Bottom Topography Research Articles

FLUCTUATIONS OF LAKE NERO DURING THE HOLOCENE<a href="#FN1"><sup>1</sup></a>

The paleohydrological condition in the Rostov depression (Yaroslavl region) has been the subject of many years of discussions. The ideas about the Holocene fluctuations of the Lake Nero level differ among researchers. We have studied the structure of bottom sediments and bottom topography in the deepest northeastern part of the lake. A bathymetric survey was carried out. Drilling with the selection of undisturbed columns, GPR profiling, radiocarbon dating and a set of lithological analyzes were performed. Stratigraphic unconformities in the structure of bottom sediments indicate a drop in the lake level during the Lateglacial and the early Holocene. The level dropped to 87 m asl, which is 7 m lower than the current water level in the lake. The size of the lake at this stage was reduced several times. From 9 to 6.5 ka BP a transgressive stage was established: the average level of the lake could have risen to 91–94 m asl, which is close to its modern level. From 6.5 to 2.4 ka BP a decrease in the level by 1–3 m below the current one is revealed, followed by a gradual increase in the level. The current level was reached 300–500 years ago. The main factor in the fluctuations in the level of Lake Nero in the Holocene is the change in the height of the runoff threshold, caused by the transformation of the Ustye, Veksa, and Kotorosl river sistems. This transformation was associated both with regional changes in fluvial activity and with the processes of self-development of river channels.

A hybrid boundary element method based model for wave interaction with submerged viscoelastic plates with an arbitrary bottom profile in frequency and time domain

This study investigates the scattering of surface ocean waves by a submerged viscoelastic plate placed over the variable bottom topography under the assumptions of linear theory. The solution is derived using the hybrid boundary element method. The boundary element method is faster and easier to use when compared to the most widely used analytical method, such as the eigenfunction expansion method. Moreover, the application of analytical methods is restricted to structures with regular geometries and flat sea bottom. However, the present solution technique works for the plate at any angle placed over the variable bottom topography. Furthermore, as a particular case, the scattering problem is analyzed when a rigid wall is placed downstream. Energy balance relations are derived to check the accuracy of the computed numerical results. The effect of sinusoidally varying bottom topography, damping parameter, and plate edge conditions on the Bragg resonance phenomenon is analyzed. Initially, the solutions are presented in the frequency domain using the hybrid boundary element method and then extended to the time domain using the Fourier transform. It is observed that when the edges of the submerged plate are fixed, the Bragg resonance occurs at lower values of the frequency parameter. However, the Bragg resonance occurs around the primary Bragg value when the plate has free edges. For certain incident wave frequencies, the viscoelastic plate that completely covers the undulating bed dissipates a greater amount of wave energy than when the plate only partially covers the seabed.

Energy transfer from sub-inertial Kelvin waves to continental shelf waves at a transverse bottom escarpment

We consider barotropic coastally-trapped Kelvin waves of tidal origin along a straight coast that propagate from deeper water across a transverse bottom escarpment into a more shallow region. The M2 component, which has a frequency above the inertial frequency f, is modified by crossing the escarpment, but continues basically as a Kelvin wave into the shallow region. For tidal components that have frequencies smaller than f, like K1, some of the energy in the Kelvin wave is converted into a continental shelf wave (CSW) that follows the escarpment with shallow water to the right (in the northern hemisphere). The theory is applied to the shelf north-west of Norway where the deep Norwegian Sea is separated from the much shallower Barents Sea by an escarpment reaching from the north-Norwegian coast towards Spitsbergen. By introducing an idealized bottom topography and coastal geometry, analytical calculations and numerical modeling are used to investigate the energy flux in CSWs towards Spitsbergen caused by sub-inertial Kelvin wave motion along the west coast of Norway. Both analytical and numerical calculations indicate that the CSW energy flux towards Spitsbergen is about eighty percent of the incident sub-inertial Kelvin wave energy flux, and that only twenty percent of the energy flux is transmitted into the Barents Sea in the form of sub-inertial Kelvin waves.

