Seiche Motion Research Articles

Seasonal Turbidity Linked to Physical Dynamics in a Deep Lake Following the Catastrophic 2014 Mount Polley Mine Tailings Spill

AbstractThe catastrophic August 2014 Mount Polley tailings spill, the second largest ever documented, sent ~18 Mm3 of waste plunging to the bottom of the >100 m deep West Basin of Quesnel Lake, British Columbia, a critical West Coast salmon habitat. To understand the impact of the spill on the lake, including the fate of suspended solids, we examine changes in physical water properties over 11 years (2006–2017) using water column profiles, moored timeseries, and satellite imagery. Contaminated waters were initially largely confined to the hypolimnion; however, during autumn 2014 turnover, turbid waters were mixed to the surface, resulting in the clear blue lake turning bright green. Twelve months after the spill, the lake's temperature, conductivity, and turbidity temporarily returned to pre‐spill conditions; however, initiation of mine effluent discharge in late 2015 was associated with a subsequent 15 μS cm−1 conductivity increase above historic values. Importantly, a post‐spill 1–2.5 formazin turbidity unit hypolimnetic turbidity increase was observed during spring and fall turnovers of 2015–2017, which appeared to be due to resuspension of a thin layer of unconsolidated spill‐related material from the lake bed driven by large internal seiche motions. This process implies spill contaminants may be seasonally mobilized into the water column, with potentially detrimental impacts on aquatic ecology. Our findings underscore that basin‐scale physical processes, including seasonal turnover and internal seiches, must be accounted for, even in deep lakes, to understand the long‐term impact of the ever increasing number of tailings spills into aquatic ecosystems.

LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes

Abstract. A one-dimensional (1-D) model for an enclosed basin (lake) is presented, which reproduces temperature, horizontal velocities, oxygen, carbon dioxide and methane in the basin. All prognostic variables are treated in a unified manner via a generic 1-D transport equation for horizontally averaged property. A water body interacts with underlying sediments. These sediments are represented by a set of vertical columns with heat, moisture and CH4 transport inside. The model is validated vs. a comprehensive observational data set gathered at Kuivajärvi Lake (southern Finland), demonstrating a fair agreement. The value of a key calibration constant, regulating the magnitude of methane production in sediments, corresponded well to that obtained from another two lakes. We demonstrated via surface seiche parameterization that the near-bottom turbulence induced by surface seiches is likely to significantly affect CH4 accumulation there. Furthermore, our results suggest that a gas transfer through thermocline under intense internal seiche motions is a bottleneck in quantifying greenhouse gas dynamics in dimictic lakes, which calls for further research.

Assessing the effects of severe rainstorm-induced mixing on a subtropical, subalpine lake

Severe rainstorms cause vertical mixing that modifies the internal dynamics (e.g., internal seiche, thermal structure, and velocity filed) in warm polymictic lakes. Yuan Yang Lake (YYL), a subtropical, subalpine, and seasonally stratified small lake in the north-central region of Taiwan, is normally affected by typhoons accompanied with strong wind and heavy rainfall during the summer and fall. In this study, we used the field data, statistical analysis, spectral analysis, and numerical modeling to investigate severe rainstorm-induced mixing in the lake. Statistical determination of the key meteorological and environmental conditions underlying the observed vertical mixing suggests that the vertical mixing, caused by heat loss during severe rainstorms, was likely larger than wind-induced mixing and that high inflow discharge strongly increased heat loss through advection heat. Spectral analysis revealed that internal seiches at the basin scale occurred under non-rainstorm meteorological conditions and that the internal seiches under the rainstorm were modified on the increase of the internal seiche frequencies. Based upon observed frequencies of the internal seiches, a two-dimensional model was simulated and then appropriate velocity patterns of the internal seiches were determined under non-rainstorm conditions. Moreover, the model implemented with inflow boundary condition was conducted for rainstorm events. The model results showed that the severe rainstorms promoted thermal destratification and changed vertical circulation of the basin-scale, internal seiche motion into riverine flow.

