scholarly journals COMPARISON OF TURBULENT LATERAL MIXING MODELS

1984 ◽  
Vol 1 (19) ◽  
pp. 214
Author(s):  
William G. McDougal ◽  
Robert T. Hudspeth
Keyword(s):  
Equation Of Motion ◽  
Analytic Solutions ◽  
Mixing Models ◽  
Horizontal Distance ◽  
Longshore Current ◽  
Current Profile ◽  
Beach Profile ◽  
Longshore Currents ◽  
Lateral Mixing ◽  
Wave Induced

A variety of different lateral mixing models have been employed in the equation of motion for determining wave-induced longshore currents. The equation of motion is cast into a general form which enables a comparison of the various models. Analytic solutions for longshore currents are developed for seven different mixing models. A nonplanar beach profile is employed because it has been found to be representative of many beaches and it allows for a distinction between offshore and depth scaling of eddies. The seven different mixing models include models which vary monotonically with horizontal distance offshore and models which change form at the breaker line. Numerical results indicate that the longshore current profile is rather insensitive to the form of the mixing model for nonplanar beach profiles.

scholarly journals AN HEURISTIC MODEL OF WAVE HEIGHT DISTRIBUTION IN SURF ZONE

1980 ◽  
Vol 1 (17) ◽  
pp. 15 ◽  
Author(s):  
Masaru Mizuguchi
Keyword(s):  
Surf Zone ◽  
Experimental Result ◽  
Height Distribution ◽  
Heuristic Model ◽  
Longshore Current ◽  
Current Profile ◽  
Beach Profile ◽  
Wave Height Distribution ◽  
Constant Slope ◽  
Step Type

Until now, almost every study on coastal processes has considered the basic type of two-dimensional beach profile as being of constant slope. However, as our knowledge on this problem advances, we realize the importance of the influences of the bottom configuration on the hydrodynamic phenomena in a given area. Figure 1 shows a recent experimental result on the longshore current profile on a step type beach. ( Here the step type beaches are defined as those which have a step in the bottom profile, whether the beaches are of accretion type or not.)

Nearshore mixing and dispersion

1994 ◽  
Vol 445 (1925) ◽  
pp. 561-576 ◽  
Keyword(s):  
Surf Zone ◽  
Three Dimensional ◽  
Dispersion Effect ◽  
Longshore Current ◽  
Turbulent Length Scale ◽  
Interaction Terms ◽  
Longshore Currents ◽  
Order Of Magnitude ◽  
Lateral Mixing ◽  
The One

Longshore currents have in the past been analysed assuming that the lateral mixing could be attributed to turbulent processes. It is found, however, that the mixing that can be justified by assuming an eddy viscosity v t = l√k where l is the turbulent length scale, k the turbulent kinetic energy, combined with reasonable estimates for l and k is at least an order of magnitude smaller than required to explain the measured cross-shore variations of longshore currents. In this paper, it is shown that the nonlinear interaction terms between cross-and longshore currents represent a dispersive mechanism that has an effect similar to the required mixing. The mechanism is a generalization of the one-dimensional dispersion effect in a pipe discovered by Taylor (1954) and the three-dimensional dispersion in ocean currents on the continental shelf found by Fischer (1978). Numerical results are given for the dispersion effect, for the ensuing cross-shore variation of the longshore current and for the vertical profiles of the longshore currents inside as well as outside the surf zone. It is found that the dispersion effect is at least an order of magnitude larger than the turbulent mixing and that the characteristics of the results are in agreement with the sparse experimental data material available.

scholarly journals THREE DIMENSIONAL FLOW PROFILES ON LITTORAL BEACHES

1988 ◽  
Vol 1 (21) ◽  
pp. 52 ◽  
Author(s):  
Ib A. Svendsen ◽  
Rene S. Lorenz
Keyword(s):  
Perturbation Method ◽  
Poisson Equation ◽  
Surf Zone ◽  
Three Dimensional ◽  
Longshore Current ◽  
Current Profile ◽  
Three Dimensional Flow ◽  
Flow Profiles ◽  
Current Variation ◽  
Averaged Models

The problem of combined cross-shore and longshore currents generated by waves in and around a surf zone is considered in its full three-dimensional formulation. The equations for the two current components are decoupled and it is found that for a cylindrical coast with no longshore variations the longshore current variation with depth and distance from the shoreline satisfies a Poisson equation. This equation is solved by a perturbation method and it is shown that the longshore velocities are always larger than the velocities found by classical theory. In the simple uncoupled case, the full 3-D current profile is constructed by combining the results with cross - shore velocities determined in previous publications. Also, the total velocities are larger than velocities found from simple depth averaged models.

