A three-dimensional theory for the development and migration of deep sea sedimentary waves

doi:10.1016/S0967-0637(01)00026-7

Deep Sea Research Part I: Oceanographic Research Papers

Volume 48, Issue 11, November 2001, Pages 2497-2519

https://doi.org/10.1016/S0967-0637(01)00026-7 Get rights and content

Abstract

A perturbation model is presented for a velocity field of a bottom current flowing over a sinusoidal topography or an obstacle. The model extends existing theory by taking into account the three-dimensional Coriolis vector and an initial horizontal velocity vector at any orientation. One possible mechanism of the development of sedimentary waves in the vicinity of an obstacle by an arbitrarily oriented initial horizontal current is analyzed in detail. Space-stationary fluid particle oscillations are initiated on the downstream side of an obstacle, which can result in sedimentary waves. The model shows that their wavelength depends on latitude, water depth, obstacle width and orientation as well as the initial current direction and intensity. The model defines intervals for current velocities normal to the wave crest, for which the sedimentary waves grow (or are destroyed) or migrate in a certain direction. Information derived from bathymetric and seismic surveys, such as wavelength, height, orientation and migration direction of mudwaves, can be used to calculate the velocity component across the wave crest and to estimate the current direction, as is demonstrated for an example from the Argentine Basin (Project MUDWAVES, Site 5).

Introduction

Quasi-sinusoidal sedimentary waves of different size, characterized by wavelength and height, are commonly observed wherever a transport of fine-grained sediments occurs. We find examples in deserts, rivers and coastal environments. Abyssal mudwaves are large-scale bed forms found in many ocean basins where deep currents play an important role in sediment transport and deposition. These waves form in fine-grained sediments, and often develop on flanks of large sediment drifts (Fox et al., 1968; Hollister et al., 1974; Flood, 1988; Flood and Shor, 1988), along continental margins (Jacobi et al., 1975), and on the flanks of channel-levee systems caused by overflow of turbiditic currents (Damuth, 1979; Normark et al., 1980). The heights of these waves range from less than 1 m to more than 100 m, whereas the wavelength ranges from about 100 m up to ∼10 km. The waves can be identified in seismic profiles over significant sub-bottom depth ranges, suggesting that the waves have been built up and preserved over very long time periods (10⁴–10⁵ years).

Mudwave crests are often oriented almost parallel to the regional bottom flow direction and apparently migrate against the bottom current (upstream) and in an upslope direction (Hollister et al., 1974; Jacobi et al., 1975). Downstream migration has also been reported (Roberts and Kidd, 1979).

The behavior of sediment particles in the presence of bottom currents depends on the physics of particle movement in fluids and on processes at the boundary layer between sea-floor and water, and the velocity field as well as boundary layer processes have an influence on the sediment accumulation or the degree of erosion (McCave and Swift, 1976; Flood, 1988).

A basic theoretical approach to the evolution of sedimentary waves was developed by Queney (1947), Queney (1948), who relates a fluid flow over an initial topography to the presence of oscillations within the fluid column. The behavior of a stratified fluid medium can be described on the basis of his perturbation model, which was used to determine the influence of topography (sinusoidal topography and elongated obstacle) on atmospheric streams. Queney (1948) described different types of stationary ‘‘lee waves” caused by an elongated obstacle. According to his model, the wavelengths of lee waves depend either on the vertical-stream stratification (short stationary or gravity waves), or on the Coriolis parameter (gravity-inertia lee waves), or on the latitudinal variation of the Coriolis parameter (long geostrophic or Rossby lee waves). The direction of the horizontal current is taken perpendicular to the obstacle crest, and the Coriolis parameter represents the component of the Coriolis vector normal to the earth surface.

Early qualitative studies of the dynamics of deep-sea sedimentary waves (Normark et al., 1980; Kolla et al., 1980) make use of models developed for shallow water (Brooke, 1959; Kennedy (1963), Kennedy (1969); Reynolds, 1965; Fredsoe, 1974; Hand, 1974), in which only the gravity is taken into consideration and which therefore cannot be directly used for the explanation of the origin and geometry of deep sea sedimentary waves.

Flood (1988) proposed a lee-wave model for deep-sea sinusoidal sedimentary waves to describe the velocity field and sedimentation rates and to explain the upstream migration direction. Blumsack and Weatherly (1989) derived a mechanism for sedimentary wave growth which occurs at certain angles between the mean flow and the crest orientation due to preferential deposition at sedimentary wave crests. Both Flood (1988) and Blumsack and Weatherly (1989) use the Coriolis parameter as a scalar as defined by Queney (1948). However, because the orientation of sedimentary waves relative to north was not considered (especially for greater water depths), these solutions to determine the velocity field over the sedimentary wave topography in a deep sea environment are incomplete, as will be shown later.

The most extensive study on sedimentary wave dynamics was carried out during Project MUDWAVES (e.g., Manley and Flood (1993a), Manley and Flood (1993b); Flood et al., 1993; Weatherly, 1993). This yielded detailed three-dimensional maps of mudwave fields in the Argentine Basin. In addition, Flood et al. (1993) have discussed the interaction between bottom topography and weakly stratified flows. All models proposed so far describe only mudwave development and do not explain the onset of sedimentary waves in the deep sea in detail.