Internal seiche modes and bottom boundary‐layer dissipation in a temperate lake from acoustic measurements

Measurements with Acoustic Doppler Current Profilers (ADCPs) and a thermistor string were used to investigate the seasonal variation of internal seiches in a 5‐km‐long temperate lake and the dissipation induced by the seiches in the bottom boundary layer. Velocity data, from a bottom‐mounted 1.2‐MHz ADCP were analyzed by cross‐spectral analysis to determine the seiche modes. The first vertical mode was generally dominant but the second mode made a significant contribution at times and was present throughout the summer season. The modal periods, which were consistent with normal mode analysis, exhibited a marked seasonal change that correlated closely with the evolution of stratification. Measurements in the bottom boundary layer, by another ADCP, in pulse‐pulse coherent‐mode sampling at 4 Hz, allowed determination of the rate of turbulent kinetic energy dissipation via the Structure Function Method. Episodes of energy dissipation ~ 10‐7 W kg‐1 occurred during peak flow (~ 0.05 m s‐1) in the seiche motion (period ~ 10 h) and coincided with times of significant Reynolds stress. Between these episodes, dissipation fell below the noise level (~ 5 × 10‐9 W kg‐1). The ratio of internal wave energy to the boundary‐layer dissipation rate implies a decay time of ~ 75 h, which is similar to that for energy decay in strong seiches, indicating that boundary‐layer dissipation makes a substantial contribution to energy loss from seiche motions. A major mixing event in August caused by near‐resonant wind forcing brought metalimnion water to the surface and induced substantial mixing.

Differential cooling drives large‐scale convective circulation in Lake Tanganyika

Field data, scaling analysis, and three‐dimensional numerical experiments demonstrate that the dominant large‐scale circulation pattern during the southeast trade winds in Lake Tanganyika (East Africa) is a downwind flow in the metalimnion, with a returning southward upwind flow in the upper region of the epilimnion. This is in the opposite direction to all prior literature available on the lake, which has assumed that the southeast trade winds must drive a northward surface flow due to momentum induced by the wind. The gradient in wind speed and humidity along the length of the lake and the resulting gradient in heat exchange with the atmosphere result in warm water accumulating at the northern end of the lake. The north basin of Lake Tanganyika, thus, acts as a heat sink while the south basin is a net source of heat to the atmosphere. The resulting variation in buoyancy flux is strong enough to drive a convective flow in the upper layer in the opposite direction to the wind. A large‐scale convective circulation results in an annual exchange of 6.2 × 1012 m3 of water and an annual net transport of heat (averaging 0.2 terawatt) from the northern to the southern region of the lake. Currents in the upper 100‐m layer, with a mean flow of 0.2 Sverdrup and flow speed of 0.08 m s−1, can be described by the superposition of a parallel convective flow with the internal seiche motion.

Influence of open boundary conditions and sill height upon seiche motion in a gulf

A cross-sectional model of an idealised constant depth gulf with a sill at its entrance, connected to a deep ocean, is used to examine the barotropic and baroclinic response of the region to wind forcing. The role of the oceanic boundary condition is also considered. Calculations show that in the case of a tall sill, where the pycnocline intersects the sill, the baroclinic response of the gulf is similar to that of a lake, and internal waves cannot radiate energy out of the gulf. The barotropic response shows free surface oscillations, with nodes located close to the centre of the oceanic basin and entrance to the gulf, with associated barotropic resonant periods. As the sill height is reduced, baroclinic wave energy is radiated from the gulf into the ocean, and the form of the baroclinic response changes from a standing wave (tall sill) as in a lake to a progressive wave (no sill). The location of sea surface elevation nodes and resonant periods changes as the sill height is reduced. Calculations of the barotropic resonant periods with and without stratification could not determine if they were influenced by the presence of stratification, although published analytical theory suggests that they should be able to when energy is lost from the gulf by internal wave radiation. This inability to detect changes in barotropic resonant period due to stratification effects is due to the small change in resonant frequency produced by baroclinic effects, as shown by analytical results, and the broad peak nature of the computed resonant frequency. In the case of a closed offshore boundary (an offshore island), there is a stronger and narrower energy peak at the resonant frequency than when a barotropic radiation condition is applied. However, the influence of stratification upon the resonant frequency could not be accurately determined. Although the offshore boundary was well removed from the gulf to such an extent that any baroclinic waves reflected from it could not reach the gulf within the integration period, it did, however, slightly influence the gulf baroclinic response due to its influence on the barotropic response.