Nonrelativistic motion of a charged particle in an electromagnetic field

1998 ◽  
Vol 59 (3) ◽  
pp. 555-560
Author(s):  
C. J. McKINSTRIE ◽  
E. J. TURANO
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Plane Wave ◽  
Particle Motion ◽  
Wave Amplitude ◽  
Equation Of Motion ◽  
Analytic Solutions

The nonrelativistic motion of a charged particle in the electromagnetic field of a plane wave is studied. New analytic solutions of the equation of motion are found that manifest the dependence of the period of the particle motion on the wave amplitude.

scholarly journals NUMERICAL MODELLING OF NEARSHORE CIRCULATION

1980 ◽  
Vol 1 (17) ◽  
pp. 160 ◽  
Author(s):  
Bruce A. Ebersole ◽  
Robert A. Dalrymple
Keyword(s):  
Numerical Model ◽  
Finite Difference ◽  
Numerical Models ◽  
Bottom Topography ◽  
Rip Currents ◽  
Time Dependency ◽  
Longshore Current ◽  
Governing Equations ◽  
Nearshore Circulation ◽  
Lateral Mixing

Waves impinging on beaches induce mean flows, such as longshore and rip currents. This nearshore circulation is of fundamental importance in the study of the transport of nearshore contaminants as well as littoral materials. Analytic models of this nearshore flow {see, e.g. 4, 9, 11, 12) have been constrained to be linear (in the governing equations) and simplistic in the bottom topography. Only recently have numerical models been developed to examine more complex situations. Steady state, finite difference models (1, 14), as well as a finite element model (10), have been proposed. The numerical model, developed by Birkemeier and Dalrymple (1), allowed for time dependency. Yet, in all of these cases, the governing equations have not included the nonlinear convective accelerations or lateral mixing terms. In this study, a nonlinear numerical model is presented based on a leapfrog finite difference scheme, which includes time dependency and eddy viscosity terms. Results are shown for a planar beach showing a comparison with the analytical longshore current models (with and without lateral mixing) of Longuet-Higgins (11, 12). The longshore current over a prismatic beach profile including an offshore bar is presented next, showing the effects of the bar on the velocity profile. The circulation set-up by a rip channel inset into a plane beach is then computed. A comparison is made to the linear model of Birkemeier and Dalrymple. Finally the model is applied to the case of synchronous intersecting wave trains (4). An interesting result occurs when the waves are of different amplitudes, which could provide an explanation of the formation of finger bars on a beach.

scholarly journals Longshore current profiles and lateral mixing across the surf zone of a barred nearshore

1986 ◽  
Vol 10 (2) ◽  
pp. 149-168 ◽  
Author(s):  
Brian Greenwood ◽  
Douglas J. Sherman
Keyword(s):  
Surf Zone ◽  
Longshore Current ◽  
Lateral Mixing

scholarly journals COMPUTATION OF LONGSHORE CURRENTS

1974 ◽  
Vol 1 (14) ◽  
pp. 40 ◽  
Author(s):  
Ivar G. Jonsson ◽  
Ove Skovgaard ◽  
Torben S. Jacobsen
Keyword(s):  
Surf Zone ◽  
Numerical Algorithms ◽  
Field Measurements ◽  
Breaking Waves ◽  
Bottom Friction ◽  
Rip Currents ◽  
Longshore Current ◽  
Lateral Mixing ◽  
Set Up ◽  
The Given

The steady state profile of the longshore current induced by regular, obliquely incident, breaking waves, over a bottom with arbitrary parallel bottom contours, is predicted. A momentum approach is adopted. The wave parameters must be given at a depth outside the surf zone, where the current velocity is very small. The variation of the bottom roughness along the given bottom profile must be prescribed in advance. Depth refraction is included also in the calculation of wave set-down and set-up. Current refraction and rip-currents are excluded. The model includes two new expressions, one for the calculation of the turbulent lateral mixing, and one for the turbulent bottom friction. The term for the bottom friction is non-linear. Rapid convergent numerical algorithms are described for the solution of the governing equations. The predicted current profiles are compared with laboratory experiments and field measurements. For a plane sloping bottom, the influence of different eddy viscosities and constant values of bottom roughness is examined.

scholarly journals UNIFORM LONGSHORE CURRENT MEASUREMENTS AND CALCULATIONS

1984 ◽  
Vol 1 (19) ◽  
pp. 147 ◽  
Author(s):  
P.J. Visser
Keyword(s):  
Mathematical Model ◽  
Laboratory Experiments ◽  
Laboratory Data ◽  
Friction Model ◽  
Longshore Current ◽  
Current Generation ◽  
Longshore Currents ◽  
The Mathematical Model ◽  
Lateral Friction ◽  
Good Agreement

A description is given of laboratory experiments on uniform longshore currents and the comparison of the data with longshore current profiles predicted by a mathematical model. For the mathematical model it is assumed that longshore current generation takes place between the plunge line and the shoreline (instead of shoreward of the breaker line) and Battjes' (2,3) lateral friction model is applied. Good agreement between theory and laboratory data is achieved with realistic values of the bottom roughness.

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