Author

# P. J. Blennerhassett

Bio: P. J. Blennerhassett is an academic researcher from Imperial College London. The author has contributed to research in topics: Boundary layer & Dispersion (water waves). The author has an hindex of 1, co-authored 1 publications receiving 126 citations.

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TL;DR: In this article, a linear stability analysis of the Laminar flow of air over water confined between two infinite parallel plates was made and the conditions at which small amplitude surface waves first begin to grow were determined.

Abstract: The fully developed laminar flow of air over water confined between two infinite parallel plates was used to study nonlinear effects in the generation of surface waves. A linear stability analysis of the basic flow was made and the conditions at which small amplitude surface waves first begin to grow were determined. Then, following Stewartson & Stuart (1971), the nonlinear stability of the flow was examined and the usual parabolic equation with cubic nonlinearity obtained for the amplitude of the disturbances. The calculation of the linear stability characteristics and the coefficients appearing in the amplitude equation was a lengthy computational task, with most interest centred on the coefficient of the nonlinear terms in the amplitude equation. In two profiles, used as crude models of a boundary layer flow of air over water, the calculations indicated that, over a range of parameters, the non-linear effects would reduce the growth rate of the surface waves and hence lead to equilibrium amplitude waves.

126 citations

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TL;DR: In this article, the spectral dissipation of wind-generated waves is modeled as a function of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties.

Abstract: New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is nonzero only when a nondimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short-wave dissipation is introduced to represent the dissipation of short waves due to longer breaking waves. A reduction of the wind-wave generation of short waves is meant to account for the momentum flux absorbed by longer waves. These parameterizations are combined and calibrated with the discrete interaction approximation for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spect...

709 citations

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IFREMER

^{1}TL;DR: Ardhuin et al. as discussed by the authors used satellite Synthetic Aperture Radar data to estimate the dissipation of swell energy for a number of storms, and interpreted the increase of dissipation rate in dissipation with swell steepness as a laminar to turbulent transition of the boundary layer.

Abstract: Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to estimate the dissipation of swell energy for a number of storms. Swells can be very persistent with energy e-folding scales exceeding 20,000 km. For increasing swell steepness this scale shrinks systematically, down to 2800 km for the steepest observed swells, revealing a significant loss of swell energy. This value corresponds to a normalized energy decay in time beta = 4.2 x 10(-6) s(-1). Many processes may be responsible for this dissipation. The increase of dissipation rate in dissipation with swell steepness is interpreted as a laminar to turbulent transition of the boundary layer, with a threshold Reynolds number of the order of 100,000. These observations of swell evolution open the way for more accurate wave forecasting models, and provide a constraint on swell-induced air-sea fluxes of momentum and energy. Citation: Ardhuin, F., B. Chapron, and F. Collard (2009), Observation of swell dissipation across oceans, Geophys. Res. Lett., 36, L06607, doi: 10.1029/2008GL037030.

308 citations

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TL;DR: In this paper, the complex Ginzburg-Landau equation in one spatial dimension with periodic boundary conditions is studied from the viewpoint of effective low-dimensional behavior by three distinct methods.

Abstract: The complex Ginzburg-Landau equation in one spatial dimension with periodic boundary conditions is studied from the viewpoint of effective low-dimensional behaviour by three distinct methods. Linear stability analysis of a class of exact solutions establishes lower bounds on the dimension of the universal, or global, attractor and the Fourier spanning dimension, defined as the number of Fourier modes required to span the universal attractor. The authors use concepts from the theory of inertial manifolds to determine rigorous upper bounds on the Fourier spanning dimension, which also establishes the finite dimensionality of the universal attractor. Upper bounds on the dimension of the attractor itself are obtained by bounding (or, for some parameter values, computing exactly) the Lyapunov dimension and invoking a recent theorem that asserts that the Lyapunov dimension, defined by the Kaplan-Yorke formula with the universal (global) Lyapunov exponents, is an upper bound on the Hausdorff dimension. This study of low dimensionality in the complex Ginzburg-Landau equation allows for an examination of the current techniques used in the rigorous investigation of finite-dimensional behaviour. Contact is made with some recent results for fluid turbulence models, and the authors discuss some unexplored directions in the area of low-dimensional behaviour in the complex Ginzburg-Landau equation.

208 citations

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TL;DR: In this article, the authors describe a global database of these parameters, estimated from a well-validated numerical wave model, that uses traditional forms of the wave generation and dissipation parameterizations, and covers the years 2003-2007.

161 citations

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TL;DR: In this article, the authors present a classification,scheme for the various instabilities arising in parallel two-phase flow, and the equation governing the rate of change of the linetic energy of the disturbances is evaluated for relevant values of the physical parameters.

152 citations