 31 nm s−2 in gravity and −11 mm in height. Modelled loading is compared with observations of the superconducting gravimeter T020 for years 1994–2002. The combination of HIRLAM and a tide gauge record decreases RMS of gravity residuals by 14% compared to single admittance in air pressure corrections without sea level data. Regression of gravity residuals on the tide gauge record at Helsinki (at 30 km distance) gives a gravity effect of 26 nm s−2 m−1 for Baltic loading.The gravity station is co-located with a permanent GPS station. We have also associated the loading effects of the atmosphere and of the Baltic Sea with temporal height variations. The range of modelled vertical motion due to air pressure was 46 mm and that due to sea level 18 mm. The total range was 38 mm. The effects of the Baltic Sea and of the atmosphere partly cancel each other, since at longer periods the inverse barometer assumption is valid. Regression of the modelled height on local air pressure gives −0.37 mm hPa−1, corresponding approximately to width 6° for pressure system.We have tested the models using one year of daily GPS data. Multilinear regression on local air pressure and sea level in Helsinki gives the coefficient −0.34 mm hPa−1 for pressure, and −11 mm m−1 for sea level. These match model values. Loading by air pressure and Baltic Sea explains nearly 40% of the variance of daily GPS height solutions.  相似文献   

12.
The nutrient load on the Gulf of Finland, the Baltic Sea, is estimated taking into account the export of nutrients from Lake Ladoga with Neva runoff, from the Chudsko-Pskovskoe Lake with Narva runoff, from a partial watershed of the Gulf of Finland, and wastewater discharges from St. Petersburg. The data used include the materials of state monitoring of water bodies and state statistical reports on northwestern Russia, materials of GUP Vodokanal Sankt Peterburga, the results of earlier researches of water quality formation in Lake Ladoga, the Gulf of Finland, and on their catchment, and the results of calculation of nutrient load on the gulf with the use of a model developed in the Institute of Limnology, RAS. Currently, the annual nutrient load on the Gulf of Finland is ∼5200 t Ptot and 70800 t Ntot. The phosphorus load exceeds the admissible levels recommended by the Helsinki Commission, thus suggesting the need to search for real ways to reduce the load in the future.  相似文献   

13.
Integrated observations were made on the South China Sea shelf at 19°37’ N, 112°04’ E, under strong wind and heavy raining weather conditions in August 2005. Current data were obtained using a moored 150-kHz Acoustic Doppler Current Profiler, turbulent kinetic energy dissipation rate were measured with TurboMapII, and temperature was recorded by thermistor chains. Both the mixed layer thickness and the corresponding mean dissipation rate increased after the strong wind bursts. Average surface mixed layer thickness was 13.4 m pre-wind and 22.4 m post-wind, and the average turbulent dissipation rate in the mixed layer pre-wind and post-wind were 4.26 × 10?7 and 1.09 × 10?6 Wkg?1, respectively. The post-wind dissipation rate was 2.5 times larger than the pre-wind dissipation rate in the interior layer and four times larger in the intermediate water column. Spectra and vertical mode analysis revealed that near-inertial motion post-wind, especially with high modes, was strengthened and propagated downward toward the intermediate layer. The downward group velocity of near-inertial current was about 8.1 × 10?5 ms?1 during the strong wind bursts. The mean percentage of wind work transmitted into the intermediate layer is about 4.2 %. The ratio of post-wind high-mode energy to total horizontal kinetic energy increased below the surface mixed layer, which would have caused instabilities and result in turbulent mixing. Based on these data, we discuss a previous parameterization that relates dissipation rate, stratification, and shear variance calculated from baroclinic currents with high modes (higher than mode 1) which concentrate a large fraction of energy.  相似文献   

14.
15.
An analysis of the extreme wave conditions in 1958–2002 in the North Sea as obtained from a regional model hindcast is presented. The model was driven by hourly wind fields obtained from a regional atmosphere model forced with reanalysis data from the National Center for Environmental Prediction (NCEP/NCAR). Furthermore, observed sea ice conditions from the Norwegian Meteorological Institute have been accounted for in the simulation. It is shown that the model is capable of reproducing extreme wave height statistics at a reasonable degree of approximation. The analysis of severe wave height events reveals that for much of the Southern North Sea, their number has increased since the beginning of the simulation period (1958), although the increase has attenuated later and leveled off around about 1985. On the other hand, the intensity and duration of severe wave height events decreased within the last few years of the simulation so that annual 99%-ile wave heights have also reduced since about 1990–1995. For the UK North Sea coast, a different behavior was found characterized by a reduction in severe wave conditions over much of the hindcast period.  相似文献   