A Two-Step Lagrange–Galerkin Scheme for the Shallow Water Equations with a Transmission Boundary Condition and Its Application to the Bay of Bengal Region—Part I: Flat Bottom Topography

A two-step Lagrange–Galerkin scheme for the shallow water equations with a transmission boundary condition (TBC) is presented. First, we show the experimental order of convergence to see the second-order accuracy in time realized by the two-step methods for conservative and non-conservative material derivatives along the trajectory of fluid particles. Second, we observe the effect of the TBC in a simple domain, and the artificial reflection is removed significantly when the wave touches the TBC. Third, we apply the scheme to a practical domain with islands, namely, the Bay of Bengal region, and observe the effect of the TBC again for the practical domain; the artificial reflections are removed significantly from the transmission boundaries on open sea boundaries. We also study the effect of a position of an open sea boundary with the TBC and reveal that it is sufficiently small to neglect. The numerical results in this study show that the scheme has the following properties: (i) the same advantages of Lagrange–Galerkin methods (the CFL-free robustness for convection-dominated problems and the symmetry of the matrices for the system of linear equations); (ii) second-order accuracy in time by the two-step methods; (iii) mass preservation of the function for the water level from the reference height (until the contact with the transmission boundaries of the wave); and (iv) no significant artificial reflection from the transmission boundaries. The numerical results by the scheme presented in this paper are for the flat bottom topography of the domain. In the next part of this work, Part II, the scheme will be applied to rapidly varying bottom surfaces and a real bottom topography of the Bay of Bengal region.

Spatial-temporal characteristics of the oceanic bottom mixed layer in the South China Sea

The oceanic bottom mixed layer (BML) plays an important role in transporting mass, heat, and momentum between the ocean interior and the bottom boundary. However, the spatial-temporal characteristics of the BML in the South China Sea (SCS) is not well understood. Using 514 full-depth temperature and salinity profiles collected during the time period from 2004 to 2018 and two particularly deployed hydrographic moorings, the temporal and spatial variations of the BML have been analyzed. The results show that the BML in the SCS exhibits significant inhomogeneity, with thickness and stability varying across different regions. Specifically, the BML is relatively thin and stable over the continental shelf and deep-sea regions, while it is thicker and less stable over the northern continental slope. The mean, median, and one standard deviation values of BML thickness over the entire SCS were found to be 73 m, 56 m, and 55 m, respectively. Further analysis reveals that energetic high-frequency dynamic processes, coupled with steep bottom topography, contribute to strong tidal dissipation and vertical mixing near the bottom over the continental slope, resulting in thicker BMLs. Conversely, dynamic processes in the deep ocean are less energetic and low-frequency, the topography is relatively smooth, and tidal dissipation and bottom vertical mixing are weaker, leading to a thinner BML. These findings enhance our understanding of the BML dynamics in the SCS and other marginal seas and provide insights to improve parameterizations of physical processes in ocean models.

Freak wave in a two-dimensional directional wavefield with bottom topography change. Part 1. Normal incidence wave

In the propagation and evolution of sea waves, previous studies pointed out that the occurrence of the freak wave height is significantly related to the quasi-resonant four-wave interaction in the modulated waves. From numerical--experimental study over an uneven bottom, the nonlinear effect caused by the bathymetry change also contributes to the occurrence of extreme events in unidirectional waves. To comprehensively analyse the two-dimensional wavefield, this study develops an evolution model for a directional random wavefield based on the depth-modified nonlinear Schrödinger equation, which considers the nonlinear resonant interactions and the wave shoaling the shallow water. Through Monte Carlo simulation, we discuss the directional effect on the four-wave interaction in the wave train and the maximum wave height distribution from deep to shallow water with a slow varying slope. The numerical result indicates that the directional spreading has a dispersion effect on the freak wave height. In a shallow-water environment, this effect becomes weak, and the bottom topography change is the main influencing factor in the wave evolution.