Submarine earthquake geology along the North Anatolia Fault in the Marmara Sea, Turkey: A model for transform basin sedimentation

The submerged portions of the North Anatolia Fault system beneath the Marmara Sea were studied with high-resolution multibeam bathymetry, subbottom profiling and sediment cores. The major objectives were to learn about the seismic and tectonic history of the fault from the stratigraphic record at a scale similar to paleoseismic studies on land and to develop tools for submarine earthquake geology that can be applied to fault-controlled basins in general. We focused on Holocene sediment in several Marmara Sea basins of different sizes. The approach was to test whether: (1) the depocenters of the larger basins contain a record of all historic Ms > 7 earthquakes within the Marmara Sea region; (2) the small transform basins record earthquakes that rupture through them; (3) vertical and strike-slip Holocene deformation can be quantified; and (4) the effects of an earthquake generally includes both primary structural features due to rupture of the sea floor, such as strata offset, scarps and tilting, as well as secondary effects due to shaking, such as mass-wasting and gravitational flows. We found evidence of earthquakes that we correlate with historic events in 181 AD, 740 AD, 1063 AD, 1343 AD, 1509 AD, 1766 AD, 1894 AD and 1912 AD. The geologic evidence is primarily from those basins adjacent to the rupture as inferred from historic data. This suggests that coseismic deformation of the sea floor along the rupture is a critical factor in the sedimentary record. We propose a qualitative sedimentation model that relates this coseismic deformation to mass-wasting of the slope, scour of the basin floor, seiche motions and homogenite deposition. Frequent earthquake activity sheds sediments from the flanks, contributes to the much thicker sediment on the basin floor and decreases the likelihood of sediment failures in response to normal marine gravity-driven processes. The surveying techniques and approaches used have therefore the potential of documenting earthquake ruptures of fault segments and to extend the earthquake record far before the known history, thus improving hazard evaluations and the fundamental understanding of earthquake process.

Periodic Diffusional Mass Transfer near Sediment/Water Interface: Theory

Time-variable (periodic) flow over a lake bed, and the associated boundary layer development, have the potential to control or at least influence rates of mass transfer across the sediment/water interface. An analysis for instantaneous and time averaged flux of a material across the sediment/water interface for infinite supply in the water and infinite sink in the sediment is presented. The water flow above the interface is characterized by the shear velocity (U*) which is a periodic function of time with a maximum amplitude of (U*0) as may be typical of an internal seiche (internal standing wave) motion in a density stratified lake. The relationship between the shear velocity on the lake bed and the wind shear on the lake surface is illustrated for an extremely simplified two-layered lake of constant depth. For a less restrictive analysis, shear velocities on a lake bed have to be obtained either from field measurements or from a three-dimensional lake circulation model driven by atmospheric forcing including wind. Smaller and wind-sheltered lakes will have lower (U*0) and periodicities (T). The response of the diffusive boundary layer was related to the period of the periodic motion (T), Schmidt number (Sc), and shear velocity (U*). The vertical diffusive flux at the sediment/water interface was expressed by a Sherwood number (Sh), either instantaneous or time averaged. The mean Sherwood number (Shave) varies with shear velocity of the wave motion over the sediment bed, Schmidt number (Sc) and the period (T) due to the response of the diffusive boundary layer to the time variable water velocity. Effective diffusive boundary layers develop only at low shear velocities. Where they do, maximum and minimum boundary layer thickness depends on all three independent variables (T, Sc, and U*0). The diffusive boundary layer strongly affects sediment/water mass transfer, i.e., Sherwood numbers. Mass transfer averaged over a period can be substantially less than that produced by steady-state flow at the same U*0 and Sc. At Sc=500, typical for dissolved oxygen, the mass transfer ratio can be reduced to 60% of steady state, depending on the internal wave period (T).

The Internal Seiches in Gullmar Fjord. Part I: Dynamics

Abstract Internal seiche motions with period 1–3 days in Gullmar Fjord are investigated based on mooring data with high vertical and time resolution. The period and structure of the internal seiches are well described by a simple analytical three-layer model taking into account blocking of the basin water at the sill. Energy budgets for forcing and damping of the seiches are estimated. The internal seiches are forced by direct wind stress on the surface and by internal coastal waves of frequency close to the seiches, the latter contribution being a little larger. The e-folding timescale for the internal seiche damping is approximately equal to the seiche periods, which means that the seiches are effectively damped, but also that the forcing must be in near resonance in order to maintain the observed seiche motions. In the basin water the seiches manifest themselves with large vertical motions and clear upward phase propagation. The phase propagation is related with a continuous, rather than strictly layer...