16.
A numerical study of irregular waves in the Norwegian continental shelf wind farm (HAVSUL-II) was conducted using 3rd generation spectral wave models. The study was composed of two parts: the study of the effect of a single windmill monopile in the local incoming wave field using an empirical JONSWAP spectrum, and a wave hindcast study in the wind farm area using realistic incoming wave spectra obtained from large scale simulations for the 1991-1992 winter period. In the single windmill monopile study the SWAN wave model was used, while the hindcast study was conducted by successively nesting from a coarse grid using the WAM model up to a high-resolution (56 m) grid covering 26.2 km2 of the HAVSUL-II windmill farm using the SWAN model. The effect of a single monopile on incident waves with realistic spectra was also studied. In the single windmill study the monopile was represented as a closed circular obstacle and in the hindcast study it was represented as a dry grid point. The results showed that the single windmill monopile creates a shadow zone in the down wave region with lower significant wave height (Hs) values and a slight increase of Hs in the up wave region. The effects of the windmill monopile on the wave field were found to be dependent on the directional distribution of the incoming wave spectrum and also on the wave diffraction and reflection. The hindcast study showed that the group of windmill monopiles may contribute to the reduction of the wave energy inside the offshore wind farm and that once the waves enter into the offshore wind farm they experience modifications due to the presence of the windmill monopiles, which cause a blocking of the wave energy propagation resulting in an altered distribution of the Hs field.  相似文献   

17.
When modelling is used for investigating estuarine systems, a choice generally has to be made between applying simple mass-balance considerations or using a process-resolving three-dimensional (3-D) numerical circulation model. In the present investigation of the Gulf of Finland, a gradually mixed estuary in the Baltic Sea, it is demonstrated how Lagrangian-trajectory analysis applied to the output from a 3-D model minimizes the disadvantages associated with both of the modelling techniques referred to above. This formalism made it possible to demonstrate that the main part of the Gulf is dominated by water originating from the Baltic proper, and that the most pronounced mixing with fresh water from the river Neva takes place over a limited zone in the inner part of the Gulf. Dynamical insights were furthermore obtained by using the Lagrangian formalism to construct overturning stream-functions for the two source waters.  相似文献   

18.
In this study, we aim to map the Curie point depth surface for the northern Red Sea rift region and its surroundings based on the spectral analysis of aeromagnetic data. Spectral analysis technique was used to estimate the boundaries (top and bottom) of the magnetized crust. The Curie point depth (CPD) estimates of the Red Sea rift from 112 overlapping blocks vary from 5 to 20 km. The depths obtained for the bottom of the magnetized crust are assumed to correspond to Curie point depths where the magnetic layer loses its magnetization. Intermediate to deep Curie point depth anomalies (10–16 km) were observed in southern and central Sinai and the Gulf of Suez (intermediate heat flow) due to the uplifted basement rocks. The shallowest CPD of 5 km (associated with very high heat flow, ~235 mW m?2) is located at/around the axial trough of the Red Sea rift region especially at Brothers Island and Conrad Deep due to its association with both the concentration of rifting to the axial depression and the magmatic activity, whereas, beneath the Gulf of Aqaba, three Curie point depth anomalies belonging to three major basins vary from 10 km in the north to about 14 km in the south (with a mean heat flow of about 85 mW m?2). Moreover, low CPD anomalies (high heat flow) were also observed beneath some localities in the northern part of the Gulf of Suez at Hammam Fraun, at Esna city along River Nile, at west Ras Gharib in the eastern desert and at Safaga along the western shore line of the Red Sea rift. These resulted from deviatoric tensional stresses developing in the lithosphere which contribute to its further extension and may be due to the opening of the Gulf of Suez and/or the Red Sea rift. Furthermore, low CPD (with high heat flow anomaly) was observed in the eastern border of the study area, beneath northern Arabia, due to the quasi-vertical low-velocity anomaly which extends into the lower mantle and may be related to volcanism in northern Arabia. Dense microearthquakes seem to occur in areas where the lateral gradients of the CPD are steep (e.g. entrance of the Gulf of Suez and Brothers Island in the Red Sea). These areas may correspond to the boundaries between high and low thermal regions of the crust. Thus, the variations in the microseismic activity may be closely related to thermal structures of the crust. Indeed, shallow cutoff depths of seismicity can also be found in some geothermal areas (e.g. western area of Safaga city along the Red Sea coastal region and at Esna city along the River Nile). These facts indicate that the changes in the thickness of the seismogenic layer strongly depend on temperature. Generally, the shallow Curie point depth indicates that some regions in our study area are promising regions for further geothermal exploration particularly in some localities along the River Nile, Red Sea and Gulf of Suez coastal regions.  相似文献   

