Vibrations of a simply supported plate carrying an elastically mounted concentrated mass

A large number of papers and technical reports are available on the technically important problem of structural elements executing transverse vibrations and carrying concentrated masses. In general it is assumed that the attachment is perfectly rigid. On the other hand, a rather limited amount of published work is available when the mass is elastically connected to the structure. The system then exhibits a more complex behavior than in the case of rigid attachment. The present study deals with the solution of the title problem using the well-known normal mode, sinusoidal eigenfunction expansions.     

Validation of a finite difference method for the simulation of vortex-induced vibrations on a circular cylinder

The Karman Vortex Street generated by a circular cylinder is investigated by the numerical solution of the compressible Navier–Stokes equations in the incompressible Mach number range (Mach<0.3) using the Beam and Warming implicit scheme. The agreement with the fully incompressible projection method (Chorin, 1968) is fairly good while convergence time is very much better. The investigation suggests that the compressible Navier–Stokes equations may be used as an efficient alternative to study incompressible flows as well. Mach numbers just below 0.3 are enough to simulate incompressible flow behavior and at the same time do not cause numerical ill-conditioning in the solution. In addition, some relevant features of the vortices generated and carried by the wake of the cylinder could be fairly well captured.     

Weakly non-linear free oscillations in a basin of variable depth

Weakly non-linear free oscillations in a basin of variable depth filled with non-viscous fluid are investigated in terms of the long waves theory using the perturbation technique. Solutions to the initial two approximations for the horizontal velocity component and free surface departure are numerically derived. An attempt is made to determine the area of applicability of the linear theory by applying a parabolic bottom profile to the basin.Translated by V. Puchkin.     

Spatial and temporal variability of the ratios between the nitrate and phosphate concentrations in the Sea of Okhotsk

The relation between the nitrate and phosphate concentrations in the Sea of Okhotsk and the bordering waters of the Pacific Ocean were studied. The surveys were carried out in the autumn, spring, and summer of 2001–2002. For the deepwater part of the sea, the relation [NO^? ₃] = ((14.88 ± 0.07) × [PO^3? ₄] ? 5.46 ± 0.17) was found. The coefficients in the equation given are statistically different from those in the similar equation for the Pacific waters: [NO^? ₃] = (16.05 ± 0.15) × [PO^3? ₄]-(7.23 ± 0.36). In the northern part of the sea; on the shelf; in the slope area; and, especially, in the deep waters of the TINRO Depression, the linear dependence between the phosphate and nitrate concentrations was distorted. This feature was described in terms of nitrate deficiency. The maximum values of this deficiency were found in the near-bottom waters. The principal processes that might cause the nitrate deficiency were considered: the difference in the oxidation rates of the nitrogen and phosphorus organic compounds, the matter transfer between the continent and the sea, the different efficiency of the biogenic burial of nitrogen and phosphorus in the bottom sediments, and the denitrification in the upper layer of the bottom sediments. It was shown that the most probable cause of the nitrate deficiency was the denitrification. The loss of inorganic nitrogen owing to the supply of the waters of the Sea of Okhotsk to the Pacific Ocean was estimated as ～2.5 × 10¹¹ mol N/year.     

Rock magnetic records of the sediments of the eastern Arabian Sea: Evidence for late Quaternary climatic change

Rock-magnetic measurements along with grain size, acid-insoluble residue (AIR), organic carbon (OC), CaCO₃ and δ¹⁸O of the planktonic foraminifers of the sediments were determined for 15 gravity cores recovered from the western continental margin of India. Magnetic susceptibility (MS) values in the surficial sediments reflect the land-derived input and, in general, are the highest in terrigenous sediment-dominated sections of the cores off Saurashtra–Ratnagiri, followed by the sediments off Indus–Gulf of Kachchh and then Mangalore–Cape Comorin.

The down-core variations in mineral magnetic parameters reveal that the glacial sediments off the Indus are characterized by low MS values/S-ratios associated with high AIR-content, low OC/CaCO₃ contents and relatively high δ¹⁸O values, while those off SW India are characterized by low MS values/high S-ratio% associated with low AIR content, and relatively high OC, CaCO₃ and δ¹⁸O values. Conversely, the Early Holocene sediments of all cores are characterized by high MS values/S-ratio% associated with high AIR content, low OC, CaCO₃ contents and gradually decreased δ¹⁸O values. These results imply that during the Last Glacial Maximum (LGM), the cores off northwestern India received abundant continental supply leading to the predominance of eolian/fluvial sedimentation. In the SW region the influence of hinterland flux is less evident during this period, but convective mixing associated with the NE monsoon resulted in increased productivity. During the early Holocene intense SW monsoon conditions resulted in high precipitation on land, which in turn contributed increased AIR content/MS values in the continental margin sediments. A shallow water core off Kochi further suggests that the intense SW monsoon conditions prevailed until about 5 ka. The late Holocene organic-rich sediments of the SW margin of India were, however, subjected to early diagenesis at different intervals in the cores. Therefore, caution is needed when interpreting regional climatic change from down-core changes in sediment magnetic properties.     