Dissipation of incident wave energy by two floating horizontal porous plates over a trench type bottom

ABSTRACT This work investigates the scattering of oblique incident waves by two floating horizontal porous plates over a trench-type sea bed to study the role of different pairs of barriers in dissipating the incident wave energy. This problem is modelled based on Darcy's law for flow past a porous structure. Havelock's expansions of water wave potentials, suitable matching conditions, and the algebraic least-square method handle the boundary value problem. The role of the horizontal porous plates is studied by analysing the scattering coefficients, energy loss, hydrodynamic wave force and free surface elevation through graphs which show a periodic oscillatory pattern as a function of gap length. The study reveals that if the porous effect parameter of plates or the length of plates is increased, more energy is dissipated and the plates experience less wave force, and the free surface elevation on the lee side is decreased. The present results also signify that as compared to rigid plates, significant changes are found in wave scattering coefficients, hydrodynamic force and free surface elevation due to the consideration of one porous plate along with one rigid plate and also two porous plates, where a pair of porous plates are more effective as compared to one porous plate. The present study reveals that the scattering of water waves by two floating horizontal porous plates over uneven bottom topography plays a vital role in constructing floating structures having more staying power in harsh wave environments.

Topographic Trapping of the Leeuwin Current and Its Impact on the 2010/11 Ningaloo Niño

Abstract Previous theoretical studies suggest that the topography along the west coast of Australia plays an important role in strengthening and trapping the Leeuwin Current (LC) at the coast. To isolate and quantify the effect of the continental shelf and slope on the LC and Ningaloo Niño, high-resolution (1/12°) ocean general circulation model experiments with different bottom topographies are performed. The “control” experiment uses a realistic bottom topography along the west coast of Australia, whereas the sensitivity (“no-shelf”) experiment uses a modified topography with no continental shelf and slope near the coast. The mean and variability of LC are realistically simulated in the control experiment. Compared to the control experiment, the strength of LC in the no-shelf experiment decreased by about 28%. The continental shelf influences the development of the 2010/11 Ningaloo Niño through modulating the LC variability: in August–October 2010 and January–February 2011, the LC in the control experiment is enhanced much more than that in the no-shelf experiment. As a result, the upper-50-m ocean temperature in the control experiment is about 26% warmer than the no-shelf experiment from September 2010 to March 2011. Different evolution of SST warming is also found in the two experiments. Comparisons of oceanic processes in the two experiments show that the shelf-slope topography can effectively trap the positive sea level anomaly at the coast in the control experiment while more Rossby waves radiate from the coast in the no-shelf experiment, resulting in a weaker LC.

Wash waves generated by ship moving across a depth change

Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography is investigated by numerical simulations based on a Mixed Euler–Lagrange (MEL) method. The transition is accomplished by the ship traveling from the deep water into shallow water via a step bottom. A small tsunami would be created after this transition. However, the unsteady wave-making resistance induced by this new phenomenon has not been well documented by literature. Therefore, the main purpose of the present study is to quantify the effects of an uneven bottom on the unsteady wash waves and wave-making resistance acting on the ship. An upwind differential scheme is commonly used in the Euler method to deal with the convection terms on free-surface condition to prevent waves in upstream. Evidently, it cannot be applied to the present problem when the ship-generated waves could propagate upstream. A MEL method is therefore employed to investigate the upstream wave generated by the ship moving over the uneven bottom. The central differential scheme provides more accurate results, but it is not unconditionally stable. Simulation results show that the hydrodynamic interaction between the ship and the uneven bottom could initiate an upstream tsunami, as well as unsteady wave-making resistance on ships. The unsteady wave-making resistance oscillates periodically, and the amplitude and period of the oscillations are highly dependent on speed and water depth.

