WAVE AND CURRENT INTERACTIONS IN SHALLOW WATER

1986 ◽  
Vol 1 (20) ◽  
pp. 125
Author(s):  
Sung B. Yoon ◽  
Philip L.F. Liu
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Large Scale ◽  
Evolution Equations ◽  
Small Scale ◽  
Length Scale ◽  
Rip Currents ◽  
Coastal Currents ◽  
Protection Measures ◽  
Incident Cases

Interactions between waves and currents are common and important phenomena in the coastal zone. Coastal currents, such as longshore currents, rip currents, and river flows, can significantly change wave heights and directions of wave propagation. Consequently, the design for shoreline protection measures must be adjusted accordingly. Various theories for wave-current interactions exist and have been reviewed by Peregrine and Jonsson (1983). Most of these theories are developed for large-scale currents where the length-scale for the current variation is much greater than the typical wavelength. These theories cannot be applied to the coastal currents which are small-scale currents. In this paper, the interactions between currents and nonlinear shallow water waves are investigated. Boussinesq equations are used to derive evolution equations for spectral wave components. The current intensity is assumed to be larger than the leading wave orbital velocity and smaller than the group velocity. The length-scale of the current is much shorter than those assumed in the existing large-scale theories. To facilitate numerical computations, the parabolic approximation is applied and a simplified model is developed. A numerical example is given for the refraction and diffraction of cnoidal waves over a rip current on a sloping topography. Both normal and oblique incident cases are examined.

ABUNDANT SOLUTIONS OF CERTAIN NONLINEAR EVOLUTION EQUATIONS ARISING IN SHALLOW WATER WAVES

2020 ◽  
Vol 9 (4) ◽  
pp. 1795-1801
Author(s):  
P. Kumari ◽  
R. K. Gupta ◽  
S. Kumar
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Shallow Water Waves

scholarly journals A multifractal model for the momentum transfer process in wall-bounded flows

2017 ◽  
Vol 824 ◽  
Author(s):  
X. I. A. Yang ◽  
A. Lozano-Durán
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Small Scale ◽  
Length Scale ◽  
Cascade Process ◽  
Outer Length ◽  
Multifractal Formalism ◽  
Multiplicative Process ◽  
Stress Fluctuation

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation $\unicode[STIX]{x1D70F}_{l}^{\prime }$, where $l$ is the filtering length scale. According to the multifractal formalism, $\langle {\unicode[STIX]{x1D70F}^{\prime }}^{2}\rangle \sim \log (Re_{\unicode[STIX]{x1D70F}})$ and $\langle \exp (p\unicode[STIX]{x1D70F}_{l}^{\prime })\rangle \sim (L/l)^{\unicode[STIX]{x1D701}_{p}}$ in the log-region, where $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, $p$ is a real number, $L$ is an outer length scale and $\unicode[STIX]{x1D701}_{p}$ is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at $Re_{\unicode[STIX]{x1D70F}}=4200$.

scholarly journals Comment on “Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension” [Nonlinear Dyn,  doi:10.1007/s11071-017-3938-7]

2021 ◽  
Author(s):  
Piotr Rozmej ◽  
Anna Karczewska
Keyword(s):  
Surface Tension ◽  
Shallow Water ◽  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Two Dimensional ◽  
Shallow Water Waves ◽  
Small Parameters ◽  
Fifth Order

AbstractThe authors of the paper “Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension” Fokou et al. (Nonlinear Dyn 91:1177–1189, 2018) claim that they derived the equation which generalizes the KdV equation to two space dimensions both in first and second order in small parameters. Moreover, they claim to obtain soliton solution to the derived first-order (2+1)-dimensional equation. The equation has been obtained by applying the perturbation method Burde (J Phys A: Math Theor 46:075501, 2013) for small parameters of the same order. The results, if correct, would be significant. In this comment, it is shown that the derivation presented in Fokou et al. (Nonlinear Dyn 91:1177–1189, 2018) is inconsistent because it violates fundamental properties of the velocity potential. Therefore, the results, particularly the new evolution equation and the dynamics that it describes, bear no relation to the problem under consideration.

On the vorticity transport due to dissipating or breaking waves in shallow-water flow

2000 ◽  
Vol 407 ◽  
pp. 235-263 ◽  
Author(s):  
OLIVER BÜHLER
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Small Scale ◽  
Practical Consideration ◽  
Mean Flow ◽  
Vorticity Transport

