Communications on Hydraulics
Department of Civil Engineering
A MATHEMATICAL MODEL OF UNIFORM LONGSHORE CURRENTS AND THE COMPARISON WITH LABORATORY DATA
P.J. Visser
Report No. 84 - 2
Laboratory of Fluid Mechanics Department of Civil Engineering Delft University of Technology P.O. Box 5048
2600 GA Delft, The Netherlands
CONTENTS ABSTRACT
1. INTRODUCTION
2. GENERAL FORMULATION
2.1 Introduction and preliminary assumptions 2.2 Conservation of mass
2.3 Conservation of vertical momentum 2.4 Conservation of horizontal momentum
2.5 Conservation of energy for the fluctuating notion 2.6 Basic assumptions
2.7 Specific assumptions
2.8 The nearshore region, definitions
2.9 Equations for steady, uniform longshore currents 3. MODELING OF DRIVING FORCE, BOTTOM FRICTION AND
LATERAL FRICTION
3.1 Modeling of driving force 3.2 Modeling of bottom friction 3.3 Modeling of lateral friction
3.4 Implications for the longshore current model 4. NUMERICAL MODEL
4.1 Summary of equations
4.2 Calculation of elliptic integral f(e,~)
4.3 Differential equation which has to be solved 4.4 Boundary conditions 4.5 Numerical solution 5. EXPERIMENTS 5.1 Introduction 5.2 Experimental arrangement 5.3 Experimental procedure
5.4 Adjustment of correct longshore current flow 5.5 Experimental results
5.6 Discussion and conclusions
page 5 5 7 7 8 10 11 12 14 15 18 18 23 34 43 47 47 50 SI 53 53 59 59 59 61 63 66 72
6. COMPARISON OF HEASURED AND THEORETICAL RESULTS FOR THE LONGSHORE CURRENT PROFILES
6.1 Introduction
6.2 Considerations about the rate of agreement 6.3 Results of rate of agreement computations with
measured p
6.4 Analysis of computational results with measured p 6.5 Computations with a variable p
6.6 Discussion and conclusions
7. DISCUSSION, CONCLUSIONS AND RECOMMENDATIONS 7.] Discussion
7.2 Summary of conclusions
7.3 Recommendations for further research
74 74 74 76 77 84 86 88 88 93 94 ACKNOWLEDGEHENTS 95 LIST OF SYMBOLS 96 LIST OF REFERENCES ]0] APPENDICES
A. THE EFFECT OF WAVE ENERGY DISSIPATION BY BOTTOH FRICTION
ON LONGSHORE DRIVING FORCE ]04
B. SIMPLIFICATION OF ENERGY BALANCE OF TURBULENCE ]08
C. ANALYTICAL HODEL FOR P
=
110C.] Introduction 1]0
C.2 Longshore driving force ]]0
C.3 Bottom friction 11]
C.4 Lateral friction ]]2
C.5 Analytical solution 1]3
D. HEASUREHENT RESULTS (TABLES D.I-D.7) 1]6
E. VERTICAL VELOCITY PROFILES (FIGURES E.]-E.7) 124 F. RESULTS OF COMPUTATIONS OF STANDARD DEVIATION £ £(H,r)
WITH HEASURED p 128
G. FIGURES WITH COMPUTED LONGSHORE CURRENT PROFILES COMPARED
ABSTRACT
This report describes a mathematical model for uniform longshore currents and laboratory experiments on these currents, as also the comparison of theory and experiment. The longshore driving force is modeled taking into account the physical fact that dissipation of wave energy takes place shoreward of the plunge instead of in the whole surf zone as usely assumed. The bottom friction is modeled by considering the combined orbital and mean current velocity vector. This is done in several manners since it is still unclear how to combine these velocities near the bqttom. The lateral friction is modeled according to Battjes (1975, 1983).
The data obtained from the present longshore current experiments appear to be very usable to verify the theoretical results: the rate of accuracy of the measurement results is high, the longshore current profiles are uniform and these were measured in detail. The
experimental results do not confirm the often made assumption of a logarithmic vertical velocity profile.
The agreement between the longshore currents predicted by the mathematical model and the experiments is good and this has been achieved with realistic values of the bottom roughness.