Scattering of water waves by two thin vertical barriers over shelf bottom topography

In this paper, water waves interaction with two thin vertical barriers over shelf bottom topography is analysed using linearised wave theory. The associated mixed boundary value problem is solved with the aid of method involving eigenfunction expansions of the velocity potential and orthogonality relation of the eigenfunctions. Further, the resulting system of algebraic equations is solved using the least square method to find the physical quantities, that is, reflection and transmission coefficients, free surface elevation and non-dimensional horizontal force experienced by the barriers. The energy balance relation is derived from Green's identity which ensures the correctness of the present results. The obtained results are also compared with the results available in the literature for validation purpose. With the help of different plots, the effect of depth ratios, length of the barriers, angle of incidence and gap between the barriers is investigated for various values of physical parameters. The study reveals that the phenomena of zero reflection, that is, full transmission can be avoided by using non-identical barriers or asymmetric shelf bottom topography. Also, it is highlighted that the presence of two barriers instead of a single barrier over shelf topography will help to reduce the transmitted wave energy near the seashore. A generalisation of number of surface piercing barriers over the shelf bottom topography is also demonstrated.

Analysing the impact of bottom friction on shallow water waves over idealised bottom topographies

Analysing the impact of bottom friction on shallow water waves over bottom terrains is important in areas including environmental and coastal engineering as well as the oceanic and atmospheric sciences. However, current theoretical developments rely on making certain limiting assumptions about these flows and thus more development is needed to be able to further generalise this behaviour. This work uses Adomian decomposition method (ADM) to not only develop semi-analytical formulations describing this behaviour, for flat terrains, but also as reverse-engineering mechanisms to develop new closed-form solutions describing this type of phenomena. Specifically, we respectively focus on inertial geostrophic oscillations and anticyclonic vortices with finite escape times in which our results directly demonstrate the direct correlation between the constant Coriolis force, the constant bottom friction, and the overall dynamics. Additionally, we illustrate elements of dissipation-induced instability with respect to constant bottom friction in these types of flows where we also demonstrate the connection to the initial dynamics for certain cases.

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalizedG′/Gexpansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalizedG′/Gexpansion technique. The extended generalizedG′/Gexpansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial ofG′/G. The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.

A flux globalization based well-balanced path-conservative central-upwind scheme for the shallow water flows in channels

We develop a flux globalization based well-balanced (WB) path-conservative central-upwind (PCCU) scheme for the one-dimensional shallow water flows in channels. Challenges in developing numerical methods for the studied system are mainly related to the presence of nonconservative terms modeling the flow when the channel width and bottom topography are discontinuous. We use the path-conservative technique to treat these nonconservative product terms and implement this technique within the flux globalization framework, for which the friction and aforementioned nonconservative terms are incorporated into the global flux: This results in a quasi-conservative system, which is numerically solved using the Riemann-problem-solver-free central-upwind scheme. The WB property of the resulting scheme (that is, its ability to exactly preserve both still- and moving-water equilibria at the discrete level) is ensured by performing piecewise linear reconstruction for the equilibrium variables rather than the conservative variables, and then evaluating the global flux using the obtained point values of the equilibrium quantities. The robustness and excellent performance of the proposed flux globalization based WB PCCU scheme are demonstrated in several numerical examples with both continuous and discontinuous channel width and bottom topography. In these examples, we clearly demonstrate the advantage of the proposed scheme over its simpler counterparts.

Two-Layer Ocean Circulation Model with Variational Control of Turbulent Viscosity Coefficient