How tides and river flows determine estuarine bathymetries

For strongly tidal, funnel-shaped estuaries, we examine how tides and river flows determine size and shape. We also consider how long it takes for bathymetric adjustment, both to determine whether present-day bathymetry reflects prevailing forcing and how rapidly changes might occur under future forcing scenarios.Starting with the assumption of a 'synchronous' estuary (i.e., where the sea surface slope resulting from the axial gradient in phase of tidal elevation significantly exceeds the gradient in tidal amplitude ), an expression is derived for the slope of the sea bed. Thence, by integration we derive expressions for the axial depth profile and estuarine length, L, as a function of and D, the prescribed depth at the mouth. Calculated values of L are broadly consistent with observations. The synchronous estuary approach enables a number of dynamical parameters to be directly calculated and conveniently illustrated as functions of and D, namely: current amplitude Û, ratio of friction to inertia terms, estuarine length, stratification, saline intrusion length, flushing time, mean suspended sediment concentration and sediment in-fill times.Four separate derivations for the length of saline intrusion, L_I, all indicate a dependency on (U_o is the residual river flow velocity and f is the bed friction coefficient). Likely bathymetries for `mixed' estuaries can be delineated by mapping, against and D, the conditions L<sub>I</sub>/L<1,E<sub>X</sub>/L<1 (E<sub>X</sub> is the tidal excursion) alongside the Simpson-Hunter criteria D/U<sup>3</sup><50 m<sup>−2</sup> s<sup>3</sup>. This zone encompasses 24 out of 25 `randomly' selected UK estuaries.However, the length of saline intrusion in a funnel-shaped estuary is also sensitive to axial location. Observations suggest that this location corresponds to a minimum in landward intrusion of salt. By combining the derived expressions for L and L_I with this latter criterion, an expression is derived relating D_i, the depth at the centre of the intrusion, to the corresponding value of U_o. This expression indicates U_o is always close to 1 cm s⁻¹, as commonly observed. Converting from U_o to river flow, Q, provides a morphological expression linking estuarine depth to Q (with a small dependence on side slope gradients).These dynamical solutions are coupled with further generalised theory related to depth and time-mean, suspended sediment concentrations (as functions of and D). Then, by assuming the transport of fine marine sediments approximates that of a dissolved tracer, the rate of estuarine supply can be determined by combining these derived mean concentrations with estimates of flushing time, F_T, based on L_I. By further assuming that all such sediments are deposited, minimum times for these deposition rates to in-fill estuaries are determined. These times range from a decade for the shortest, shallowest estuaries to upwards of millennia in longer, deeper estuaries with smaller tidal ranges.     

Multi-decadal synthesis of benthic–pelagic coupling in the western arctic: Role of cross-shelf advective processes

Using geographic information systems (GIS) software and geostatistical techniques, we utilized three decades of water-column chlorophyll a data to examine the relative importance of autochthonous versus allochthonous sources of reduced carbon to benthic communities that occur from the northern Bering to the eastern Beaufort Sea shelf. Spatial trend analyses revealed areas of high benthic biomass (>300 g m⁻²) and chlorophyll (>150 mg m⁻²) on both the southern and northern Chukchi shelf; both areas are known as depositional centers for reduced organic matter that originates on the Bering Sea shelf and is advected northward in Anadyr and Bering shelf water masses. We found a significant correlation between biomass and chlorophyll a in the Chukchi Sea, reflective of the strong benthic–pelagic coupling in a system that is utilized heavily by benthic-feeding marine mammals. In contrast, there was no significant correlation between biomass and chlorophyll in the Beaufort Sea, which by comparison, is considerably less productive (biomass and chlorophyll, <75 g m⁻² and <50 mg m⁻², respectively). One notable exception is an area of relatively high biomass (50–100 g m⁻²) and chlorophyll (80 mg m⁻²) near Barter Island in the eastern Beaufort Sea. Compared to other adjacent areas in the Beaufort Sea, the chlorophyll values in the vicinity of Barter Island were considerably higher and likely reflect a long-hypothesized upwelling in that area and close coupling between the benthos and autochthonous production. In the Bering Sea, a drop in benthic biomass in 1994 compared with previous measurements (1974–1993) may support earlier observations that document a decline in biomass that began between the 1980s and 1990s in the Chirikov Basin and south of St. Lawrence Island. The results of this study indicate that the benthos is an excellent long-term indicator of both local and physical advective processes. In addition, this work provides further evidence that secondary production on arctic shelves can be significantly augmented by reduced carbon advected from highly productive adjacent shelves.     

Variations in wave direction estimated using first and second order Fourier coefficients

In most design applications such as alignment of the berthing structure and breakwater alignment, it becomes necessary to determine the direction of design wave. There are two different approaches to determine wave direction. One involves the use of first order Fourier coefficients (mean wave direction) while the other uses second order Fourier coefficients (principal wave direction). Both the average wave direction over the entire frequency range (0.03–0.58 Hz) and the direction corresponding to the peak frequency are used in practice. In the present study, comparison is made on wave directions estimated based on first and second order Fourier coefficients using data collected at four locations in the west and east coasts of India. Study shows that at all locations, the mean and principal wave directions for frequencies ranging from 0.07 to 0.25 Hz (±0.5 times peak frequency) co-vary with a correlation coefficient of 0.99 but at lower and higher frequencies, difference between the parameters is large. Average difference between the mean wave direction at peak frequency and the average over the frequency related to spectral energy more than 20% of maximum value is less, around 13°. Study shows that average difference in the sea and swell directions is around 39°.