Theoretical and numerical results are presented on the transport of vorticity (or potential vorticity) due to dissipating gravity waves in a shallow-water system with background rotation and bottom topography. The results are obtained under the assumption that the flow can be decomposed into small-scale gravity waves and a large-scale mean flow. The particle-following formalism of ‘generalized Lagrangian-mean’ theory is then used to derive an ‘effective mean force’ that captures the vorticity transport due to the dissipating waves. This can be achieved without neglecting other, non-dissipative, effects which is an important practical consideration. It is then shown that the effective mean force obeys the so-called ‘pseudomomentum rule’, i.e. the force is approximately equal to minus the local dissipation rate of the wave's pseudomomentum. However, it is also shown that this holds only if the underlying dissipation mechanism is momentum-conserving. This requirement has important implications for numerical simulations, and these are discussed.The novelty of the results presented here is that they have been derived within a uniform theoretical framework, that they are not restricted to small wave amplitude, ray-tracing or JWKB-type approximations, and that they also include wave dissipation by breaking, or shock formation. The theory is tested carefully against shock-capturing nonlinear numerical simulations, which includes the detailed study of a wavetrain subject to slowly varying bottom topography. The theory is also cross-checked in the appropriate asymptotic limit against recently formulated weakly nonlinear theories. In addition to the general finite-amplitude theory, detailed small-amplitude expressions for the main results are provided in which the explicit appearance of Lagrangian fields can be avoided. The motivation for this work stems partly from an on-going study of high-altitude breaking of internal gravity waves in the atmosphere, and some preliminary remarks on atmospheric applications and on three-dimensional stratified versions of these results are given.

Amplitude and frequency modulation of the small scales in a jet

2015 ◽  
Vol 772 ◽  
pp. 756-783 ◽  
Author(s):  
D. Fiscaletti ◽  
B. Ganapathisubramani ◽  
G. E. Elsinga
Keyword(s):  
Amplitude Modulation ◽  
Frequency Modulation ◽  
High Speed ◽  
Large Scale ◽  
Spectral Band ◽  
Physical Space ◽  
Small Scale ◽  
Length Scale ◽  
Air Jet ◽  
Amplitude And Frequency Modulation

The present study is an experimental investigation of the relationship between the large- and small-scale motions in the far field of an air jet at high Reynolds number. In the first part of our investigation, the analysis is based on time series of hot-wire anemometry (HWA), which are converted into space series after applying the Taylor hypothesis. By using a spectral filter, two signals are constructed, one representative of the large-scale motions ($2{\it\lambda}_{T}-L$, where ${\it\lambda}_{T}$ is the Taylor length scale, and $L$ is the integral length scale) and the other representative of the small-scale motions ($1.5{-}5{\it\eta}$, where ${\it\eta}$ is the Kolmogorov length scale). The small-scale signal is found to be modulated both in amplitude and in frequency by the energy-containing scales in an analogous way, both at the centreline and around the centreline. In particular, for positive fluctuations of the large-scale signal, the small-scale signal is locally stronger in amplitude (amplitude modulation), and it locally exhibits a higher number of local maxima and minima (frequency modulation). The extent of this modulation is quantified based on the strength of the large-scale fluctuations. The response of the small-scale motions to amplitude modulation can be considered instantaneous, being on the order of one Kolmogorov time scale. In the second part of our investigation we use long-range ${\it\mu}$PIV to study the behaviour of the small-scale motions in relation to their position in either high-speed or low-speed regions of the flow. The spatially resolved velocity vector fields allow us to quantify amplitude modulation directly in physical space. From this direct estimation in physical space, amplitude modulation is only 25 % of the value measured from HWA. The remaining 75 % comes from the fixed spectral band filter used to obtain the large- and small-scale signals, which does not consider the local convection velocity. A very similar overestimation of amplitude modulation when quantified in the time-frame is also obtained analytically. Furthermore, the size of the structures of intense vorticity does not change significantly in relation to the large-scale velocity fluctuation, meaning that there is no significant spatial frequency modulation. The remaining amplitude modulation in space can be explained as a statistical coupling between the strength of the structures of vorticity and their preferential location inside large-scale high-velocity regions. Finally, the implications that the present findings have on amplitude and frequency modulation in turbulent boundary layers (TBLs) are discussed.

Spontaneous Imbalance and Hybrid Vortex–Gravity Structures

2009 ◽  
Vol 66 (5) ◽  
pp. 1315-1326 ◽  
Author(s):  
Michael E. McIntyre
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
General Rule ◽  
Radiation Reaction ◽  
Water Dynamics ◽  
Small Scale ◽  
Wave Source ◽  
Vortical Motion ◽  
Inertia Gravity Waves

Abstract After reviewing the background, this article discusses the recently discovered examples of hybrid propagating structures consisting of vortex dipoles and comoving gravity waves undergoing wave capture. It is shown how these examples fall outside the scope of the Lighthill theory of spontaneous imbalance and, concomitantly, outside the scope of shallow-water dynamics. Besides the fact that going from shallow-water to continuous stratification allows disparate vertical scales—small for inertia–gravity waves and large for vortical motion—the key points are 1) that by contrast with cases covered by the Lighthill theory, the wave source feels a substantial radiation reaction when Rossby numbers R ≳ 1, so that the source cannot be prescribed in advance; 2) that examples of this sort may supply exceptions to the general rule that spontaneous imbalance is exponentially small in R; and 3) that unsteady vortical motion in continuous stratification can stay close to balance thanks to three quite separate mechanisms. These are as follows: first, the near-suppression, by the Lighthill mechanism, of large-scale imbalance (inertia–gravity waves of large horizontal scale), where “large” means large relative to a Rossby deformation length LD characterizing the vortical motion; second, the flaccidity, and hence near-steadiness, of LD-wide jets that meander and form loops, Gulf-Stream-like, on streamwise scales ≫ LD; and third, the dissipation of small-scale imbalance by wave capture leading to wave breaking, which is generically probable in an environment of random shear and straining. Shallow-water models include the first two mechanisms but exclude the third.