In this paper, a perturbation model for the velocity field over a sinusoidal topography and an elongated obstacle is proposed, which includes (1) the orientation of sedimentary waves relative to north (three-dimensional Coriolis vector) and (2) an arbitrarily oriented mean flow velocity vector. A phase analysis of the sedimentation rate variation over a sedimentary wave topography allows to divide the sedimentation rate into two components: the growth rate, which causes a growth or a destruction of the sedimentary waves, and the migration rate, which causes their apparent migration. These are controlled by the sedimentary wave geometry and location and by the horizontal velocity. The direction of the horizontal velocity and its magnitude normal to the wave crest can be estimated from the behavior of the two sedimentation rate components. To illustrate the impact of the growth and migration rates, a simple modeling of deposition leading to a topography change is carried out.

A possible mechanism of sedimentary wave creation on the downstream side of an elongated obstacle, at first studied by Queney for a stratified fluid with strong stability, is developed for the deep sea situation with weak stability. The frequency analysis of the sedimentation rate variation in the vicinity of an elongated obstacle allows estimation of the geometry of sedimentary waves and conditions for their creation. The model predictions are applied to mudwave fields investigated during Project MUDWAVES (Flood et al., 1993).

Section snippets

Velocity field perturbation over a sinusoidal topography

Given a laminar flow, the perturbations of the velocity due to bottom topography depend on (1) the initial horizontal velocity vector of the fluid medium, (2) the shape of the initial topography, (3) external forces (Coriolis force and gravity) and (4) vertical fluid stratification. The hydrodynamic equations for incompressible, non-viscous fluids on the earth's surface are given by LeBlond and Mysak (1978): $ρ D U d t+ρ f × U + ∇ p−ρ G =0, Dρ d t=0, ∇ · U =0,$ where $D d t=∂ ∂t+ U · ∇$ describes the total derivative with

Development and migration of sedimentary waves (method of the phase analysis)

To investigate the relationship between a bottom current, an initial topography and its modification by sedimentation, we start with the stationary oscillation of fluid particles in the water column over a sinusoidal topography. If sediment particles are present in the water column, their accumulation directly depends on the ambient current velocity at the sea floor. Depositional processes may vary from deposition through winnowing to erosion with increasing velocity. Regular velocity

One possible mechanism of sedimentary wave creation (frequency analysis)

By assuming that the stationary oscillations of water column particles are responsible for laterally variable velocities in laminar currents, we can predict a characteristic accumulation pattern as a result. If the currents act over sufficiently long time intervals and the oscillations of the water column can be fixed in space by topographic features such as sea-mounts, ridges or slumps, sedimentary waves can be generated.

To model the quantitative evolution of sedimentary waves in the deep sea,

Comparison to existing models

The first effort to understand oscillatory behavior in the presence of currents/flows was undertaken by Queney (1947), Queney (1948) with application to atmospheric flow using specific physical parameters of air as stability and compressibility. He provided a perturbation theory for flow over a sinusoidal topography, which, however, was simplified by assuming a flow perpendicular to wave crests and treating the Coriolis force as a scalar.

Flood (1988) applied this approach directly to ocean

Application to field observations

To relate bathymetric and seismic data to the characteristics of the acting bottom currents, we make use of the relationships presented above to estimate the normal-crest velocity component U₀, to derive the orientation of the current flow, and to determine whether the mudwave topography will be stationary and whether the observed migration direction is consistent with the model predictions. To determine the interval of current velocities for a given wavelength and geographic location for which

Conclusions

To date, existing theoretical models for the description of sedimentary wave dynamics in water do not take into account all factors that are important for the onset and development of deep sea sedimentary waves. These factors are the three-dimensional Coriolis vector and an arbitrarily oriented initial horizontal velocity vector. The model for the velocity perturbation field over a sinusoidal topography proposed in this paper provides a new solution, which can also be used to relate structural

Acknowledgements

This research was funded by the Senator für Bildung und Wissenschaft der Hansestadt Bremen and the Deutsche Forschungsgemeinschaft. This publication is contribution no. 318 of the Special Research Project 261: The South Atlantic in the Late Quaternary. We want to thank L. Zühlsdorff, H. von Lom, A. Macario, Christoph and David Völker for reviewing the manuscript and providing helpful advice.

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A three-dimensional theory for the development and migration of deep sea sedimentary waves

Abstract

Introduction

Section snippets

Velocity field perturbation over a sinusoidal topography

Development and migration of sedimentary waves (method of the phase analysis)

One possible mechanism of sedimentary wave creation (frequency analysis)

Comparison to existing models

Application to field observations

Conclusions

Acknowledgements

Deep-sea Research II

Deep-sea Research

Deep-sea Research

Deep-sea Research

Deep-sea Research II

Marine Geology

Marine Geology

Deep-sea Research II

Deep-sea Research II

Marine Geology

Marine Geology

Deep-Sea Research II

Shearing flow over a wavy boundary

Journal of Fluid Mechanics