The development of a variational method for solving the problem of quasi-geostrophic dynamics in a two-layer periodic channel is considered. The development of the method is as follows. First, the formulation of the variational problem is generalized: the turbulent exchange coefficient of a quasi-geostrophic potential vorticity (QGPV) is included in the control vector. Secondly, the solution area more accurately describes the size of the Antarctic Circumpolar Current (ACC). Using the selection of linear meridional transport and the expansion of the solution in a Fourier series, the problem is reduced to a nonlinear system of ordinary differential equations (ODEs) in time. The doubly connected domain leads to the fact that the solution of the ODE must satisfy an additional stationary relation that determines the transport of the ACC. The variational algorithm is reduced to solving a system of forward and adjoint equations minimizing the mean squared error of the stationary relation. The QGPV turbulent exchange coefficient is determined in the process of solving the optimal problem. The numerical runs are carried out for a periodic channel simulating the water area of the ACC in the Southern Ocean. The characteristics of stationary current regimes are studied for different values of the model parameters. Typical is a sinusoidal circulation in both layers with a linear transfer with the wind, depending on the bottom topography. In some cases, under the sinusoidal, in the lower layer, a cellular circulation is formed, and sometimes an undercurrent occurs. In this case, the solution of the optimal problem is characterized by a low value of the turbulent viscosity coefficient and a low transport in the lower layer.

SPATIAL DISTRIBUTION OF AMPLITUDES OF INTERNAL TIDAL WAVES ON THE NORTH-EASTERN SHELF OF SAKHALIN

The transformation of a multicomponent barotropic tide in the Sea of Okhotsk is considered in the framework of fully nonlinear non-hydrostatic calculations. The data of the tidal model and parameterized bottom topography and vertical profiles of sea water density based on data from open international atlases are used to initialize the model. Estimates of the wave amplitudes of the diurnal and semidiurnal baroclinic tides in terms of the displacement of isopycnal surfaces at different horizons are obtained and presented in the form of geographical maps. It is shown that the distribution of amplitudes significantly depends on depth, has a complex spatial structure with a noticeable predominance of the amplitudes of baroclinic waves of the diurnal period and the main extrema located on the shelf opposite Cape Elizabeth, Okhinsky Isthmus and Cape Patience. The implemented approach to mapping the amplitudes of internal tides can be applied to other shelf areas of the seas of the Russian Federation and used for predictions of these phenomena, including engineering assessments for the design and operation of marine infrastructure.

Lake stratification in the Brazilian Amazon: Types and the first description of permanent meromixia

An investigation into the physical and chemical stratification processes of the waters of 45 lakes in Central Amazonian was carried out, based on data from 1995 to 2022. Stratification profile and behavior; partial and total circulation trends; seasonality; classification and typology of the lakes of the Amazon plain were considered. The purpose of this study was to identify the limnological, hydrological and geomorphological factors most relevant to the stratification processes. Monitoring data were obtained from daily and seasonal samplings. Among the analyzed parameters are temperature; density; transparency; euphotic zone; attenuation coefficient; incident and refracted radiation profile; dissolved oxygen, conductivity, pH, salinity, suspended material and turbidity concentrations; climatic and hydrological factors; level of protection of the shores; topography of shore and bottom; shape and geometric pattern of lakes. PCA, Cluster and Pearson's analysis and numerical models were applied to the results. Lakes with total circulation patterns, multiple layered circulations, varying degrees of polymixy, and lakes with seasonal and permanent meromixy were identified. The concentration of total solids, depth, morphometry, intensity of the refracted radiation and the action of the winds were the factors considered preponderant for the identification of the stratification processes. Hydrological models were established based on the classification and typology of the lakes studied. The simulation results allowed the following conclusions: a) coefficients t1 and t2 < 0 suggest increase; b) 0< t1 and t2 < 1 is equivalent to a curve with linear trend; c) t1 and t2 > 1 is equivalent to a curve with a tendency to stratification; d) the higher the numerical value of t1,2, means resistant stratification (permanent meromixia).