scholarly journals Towards fast large-scale flood simulations using 2D Shallow water modelling with depth-dependant porosity

2020 ◽  
Author(s):  
Vita Ayoub ◽  
Carole Delenne ◽  
Patrick Matgen ◽  
Pascal Finaud-Guyot ◽  
Renaud Hostache
Keyword(s):  
Shallow Water ◽  
Spatial Data ◽  
Large Scale ◽  
Model Performance ◽  
Water Model ◽  
Computational Time ◽  
Small Scale ◽  
Test Case ◽  
Strong Impact ◽  
Flood Simulations

<p><span>In hydrodynamic modelling, the mesh resolution has a strong impact on run time and result accuracy. Coarser meshes allow faster simulations but often at the cost of accuracy. Conversely, finer meshes offer a better description of complex geometries but require much longer computational time, which makes their use at a large scale challenging. In this context, we aim to assess the potential of a two-dimensional shallow water model with depth-dependant porosity (SW2D-DDP) for flood simulations at a large scale. This modelling approach relies on nesting a sub-grid mesh containing high-resolution topographic and bathymetric data within each computational cell via a so-called depth-dependant storage porosity. It enables therefore faster simulations on rather coarse grids while preserving small-scale topography information. The July 2007 flood event in the Severn River basin (UK) is used as a test case, for which hydrometric measurements and spatial data are available for evaluation. A sensitivity analysis is carried out to investigate the porosity influence on the model performance in comparison with other classical parameters such as boundary conditions.</span></p>

scholarly journals Non-Repeatability, Scale- and Model Effects in Laboratory Measurement of Impact Loads Induced by an Overtopped Bore on a Dike Mounted Wall

2019 ◽  
Author(s):  
Maximilian Streicher ◽  
Andreas Kortenhaus ◽  
Corrado Altomare ◽  
Steven Hughes ◽  
Krasimir Marinov ◽  
...  
Keyword(s):  
Large Scale ◽  
Scale Effects ◽  
Vertical Wall ◽  
Scale Factor ◽  
Scale Model ◽  
Small Scale ◽  
Length Scale ◽  
Force Measurements ◽  
Impact Forces ◽  
Small Scale Model

Abstract Overtopping bore impact forces on a dike mounted vertical wall were measured in similar large-scale (Froude length scale factor 1-to-4.3) and small-scale (Froude length scale factor 1-to-25) models. The differences due to scale effects were studied, by comparing the up-scaled force measurements from both models in prototype. It was noted that if a minimum layer thickness, velocity of the overtopping flow and water depth at the dike toe were maintained in the small-scale model, the resulting differences in impact force due to scale effects are within the range of differences due to non-repeatability and model effects.

scholarly journals ENGINEERING GEOLOGICAL AND GEOTECHNICAL INVESTIGATION OF LANDSLIDE EVENTS IN WILDFIRE AFFECTED AREAS OF ILIA PREFECTURE, WESTERN GREECE

2017 ◽  
Vol 43 (3) ◽  
pp. 1138 ◽  
Author(s):  
N. Depountis ◽  
S. Lainas ◽  
D. Pyrgakis ◽  
N. Sabatakakis ◽  
G. Koukis
Keyword(s):  
Large Scale ◽  
Agricultural Land ◽  
Site Investigation ◽  
Geological Mapping ◽  
Small Scale ◽  
Geotechnical Investigation ◽  
Protection Measures ◽  
Socio Economic Impact ◽  
Geological Formations ◽  
Western Greece

In August 2007 Ilia Prefecture suffered one of the most devastating wildfires that have ever happened on European level. Approximately 870km2 , mainly forest and agricultural land, were lost, more than 60 people were killed, hundreds were injured and many villages suffered extensive damage. Heavy rainfall and human activities, favoured by the loss of vegetation and the overall susceptibility of geological formations in landsliding, induced the manifestation or reactivation of various scale landslide phenomena. In order to investigate and mitigate the problem University of Patras was commissioned by the Region of Western Greece to undertake an Engineering Geological and Geotechnical investigation. Site investigation accomplished in seven municipalities focusing on several landslide events with serious socio-economic impact and as a result many small scale cases were identified. In each one of these cases large scale engineering geological mapping was conducted and remedial and protection measures were designed.

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