Resonant seiche motion in the Chesapeake Bay

Chesapeake Bay is a long and narrow estuary in which seiche motions are common phenomena. These motions are generally driven by the longitudinal (N‐S) wind at 2‐ to 3‐day time scales and are characterized by a node at the mouth and an antinode at the head of the bay. Recent observations revealed a burst of seiche activity which was, however, related to the lateral (E‐W) wind. The amplitude of current fluctuations was about 50 cm s−1 and was not simply related to the winds. The period was about 1.6 days, which was less than the natural period of the whole bay. Since the optimum wind was aligned with only a small portion of the bay (the lower reaches of the bay, about 40 km long), the primary wind effect may be active only at the entrance region. Nevertheless, it appeared that the wind‐driven current was able to trigger a resonant seiche motion in the rest of the bay. The coupled response was modeled through a two‐section conceptual model, and the results compare well with the observations.

A Review of Exchange Processes Among the Three Basins of Lake Erie

Although the three basins of Lake Erie have sharply defined individual characteristics and are profitably studied independently, water exchanges among the basins have both local and basin-wide effects in both the short and long term. In order of decreasing timescale, the major exchange mechanisms are hydraulic or riverine flow from the mouth of the Detroit River to the entrance of the Niagara River, pressure-gradient-driven subsurface flows that are the cumulative result of wind-driven surface flows, flushing due to oscillating seiche motions, and turbulent horizontal diffusion. Generally speaking, the horizontal extent of the effects of the water exchange processes correlate positively with the time scale of the process. The effects of the various exchange processes on the transfer of contaminants are discussed.

Wind‐induced internal seiches in Lake Zurich observed and modeled1

During August and September 1978, 31 current meters and 120 temperature sensors were deployed to record every 10 or 20 min at various depths at 12 moorings (with wind speed and direction at three moorings) in Lake Zurich. We explore here the baroclinic (internal seiche) response to wind impulses, observed as fluctuations in isotherm depth and current speeds. Those fluctuations and their energy spectra are compared with the predictions of two models fitted to basin topography and to the observed average thermal structure: a two‐layered variable‐depth (TVD) model developed by D. J. Schwab, fitted to basin topography and incorporating a two‐dimensional horizontal grid, and C. H. Mortimer’s two‐layered modification of a simpler procedure originally developed for surface seiche calculations by A. Defant.The dominant responses to wind impulses were internal seiches of the first longitudinal mode (average period 44 h). Weaker signals from the second (24 h) and third (17 h) modes were also seen in spectra of temperature and current fluctuations. The models displayed patterns of thermocline displacement and current which, in periodicity and structure, were closely similar to those observed. Predictions of the Defant model were less precise, particularly for current.Founded on linear theory and neglecting the effects of rotation, the models were unable to reproduce two features occasionally seen in the lake motions: clockwise or anticlockwise rotation of current direction; and internal surges arising when storms induced large‐amplitude downstrokes of the thermocline at one basin end or the other. The lake’s internal response was principally dependent on the timing, strength, and duration of the wind impulse, relative to and interacting with internal seiche motions already in progress.

Tests of an extension to internal seiches of Defant's procedure for determination of surface seiche characteristics in real lakes1

The success of A. Defant's method of calculating surface seiche periods and structures in real lakes is well known. To test whether it can be adapted and applied with similar success in studies of internal seiches in stratified lakes, in which density structure is simulated by two homogeneous layers, we compare the predictions of a computerized version of Mortimer's modified Defant procedure against observations of internal seiche motion in eight lake basins and (in three examples) against the results of more elaborate models. The acceptably close agreement inspires confidence that the modified method is useful for practical predictions which, although approximate, described the principal characteristics of the often large water mass displacements and oscillations. Through their influence on mixing and dispersal, those motions profoundly affect the chemical and biological economies of many lakes. To aid in microcomputer and even pocket calculator applications, we set out steps in the calculation in tabular flow‐chart form. A comparable table for surface seiche calculation is added.The procedure is not applicable to large lakes in which effects of the earth's rotation are dominant; but for the two largest basins tested here (Léman and Ness) a modification is introduced to take approximate account of rotation.

The climatology of internal waves in a deep temperate lake

Kootenay Lake is a long (100 km), deep (140 m), dimictic lake in southeastern British Columbia. Internal waves were observed over an 18‐month period using three thermistor chains moored along the major axis of the lake. To characterize their seasonal aspects, four types of oscillations are recognized: (1) classical seiches with amplitudes of 10–30 m and periods of 1–2 weeks, (2) intrabasin waves with periods of 2–4 days, (3) large‐amplitude waves resembling nonlinear surges, and (4) high‐frequency waves associated with both the internal surge and large‐amplitude internal seiche motions. The periods of the major components of the internal wave field are determined mainly by morphometry but vary seasonally with stratification. Thus the wind, which not only forces internal waves but can also modify stratification, is important. In large lakes like Kootenay, the thermal structure may vary not only spatially but also temporally at periods comparable to those of the internal waves themselves. Hence the shape and frequency of these waves may be altered as they pass through the lake.

