David R. Fuhrman

Flow and sediment transport induced by a plunging solitary wave

[1] Two parallel experiments involving the evolution and runup of plunging solitary waves on a sloping bed were conducted: (1) a rigid-bed experiment, allowing direct (hot film) measurements of bed shear stresses and (2) a sediment-bed experiment, allowing for the measurement of pore water pressures and for observation of the morphological changes. The two experimental conditions were kept as similar as possible. The experiments showed that the complete sequence of the plunging solitary wave involves the following processes: shoaling and wave breaking; runup; rundown and hydraulic jump; and trailing wave. The bed shear stress measurements showed that the mean bed shear stress increases tremendously (with respect to that in the approaching wave boundary layer), by as much as a factor of 8, in the runup and rundown stages, and that the RMS value of the fluctuating component of the bed shear stress is also affected, by as much as a factor of 2, in the runup and hydraulic jump stages. The pore water pressure measurements showed that the sediment at (or near) the surface of the bed experiences upward directed pressure gradient forces during the down-rush phase. The magnitude of this force can reach values as much as approximately 30% of the submerged weight of the sediment. The experiments further showed that the sediment transport occurs in the sheet flow regime for a substantial portion of the beach covering the area where the entire sequence of the wave breaking takes place. The bed morphology is explained qualitatively in terms of the measured bed shear stress and the pressure gradient forces.

Numerical investigation of flow and scour around a vertical circular cylinder

Flow and scour around a vertical cylinder exposed to current are investigated by using a three-dimensional numerical model based on incompressible Reynolds-averaged Navier–Stokes equations. The model incorporates (i) k-ω turbulence closure, (ii) vortex-shedding processes, (iii) sediment transport (both bed and suspended load), as well as (iv) bed morphology. The influence of vortex shedding and suspended load on the scour are specifically investigated. For the selected geometry and flow conditions, it is found that the equilibrium scour depth is decreased by 50% when the suspended sediment transport is not accounted for. Alternatively, the effects of vortex shedding are found to be limited to the very early stage of the scour process. Flow features such as the horseshoe vortex, as well as lee-wake vortices, including their vertical frequency variation, are discussed. Large-scale counter-rotating streamwise phase-averaged vortices in the lee wake are likewise demonstrated via numerical flow visualization. These features are linked to scour around a vertical pile in a steady current.

A numerical study of crescent waves

In this paper, a high-order Boussinesq model is used to conduct a systematic numerical study of crescent (or horseshoe) water wave patterns in a tank, arising from the instability of steep deep-water waves to three-dimensional disturbances. The most unstable phase-locked (L2) crescent patterns are investigated, and comparisons with experimental measurements confirm the quantitative accuracy of the model. The unstable growth rate is also investigated, as are the effects of variable nonlinearity. The dominant physical mechanism is clearly demonstrated (through time and space series analysis) to be the established quintet resonant interaction, involving the primary wave with a pair of symmetric satellites. A numerical investigation into oscillating crescent patterns is also included, and a detailed account of the complicated oscillation cycle is presented. These patterns are shown to arise from quintet resonant interactions involving the primary wave with two unsymmetric satellite pairs. Pre-existing methods for analysing the stability of steep deep-water plane waves subject to three-dimensional perturbations are extended to provide accurate quantitative estimates for the oscillation period. A possible explanation for their selection in experiments is also provided. Finally, we use the model to conduct a series of experiments involving competition between various unstable modes. The results generally show that multiple instabilities can grow simultaneously, provided that they are of roughly equivalent strength. Results using random perturbations also match observations in physical experiments both in the form (i.e. two- or three-dimensional) and the location of the initial instability. The computational results are the first examples of highly nonlinear (to the breaking point) deep-water wave modeling in two horizontal dimensions with a Boussinesq model. The efficiency of the model has allowed for a quantitative study of these phenomena at significantly larger spatial and temporal scales than have been demonstrated previously, providing new insight into the complicated physical processes involved.

Numerical simulation of lowest-order short-crested wave instabilities

A numerical study of doubly periodic deep-water short-crested wave instabilities, arising from various quartet resonant interactions, is conducted using a high-order Boussinesq-type model. The model is first verified through a series of simulations involving classical class I plane wave instabilities. These correctly lead to well-known (nearly symmetric) recurrence cycles below a previously established breaking threshold steepness, and to an asymmetric evolution (characterized by a permanent transfer of energy to the lower side-band) above this threshold, with dissipation from a smoothing filter promoting this behaviour in these cases. A series of class Ia short-crested wave instabilities, near the plane wave limit, are then considered, covering a wide range of incident wave steepness. A close match with theoretical growth rates is demonstrated near the inception. It is shown that the unstable evolution of these initially three-dimensional waves leads to an asymmetric evolution, even for weakly nonlinear cases presumably well below breaking. This is characterized by an energy transfer to the lower side-band, which is also accompanied by a similar transfer to more distant upper side-bands. At larger steepness, the evolution leads to a permanent downshift of both the mean and peak frequencies, driven in part by dissipation, effectively breaking the quasi-recurrence cycle. A single case involving a class Ib short-crested wave instability at relatively large steepness is also considered, which demonstrates a reasonably similar evolution. These simulations consider the simplest physical situations involving three-dimensional instabilities of genuinely three-dimensional progressive waves, revealing qualitative differences from classical two-dimensional descriptions. This study is therefore of fundamental importance in understanding the development of three-dimensional wave spectra.

