scholarly journals Gerstner waves in the presence of mean currents and rotation

2017 ◽  
Vol 820 ◽  
pp. 511-528 ◽  
Author(s):  
A. Constantin ◽  
S. G. Monismith
Keyword(s):  
Free Surface ◽  
Wind Waves ◽  
Nonlinear Phenomenon ◽  
Fast Mode ◽  
Lagrangian Analysis ◽  
Vertical Scale ◽  
The Mean ◽  
Gerstner Waves ◽  
Mean Current ◽  
O 10

We present a Lagrangian analysis of nonlinear surface waves propagating zonally on a zonal current in the presence of the Earth’s rotation that shows the existence of two modes of wave motion. The first, ‘fast’ mode, one with wavelengths commonly found for wind waves and swell in the ocean, represents the wave–current interaction counterpart of the rotationally modified Gerstner waves found first by Pollard (J. Geophys. Res., vol. 75, 1970, pp. 5895–5898) that quite closely resemble Stokes waves. The second, slower, mode has a period nearly equal to the inertial period and has a small vertical scale such that very long, e.g. $O(10^{4}~\text{km})$ wavelength, waves have velocities etc. that decay exponentially from the free surface over a scale of $O(10~\text{m})$ that is proportional to the strength of the mean current. In both cases, the particle trajectories are closed in a frame of reference moving with the mean current, with particle motions in the second mode describing inertial circles. Given that the linear analysis of the governing Eulerian equations only captures the fast mode, the slow mode is a fundamentally nonlinear phenomenon in which very small free surface deflections are manifestations of an energetic current.

Nonlinear resonance of free surface waves in a current over a sinusoidal bottom: a numerical study

1994 ◽  
Vol 279 ◽  
pp. 377-405 ◽  
Author(s):  
Paolo Sammarco ◽  
Chiang C. Mei ◽  
Karsten Trulsen
Keyword(s):  
Free Surface ◽  
Numerical Study ◽  
Fixed Bed ◽  
Nonlinear Resonance ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Free Surface Waves ◽  
Linearized Theory ◽  
The Mean ◽  
Mean Current

We examine the free surface flow over a fixed bed covered by rigid sinusoidal dunes. The mean current velocity is near the critical value at which the linearized theory predicts unbounded response. By allowing transients we examine the instability of the steady and nonlinear solution of Mei (1969) and the possibility of chaos when the current has a small oscillatory component.

scholarly journals On the performance of a photosystem II reaction centre-based photocell

2017 ◽  
Vol 8 (10) ◽  
pp. 6871-6880 ◽  
Author(s):  
Richard Stones ◽  
Hoda Hossein-Nejad ◽  
Rienk van Grondelle ◽  
Alexandra Olaya-Castro
Keyword(s):  
Photosystem Ii ◽  
Current Noise ◽  
Reaction Centre ◽  
Electron Counting ◽  
The Mean ◽  
Counting Statistics ◽  
Mean Current

We investigate the performance of a theoretical photosystem II reaction centre-inspired photocell device through the framework of electron counting statistics. In particular we look at the effect of a structured vibrational environment on the mean current and current noise.

scholarly journals Submesoscale Instability and Generation of Mesoscale Anticyclones near a Separation of the California Undercurrent

2015 ◽  
Vol 45 (3) ◽  
pp. 613-629 ◽  
Author(s):  
M. Jeroen Molemaker ◽  
James C. McWilliams ◽  
William K. Dewar
Keyword(s):  
Computational Grid ◽  
Relative Vorticity ◽  
Monterey Bay ◽  
Depth Range ◽  
Narrow Strip ◽  
Centrifugal Instability ◽  
The Mean ◽  
Flow Inertia ◽  
Mean Current ◽  
Current Pathway

