1- INTRODUCTION: CNOIDAL WAVE THEORY IS BASED ON EQUATIONS DEVELOPED BY KORTEWEG AND DE VRIES. THE RESULTING EQUATIONS CONTAIN JACOBIAN ELLIPTICAL FUNCTIONS. THE DEEP WATER LIMIT OF CNOIDAL THEORY IS THE SMALL-AMPLITUDE WAVE THEORY AND THE SHALLOW WATER LIMIT IS THE SOLITARY WAVE THEORY. AN ADVANTAGE OF CNOIDAL WAVE THEORY IS THAT IT GIVES THE ANALYTICAL SOLUTION FOR WEAKLY NONLINEAR BOUSSINESQ WAVES OF CONSTANT FORM. IT IS, THEREFORE, POSSIBLE TO DERIVE SOME OF THE PRINCIPAL PROPERTIES OF BOUSSINESQ WAVES BY APPLYING CNOIDAL WAVE THEORY. IN THIS PAPER, ANALYTICAL SOLUTION OF CNOIDAL WAVE HEIGHT VARIATION DUE TO SHOALING IS OBTAINED.2- BRIEF DESCRIPTION OF THE STUDY: IN THIS STUDY, SHOALING OF CNOIDAL WAVES PROPAGATING NORMAL TO A GENTLY SLOPING BEACH WITH STRAIGHT AND PARALLEL BOTTOM CONTOURS IS SOLVED ANALYTICALLY. BASED ON THE CONSERVATION OF ENERGY IN THE ABSENCE OF DISSIPATION, THE ENERGY FLUX PER UNIT ALONGSHORE LENGTH IS CONSTANT. UNLIKE THE LINEAR WAVE THEORY, WAVE PROPERTIES SUCH AS WAVE LENGTH AND WAVE CELERITY ARE NOT ONLY DEPENDENT ON WATER DEPTH AND WAVE PERIOD BUT ALSO ON WAVE HEIGHT.

INTRODUCTION: NUMERICAL STUDY OF FLOW BEHAVIOR IN RIVERS AND COASTS HAS AN INTERESTING RANGE OF APPLICATIONS IN FIELDS SUCH AS RIVER HYDRAULICS, ENVIRONMENTAL HYDRAULICS AND OTHER SIMILAR ACTIVITIES. IN THIS WORK THE FORMULATION OF A FINITE ELEMENT NUMERICAL MODEL FOR THE SHALLOW WATER EQUATIONS IS INTRODUCED AND THE MODEL IS TESTED USING SOME STANDARD EXAMPLES CITED IN THE LITERATURE. THE DEPTH INTEGRATED SHALLOW WATER EQUATIONS GOVERN THE HYDRODYNAMICS IN THE SHALLOW WATER BODIES AND ONE OF SUITABLE NUMERICAL TECHNIQUES OF THESE PDES IS THE CBS FINITE ELEMENT ALGORITHM.

IN THIS PAPER, THE MESHLESS METHOD IS INTRODUCED TO THE HYDRAULICS. AN ELEMENT FREE GALERKIN (EFG)METHOD FOR SIMULATION OF TWO-DIMENSIONAL SHALLOW WATER FLOWS IS PRESENTED AND ITS IMPLEMENTATION ISDESCRIBED. IN THIS METHOD ONLY THE NODAL DATA WHICH MAY BE THE SAME AS THOSE USED IN THE FINITE ELEMENTMETHODS (FEMS) AND A DESCRIPTION OF THE DOMAIN BOUNDARY GEOMETRY ARE NECESSARY, NO ELEMENT OR GRIDCONNECTIVITY IS NEEDED. IN THE EFG METHOD THE MOVING LEAST SQUARES (MLS) INTERPOLATIONS IS USED TOCONSTRUCT THE TRIAL FUNCTIONS. THE MODELLED DOMAIN IS REPRESENTED THOROUGH THE NODAL POINTS. A GALERKINMETHOD IS APPLIED TO DISCRETIZE THE GOVERNING DIFFERENTIAL EQUATIONS, RESULTING IN A SIMULTANEOUS EQUATIONSYSTEM. AN UNDERLYING CELL STRUCTURE FOR CALCULATION OF THE INTEGRALS IS USED. THE SENSITIVITY ANALYSIS ISPROPOSED TO DETERMINE THE INFLUENCE OF THE DIFFERENT PARAMETERS OF THE EFG METHOD WITH SOLVING MOVINGCONE PROBLEM. TO VERIFY THE EFFICIENCY OF THE PROPOSED METHOD THE SHOALING PROBLEM IS ANALYZED.