19.
Source term balance in a severe storm in the Southern North Sea   总被引:1,自引:1,他引:0  
This paper presents the results of a wave hindcast of a severe storm in the Southern North Sea to verify recently developed deep and shallow water source terms. The work was carried out in the framework of the ONR funded NOPP project (Tolman et al. 2013) in which deep and shallow water source terms were developed for use in third-generation wave prediction models. These deep water source terms for whitecapping, wind input and nonlinear interactions were developed, implemented and tested primarily in the WAVEWATCH III model, whereas shallow water source terms for depth-limited wave breaking and triad interactions were developed, implemented and tested primarily in the SWAN wave model. So far, the new deep-water source terms for whitecapping were not fully tested in shallow environments. Similarly, the shallow water source terms were not yet tested in large inter-mediate depth areas like the North Sea. As a first step in assessing the performance of these newly developed source terms, the source term balance and the effect of different physical settings on the prediction of wave heights and wave periods in the relatively shallow North Sea was analysed. The December 2013 storm was hindcast with a SWAN model implementation for the North Sea. Spectral wave boundary conditions were obtained from an Atlantic Ocean WAVEWATCH III model implementation and the model was driven by hourly CFSR wind fields. In the southern part of the North Sea, current and water level effects were included. The hindcast was performed with five different settings for whitecapping, viz. three Komen type whitecapping formulations, the saturation-based whitecapping by Van der Westhuysen et al. (2007) and the recently developed ST6 whitecapping as described by Zieger et al. (2015). Results of the wave hindcast were compared with buoy measurements at location K13 collected by the Dutch Ministry of Transport and Public Works. An analysis was made of the source term balance at three locations, the deep water location North Cormorant, the inter-mediate depth location K13 and at location Wielingen, a shallow water location close to the Dutch coast. The results indicate that at deep water the source terms for wind input, whitecapping and nonlinear four-wave interactions are of the same magnitude. At the inter-mediate depth location K13, bottom friction plays a significant role, whereas at the shallow water location Wielingen also depth-limited wave breaking becomes important.  相似文献   

20.
This paper presents random vibrations of the Baltic drilling platform subjected to water waves and wind loads. The platform structure is discretized by the finite element method. Linear beam or truss elements can be used. The structure parameters (i.e. mass, damping and stiffness) are assumed as deterministic. Soil is modelled as an elastic half-space that possesses deterministic or random parameters. Soil–structure interaction is idealized as a system of spring–dashpot elements connecting the structure and subsoil. The parameters of these elements can be random or deterministic. The sea surface is described by the one-dimensional wave spectrum that was proposed by Striekalov and Massel24 for inland seas. It is suitable for the Baltic Sea. The wind velocity is described by the well-known Davenport spectrum. The water and wind loads are treated as stationary ergodic processes. Gaussian distributions and zero means of these processes are assumed. In addition to this, waves and wind loads are considered as independent. Such an assumption corresponds to the situation when the storm sea is fully developed. A frequency-domain random-vibration approach is utilized to obtain the dynamic response of the platform. The equations of motion of the problem were solved using modal reduction. The numerical calculations were made with a specially written computer program. From the results obtained, it is concluded that the wind influence on the response of the platform can be neglected. If random parameters are assumed for the subsoil, then the response of the system describes in a more realistic way the dynamic behaviour of the platform. The velocity coupling due to soil and hydrodynamical damping is negligible. This paper is a condensation of the author's Ph.D. thesis presented at the Technical University of Gdańsk in July 1985.  相似文献   

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