AbstractThe California Undercurrent (CUC) flows poleward mostly along the continental slope. It develops a narrow strip of large negative vertical vorticity through the turbulent boundary layer and bottom stress. In several downstream locations, the current separates, aided by topographic curvature and flow inertia, in particular near Point Sur Ridge, south of Monterey Bay. When this happens the high-vorticity strip undergoes rapid instability that appears to be mesoscale in “eddy-resolving” simulations but is substantially submesoscale with a finer computational grid. The negative relative vorticity in the CUC is larger than the background rotation f, and Ertel potential vorticity is negative. This instigates ageostrophic centrifugal instability. The submesoscale turbulence is partly unbalanced, has elevated local dissipation and mixing, and leads to dilution of the extreme vorticity values. Farther downstream, the submesoscale activity abates, and the remaining eddy motions exhibit an upscale organization into the mesoscale, resulting in long-lived coherent anticyclones in the depth range of 100–500 m (previously called Cuddies) that move into the gyre interior in a generally southwestward direction. In addition to the energy and mixing effects of the postseparation instability, there is are significant local topographic form stress and bottom torque that retard the CUC and steer the mean current pathway.

scholarly journals Probabilistic Bearing Capacity of a Pavement Resting on Fibre Reinforced Embankment Considering Soil Spatial Variability

2021 ◽  
Vol 7 ◽  
Author(s):  
Kouseya Choudhuri ◽  
Debarghya Chakraborty
Keyword(s):  
Spatial Variability ◽  
Soil Properties ◽  
Bearing Capacity ◽  
Coefficient Of Variation ◽  
Friction Angle ◽  
Horizontal Scale ◽  
Vertical Scale ◽  
Scale Of Fluctuation ◽  
The Mean ◽  
The Finite Difference Method

This paper intends to examine the influence of spatial variability of soil properties on the probabilistic bearing capacity of a pavement located on the crest of a fibre reinforced embankment. An anisotropic random field, in combination with the finite difference method, is used to carry out the probabilistic analyses. The cohesion and internal friction angle of the soil are assumed to be lognormally distributed. The Monte Carlo simulations are carried out to obtain the mean and coefficient of variation of the pavement bearing capacity. The mean bearing capacity of the pavement is found to decrease with the increase in horizontal scale of fluctuation for a constant vertical scale of fluctuation; whereas, the coefficient of variation of the bearing capacity increases with the increase in horizontal scale of fluctuation. However, both the mean and coefficient of variation of bearing capacity of the pavement are observed to be increasing with the increase in vertical scale of fluctuation for a constant horizontal scale of fluctuation. Apart from the different scales of fluctuation, the effects of out of the plane length of the embankment and randomness in soil properties on the probabilistic bearing capacity are also investigated in the present study.

scholarly journals Assessment of CFD turbulence models for free surface flow simulation and 1-D modelling for water level calculations over a broad-crested weir floodway

Water SA ◽  
2019 ◽  
Vol 45 (3 July) ◽  
Author(s):  
Ahmed M Helmi
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Water Level ◽  
Dimensional Analysis ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Cfd Simulations ◽  
One Dimensional ◽  
The Mean ◽  
The One

Floodways, where a road embankment is permitted to be overtopped by flood water, are usually designed as broad-crested weirs. Determination of the water level above the floodway is crucial and related to road safety. Hydraulic performance of floodways can be assessed numerically using 1-D modelling or 3-D simulation using computational fluid dynamics (CFD) packages. Turbulence modelling is one of the key elements in CFD simulations. A wide variety of turbulence models are utilized in CFD packages; in order to identify the most relevant turbulence model for the case in question, 96 3-D CFD simulations were conducted using Flow-3D package, for 24 broad-crested weir configurations selected based on experimental data from a previous study. Four turbulence models (one-equation, k-ε, RNG k-ε, and k-ω) ere examined for each configuration. The volume of fluid (VOF) algorithm was adopted for free water surface determination. In addition, 24 1-D simulations using HEC-RAS-1-D were conducted for comparison with CFD results and experimental data. Validation of the simulated water free surface profiles versus the experimental measurements was carried out by the evaluation of the mean absolute error, the mean relative error percentage, and the root mean square error. It was concluded that the minimum error in simulating the full upstream to downstream free surface profile is achieved by using one-equation turbulence model with mixing length equal to 7% of the smallest domain dimension. Nevertheless, for the broad-crested weir upstream section, no significant difference in accuracy was found between all turbulence models and the one-dimensional analysis results, due to the low turbulence intensity at this part. For engineering design purposes, in which the water level is the main concern at the location of the flood way, the one-dimensional analysis has sufficient accuracy to determine the water level.