INTRODUCTIONESTUARIES ARE SENSITIVE COASTAL ENVIRONMENTS TO POLLUTION WHERE ECOLOGICAL FEATURES HAVE CONTROLLED BY QUALITY OF WATER AND SEDIMENT SOURCES. THESE ENVIRONMENTS ARE FACING TO CONTAMINATION, SHOALING, SEASONAL FLASH FLOODS, STORM SURGE, BLOCKAGE OF INLETS, AND ANTHROPOMORPHIC CHANGES. COASTAL SEDIMENTARY ENVIRONMENTS AT THE NORTH OF THE PERSIAN GULF WERE AFFECTED SINCE LAST TWO DECADES BY RAPID GROWTH OF INDUSTRIAL PLANTS AND LAND DEVELOPMENT PROJECTS ([1] [2])….

INTRODUCTION: TIDAL WAVES PROPAGATION ARE MAINLY CONTROLLED BY THE CORIOLIS, REFLECTION, SHOALING AND FRICTION EFFECTS, WHICH THE LAST TWO FACTORS ARE RESTRICTED TO SHALLOW WATER BASINS. ON THE OTHER HAND, THE BOUNDARIES OF BASIN GEOMETRY AND THE CORIOLIS EFFECT RESULT TO THE DEVELOPMENT OF AMPHIDROMIC SYSTEMS WITH ZERO TIDAL RANGE AT AMPHIDROMIC POINTS. THESE CAN BE DEPICTED BY CO-TIDAL LINES, WHICH LINK ALL THE POINTS WITH THE SAME TIDAL PHASE, AND CO-RANGE LINES WHICH CONNECT POINTS HAVING THE SAME TIDAL RANGE [1]...

INTRODUCTION: SHOALING DUE TO SEDIMENTATION IS ONE O THE MAJOR PROBLEMS IN NAVIGATION CHANNELS. TIDAL CURRENTS AND CURRENTS DUE TO BREAKING EFFECTS ARE MAIN REASONS OF SEDIMENTATION AND EROSION IN THESE CHANNELS. IF TIDAL CURRENTS FLOW ALONG THE CHANNELS, USUALLY WE EXPECT TO HAVE UNIFORM SEDIMENTATION OR EROSION BUT THE FACT IS SOMETHING ELSE, SO THAT IT IS IN THE FORM OF PAIRED HOLES AND HILLS, CALLED “RIPPLE”. IN THIS PAPER, WE STUDIED GENERATION AND DEVELOPMENT OF THESE RIPPLES IN BED OF SAJAFI PORT AT ZOHRE RIVER. FOR THIS PURPOSE, USED NUMERICAL MODELING ACCOMPANIED WITH THEORETICAL STUDIES. RESULTS PERFORMED THAT DISTANCE AND DIMENSIONS OF RIPPLES ARE RELATED TO WAVE LENGTH, CURRENT VELOCITY AND BED ROUGHNESS. IN THIS CASE, LOTS OF RESEARCHES HAVE DONE BY VARIOUS PEOPLE, RECENTLY. FOR INSTANCE WE CAN MENTION TO CHENG, H. Q., KOSTASCHUK, R. AND SHI, Z. (2004); LEO C. VAN RIJN. (2007); FAN DAIDU (2012); OURMIE’RES, Y., CHAPLIN, J. R. (2004); VILLARET, C., HUYBRECHTS, N. (2012).

1. INTRODUCTION WELL-ESTABLISHED DESIGN CRITERIA AND METHODOLOGIES GENERALLY EXIST IN ENGINEERING PRACTICE FOR VARIOUS TYPES OF RUBBLE-MOUND BREAKWATERS, DRAWING MAINLY UPON THE RESULTS OF PAST PHYSICAL MODELING EXPERIMENTS. HOWEVER, THERE IS RELATIVELY LESS CLEAR GUIDANCE CURRENTLY AVAILABLE FOR THE NUMERICAL MODELING AND HYDRAULIC DESIGN PROCEDURE, VIA APPLICATION OF THE EMPIRICAL FORMULAE, SUCH AS VAN DER MEER’S, HUDSON’S, AND VAN GENT’S, IN THE PARTICULAR CASE OF AN ABRUPT STEP-LIKE SEABED FEATURE POSSIBLY COMBINED WITH THE CURVATURE OF THE BATHYMETRY CONTOUR-LINES, NEARBY A PROPOSED LOCATION FOR NEW BREAKWATERS, AS IN FIGURE 1, PRESENTING THE LAYOUT OF A NEW HARBOR IN PROXIMITY OF THE STEP. SUCH AN OCCURRENCE IS PRONE TO A REDUCTION OF HYDRAULIC STABILITY AND INCREASED WAVE RUN-UP AND OVERTOPPING DUE TO MORE SIGNIFICANT SHOALING VELOCITIES DUE TO THE SHARP GRADIENT AND/OR WAVE FOCUSING EFFECTS DUE TO THE LENS LIKE ACTION OF THE SEABED ON WAVES AFTER WAVE PROPAGATION OVER SUCH A FORESHORE THEREBY DESERVING A MORE RIGOROUS APPROACH TO THE PRELIMINARY DESIGN, EVEN THOUGH, PHYSICAL MODELING SHALL PROVIDE THE FINAL VERDICT.