Reabsorption of Lee-Wave Energy in Bottom-Intensified Currents

Abstract While lee-wave generation has been argued to be a major sink for the 1-TW wind work on the ocean’s circulation, microstructure measurements in the Antarctic Circumpolar Currents find dissipation rates as much as an order of magnitude weaker than linear lee-wave generation predictions in bottom-intensified currents. Wave action conservation suggests that a substantial fraction of lee-wave radiation can be reabsorbed into bottom-intensified flows. Numerical simulations are conducted here to investigate generation, reabsorption, and dissipation of internal lee waves in a bottom-intensified, laterally confined jet that resembles a localized abyssal current over bottom topography. For the case of monochromatic topography with |kU0| ≈ 0.9N, where k is the along-stream topographic wavenumber, |U0| is the near-bottom flow speed, and N is the buoyancy frequency; Reynolds-decomposed energy conservation is consistent with linear wave action conservation predictions that only 14% of lee-wave generation is dissipated, with the bulk of lee-wave energy flux reabsorbed by the bottom-intensified flow. Thus, water column reabsorption needs to be taken into account as a possible mechanism for reducing the lee-wave dissipative sink for balanced circulation.

Sonar investigation of the old Nubian Villages in the bottom topography of Nasser Lake, Egypt

Underwater sonar survey using Side Scan Sonar (SSS) and Single beam Echo-sounder (SBES) was used for the investigation of the old Nubian archaeological villages buried within the bottom topography of Nasser Lake. The research objective involved emphasizing the efficiency of marine geophysical techniques in the detection of the submerged old Nubian Villages in Nasser Lake behind the High Dam, the study also aimed to study riverbed topography and determining the old course of the Nile River in the area. The resulted bathymetric maps showed that the two former banks of the Nile River in the study area were characterized by two distinct natures, while the shoreline has retreated with different extents starting from 250 m at the southern regions up to 3 km in the northern parts. The high-resolution sonar images of the bottom uncovered distinctive acoustic patterns according to difference in the returned backscatter strength. Submerged Nubian houses were detected along some areas of the eastern bank, which were found either standing over elevated rocky cliffs or built on multiple tiered levels. Precise target measurements were applied on the detected houses and different dimensions were obtained, which suggest that these houses were built according to the availability of suitable land to construct such dwellings.

Stochastic solitons in a two-layer fluid system

In this paper, stochastic one- and two-soliton solutions for the stochastic Benjamin–Ono equation modeling the nonlinear random waves in a two-layer fluid system with and without the uneven bottom topography are derived via the Gaussian white noise functional approach and the Hirota method. The effects of Gaussian white noise on the propagation and the interaction of the stochastic solitons are discussed. In the stochastic-one-soliton case, impact on the velocity is enlarged with the increase of the intensity of Gaussian white noise while the soliton amplitude and shape keep unchanged during the propagation. We also investigate the results of the stochastic-two-soliton interaction and the effects of Gaussian white noise on the interaction of stochastic two solitons. With the increase of Gaussian white noise, the velocity of two solitons causes the corresponding change, while the soliton amplitudes and shapes keep unchanged before and after the interaction. • Successfuly obtaining the stochastic one-soliton, two-soliton and N-soliton solutions of the stochastic Benjamin–Ono equation. • Investigating the effect of Gaussian white noise on propagation and interactions of the stochastic solitons. • The impact on the velocity can be greater as the intensity of Gaussian white noise increases in the stochastic one-soliton case. • The amplitude keep unchange along the propagation in the stochastic one-soliton case. • There is a change over the velocities of the stochastic two solitons when there exists white noise.

Well-Balanced Unstaggered Central Scheme Based on the Continuous Approximation of the Bottom Topography

A key difficulty of the conventional unstaggered central schemes for the shallow water equations (SWEs) is the well-balanced property that may be missed when the computational domain contains wet-dry fronts. To avoid the numerical difficulty caused by the nonconservative product, we construct a linear piecewise continuous bottom topography. We propose a new discretization of the source term on the staggered cells, and a novel “backward” step based on the water surface elevation. The core of this paper is that, we construct a map between the water surface elevation and the cell average of the free surface on the staggered cells to discretize the source term for maintaining the stationary solutions. The positivity-preserving property is obtained by using the “draining” time-step technique. A number of classical problems of the SWEs can be solved reasonably.