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

1978 ◽  
Vol 22 (04) ◽  
pp. 203-211
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Stream ◽  
The Body ◽  
Two Dimensional ◽  
Third Order ◽  
Submerged Body ◽  
The Mean ◽  
The Waves

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

The Vertical Mean Force and Moment of Submerged Bodies Under Waves

1971 ◽  
Vol 15 (03) ◽  
pp. 231-245 ◽  
Author(s):  
C. M. Lee ◽  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Added Mass ◽  
Cross Sectional Area ◽  
The Body ◽  
Slender Body ◽  
Longitudinal Distribution ◽  
Vertical Force ◽  
Sectional Area ◽  
Cross Sectional ◽  
The Mean

A neutrally buoyant slender body of arbitrary sectional form, submerged beneath a free surface, is free to respond to an incident plane progressive wave system. The fluid is assumed inviscid, incompressible, homogeneous and infinitely deep. The first-order oscillatory motion of the body and the second-order time-average vertical force and pitching moment acting on the body are obtained in terms of Kochin's function. By use of slender-body theory for a deeply submerged body, the final expressions for the mean force and the moment are shown to depend on the longitudinal distribution of sectional area and added mass and on the amplitude and the frequency of the ambient surface waves. The magnitude of the mean force for various simple geometric cylinders is compared with that of a circular cylinder of equal cross-sectional area. The mean force on a nonaxisymmetric body is often approximated by replacing the section with circular profiles of equivalent cross-sectional area. A better scheme of approximation is presented, based on a simple way of estimating the two-dimensional added mass. It is expected that the effect of the cross-sectional geometry on mean vertical force and moment will be more significant when the body is very close to the free surface.

scholarly journals Deceleration of droplets that glide along the free surface of a bath

2016 ◽  
Vol 803 ◽  
pp. 313-331 ◽  
Author(s):  
Jacob Hale ◽  
Caleb Akers
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Droplet Diameter ◽  
Reynolds Numbers ◽  
Viscous Drag ◽  
Bath Surface ◽  
Exponential Rate ◽  
Viscous Coupling ◽  
Air Film ◽  
O 10

A droplet obliquely impacting a bath surface of the same fluid can traverse along the interface while slowing at an exponential rate. The droplet rests on a thin film of air, deforms the bath surface creating a dimple and travels along the surface similarly to a wave pulse. Viscous coupling of the droplet and bath surfaces through the air film leads to viscous drag on the bath and perturbs the wave motion of the otherwise free surface. Even though the Reynolds numbers are greater than unity ($\mathit{Re}\,O(10{-}100)$), we show that the droplet’s deceleration is only due to viscous coupling through the air gap. The rate of deceleration is found to increase linearly with droplet diameter.

Experimental study of the initial stages of wind waves' spatial evolution

2011 ◽  
Vol 681 ◽  
pp. 462-498 ◽  
Author(s):  
DAN LIBERZON ◽  
LEV SHEMER
Keyword(s):  
Energy Transfer ◽  
Growth Rates ◽  
Water Surface ◽  
Wind Waves ◽  
Pressure Fluctuations ◽  
Theoretical Models ◽  
Small Scale ◽  
Wave Flume ◽  
Spatial Growth ◽  
The Mean

Despite a significant progress and numerous publications over the last few decades a comprehensive understanding of the process of waves' excitation by wind still has not been achieved. The main goal of the present work was to provide as comprehensive as possible set of experimental data that can be quantitatively compared with theoretical models. Measurements at various air flow rates and at numerous fetches were carried out in a small scale, closed-loop, 5 m long wind wave flume. Mean airflow velocity and fluctuations of the static pressure were measured at 38 vertical locations above the mean water surface simultaneously with determination of instantaneous water surface elevations by wave gauges. Instantaneous fluctuations of two velocity components were recorded for all vertical locations at a single fetch. The water surface drift velocity was determined by the particle tracking velocimetry (PTV) method. Evaluation of spatial growth rates of waves at various frequencies was performed using wave gauge records at various fetches. Phase relations between various signals were established by cross-spectral analysis. Waves' celerities and pressure fluctuation phase lags relative to the surface elevation were determined. Pressure values at the water surface were determined by extrapolating the measured vertical profile of pressure fluctuations to the mean water level and used to calculate the form drag and consequently the energy transfer rates from wind to waves. Directly obtained spatial growth rates were compared with those obtained from energy transfer calculations, as well as with previously available data.

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