INTERFACIAL SEICHE IN COMPOSITE CLOSED WATER MASS

The thermocline oscillation observed in the stratified water mass, such as, deep lakes, reservoirs and land-locked bays, are sometimes generated by the resurging effects after the stop of the wind set-up motion. The oscillation characteristics of the density interface become much complex in the case of complicated geometry, e. g. reservoirs with several branches, bays composed of many inlets, etc. The authors developed the theory for the, interfacial seiche motion in the two-layered and multi-composed water mass by applying the theory of the surface seiche. Additionally, a laboratory experiment was performed by using the model tank composed of four channel elements with rectangular cross sections. Satisfactory agreements between the theory and experiment were obtained.

A numerical computation of a seiche oscillation of the Ligurian Sea

Summary. A depth-integrated hydrodynamical model of the Ligurian Sea has shown the existence of a seiche motion of the basin with a 5.8 hr period. This result was obtained by using an open model boundary from Nice, France to Calvi, Corsica and an artificial solid boundary from Corsica to Elba and the Italian mainland. This seiche has been identified with a 5.8 hr period wave which was revealed in the sea-level variations at Genoa and Imperia.

Numerical modelling of stratified flow: a spectral approach

A numerical formulation is developed to solve the three-dimensional hydrodynamic equations which describe flow in a stratified sea.Arbitrary continuous physically realistic variations of density and eddy viscosity can be included in the model, which is sufficiently flexible to be applicable to sea areas of any horizontal extent and depth. A continuous current profile from sea surface to sea bed, is computed with the model. A method for expanding computed current profiles in terms of vertical modes is proposed and the contribution of these modes to the current profiles is considered.The time variation of the wind-induced circulation of a stratified lake in response to a suddenly imposed and maintained wind stress is examined. Calculations show that the wind-driven surface current is modulated by the internal seiche motion of the lake.

PATTERNS OF CIRCULATION AND NUTRIENT SUPPLY IN A MEDIUM RESIDENCE-TIME RESERVOIR KOOTENAY LAKE, BRITISH COLUMBIA

Kootenay Lake is a long, deep lake in the Columbia River System. It is a medium residence-time system in which the physical and chemical characteristics are influenced by the two major rivers entering the lake. To understand seasonal circulation patterns it is necessary to account for the interactive effects of three separate processes; these are mixed-layer dynamics, internal wave behaviour and the riverine circulation. Incoming river water may move laterally through the lake as a surface overflow, an intermediate depth interflow, or a near-bottom underflow. Vertical redistribution of riverine water masses is dependent upon surface-driven processes. The combined effect of both of the above processes may be altered still further by internal seiche motions, which can reposition various layers within the lake relative to the surface, where wind mixing is more intense. Construction of dams on both upstream rivers have led to changes in the timing and temperature of discharge to the lake. To predict the effec...

Application of the Galerkin method to the formulation of a three-dimensional nonlinear hydrodynamic numerical sea model

A mathematical formulation is presented for solving the three-dimensional nonlinear hydrodynamic equations, using the Galerkin method with an arbitrary set of basis functions. An explicit time splitting method is used to integrate these equations through time. The time splitting method is formulated in such a way that the advective terms, which are computationally expensive to evaluate, are integrated with a longer time step than the linear terms. The length of the time step used to integrate the linear terms is determined by the propagation speed of the gravity waves. The paper demonstrates that using this time splitting method an accurate and computationally economic solution of the full three-dimensional equations is possible. Numerical results are presented for the nonlinear seiche motion in a one-dimensional basin, and for the three-dimensional wind induced flow in a closed rectangular basin, using basis sets of cosine functions, Chebyshev polynomials and Gram-Schmidt orthogonalized polynomials.

Seiche Excitation in Port San Juan, British Columbia

Seiche motions observed in San Juan Harbour with a bottom-mounted pressure gauge have been Fourier-analyzed and interpreted in terms of a theoretical model of oscillations in a rectangular basin with an exponential depth profile. Two of the observed periods (at 14.6 and 38.5 min) are identified with resonances of the basin; two other significant low frequency peaks (at 21 and 55 min) do not coincide with resonant periods of the basin and must be due to strong external forcing. Higher frequency fluctuations (20–160 s) are attributed to swell and to its subharmonic interactions with edge waves. Key words: water waves, seiches, mathematical model, Juan de Fuca Strait, British Columbia