Third-order theory for bichromatic bi-directional water waves

A new third-order solution for bichromatic bi-directional water waves in finite depth is presented. Earlier derivations of steady bichromatic wave theories have been restricted to second-order in finite depth and third-order in infinite depth, while third-order theories in finite depth have been limited to the case of monochromatic short-crested waves. This work generalizes these earlier works. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential, and it incorporates the effect of an ambient current with the option of specifying zero net volume flux. The nonlinear dispersion relation is generalized to account for many interacting wave components with different frequencies and amplitudes, and it is verified against classical expressions from the literature. Limitations and problems with these classical expressions are identified. Next, third-order resonance curves for finite-amplitude carrier waves and their three-dimensional perturbations are calculated. The influence of nonlinearity on these curves is demonstrated and a comparison is made with the location of dominant class I and class II wave instabilities determined by classical stability analyses. Finally, third-order resonance curves for the interaction of nonlinear waves and an undular sea bottom are calculated. On the basis of these curves, the previously observed downshift/upshift of reflected/transmitted class III Bragg scatter is, for the first time, explained.

Short-crested waves in deep water : a numerical investigation of recent laboratory experiments

A numerical study of quasi-steady doubly periodic monochromatic short-crested wave patterns in deep water is conducted using a high-order Boussinesq-type model. Simulations using linear wavemaker conditions in the nonlinear model are initially used to approximate conditions from recent laboratory experiments. The computed patterns share many features with those observed in wavetanks, including bending (both frontwards and backwards) of the wave crests, dipping at the crest centrelines, and a pronounced long modulation in the direction of propagation. A new and simple explanation for these features is provided, involving the release of spurious free first harmonics, due to the neglect of steady third-order components in the three-dimensional wave generation. A comparison with the experimentally observed beat length and amplitude matches the theoretical/numerical predictions well. Additionally, direct inclusion of steady third-order components in the wave generation is shown to reduce significantly the modulations (and other unsteady features), further confirming the explanation. This numerical work makes apparent some previously unknown difficulties associated with the physical generation of even the simplest three-dimensional waves, adding significant insight into the interpretation of recent experimental observations.

Physically-consistent wall boundary conditions for the k-ω turbulence model

A model solving Reynolds-averaged Navier–Stokes equations, coupled with k-ω turbulence closure, is used to simulate steady channel flow on both hydraulically smooth and rough beds. Novel experimental data are used as model validation, with k measured directly from all three components of the fluctuating velocity signal. Both conventional k = 0 and dk/dy = 0 wall boundary conditions are considered. Results indicate that either condition can provide accurate solutions, for the bulk of the flow, over both smooth and rough beds. It is argued that the zero-gradient condition is more consistent with the near wall physics, however, as it allows direct integration through a viscous sublayer near smooth walls, while avoiding a viscous sublayer near rough walls. This is in contrast to the conventional k = 0 wall boundary condition, which forces resolution of a viscous sublayer in all circumstances. Subsequent testing demonstrates that the zero-gradient condition allows the near-bed grid spacing near rough walls to be based on the roughness length, rather than the conventional viscous length scale, hence offering significant computational advantages.

Simulation of Wave-Plus-Current Scour beneath Submarine Pipelines

AbstractA fully coupled hydrodynamic and morphologic numerical model was utilized for the simulation of wave-plus-current scour beneath submarine pipelines. The model was based on incompressible Reynolds-averaged Navier–Stokes equations, coupled with k-ω turbulence closure, with additional bed and suspended load descriptions forming the basis for seabed morphology. The model was successfully validated against experimental measurements involving scour development and eventual equilibrium in pure-current flows over a range of Shields parameters characteristic of both clear-water and live-bed regimes. This validation complements previously demonstrated accuracy for the same model in simulating pipeline scour processes in pure-wave environments. The model was subsequently utilized to simulate combined wave-plus-current scour over a wide range of combined Keulegan–Carpenter numbers and relative current strengths. The resulting equilibrium scour depths and trends were shown to be in accordance with existing exp...

Analytical and numerical models for tsunami run-up

The classical analytical solution for the run-up of periodic long waves on an infinitely long slope is presented and discussed. This leads to simple expressions for the maximum run-up and the associated flow velocity in terms of the surf similarity parameter and the amplitude to depth ratio determined at some offshore location. We use these expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that the impact is very sensitive to the beach slope. Next, we present a numerical model based on a highly accurate Boussinesq-type formulation. This model incorporates nonlinear and dispersive effects, and is extended to include a moving shoreline. As a first step, the model is verified against the non-dispersive analytical run-up solution, demonstrating good quantitative accuracy. The model is then used to study an idealized three-dimensional nearshore-generated tsunami propagating over a hypothetical sound.

Erratum for “Simulation of Wave-Plus-Current Scour beneath Submarine Pipelines” by Bjarke Eltard Larsen, David R. Fuhrman, and B. Mutlu Sumer

D5.10 Interaction of the tsunami with the seabed. Implications for wind farms, aquaculture, coastal ecosystems and marine protected areas. Fuhrman, D. R., Eltard-Larsen, B., Sumer, B. M., Baykal, C., Dogulu, N., Duha Metin, A., Can Aydin, D., Yalciner, A. C., Omira, R., Lorenço, N. & Baptista, M. A., 2015, 57 p. Research output: Book/Report › Report – Annual report year: 2015 › Research › peer-review