NEARSHORE CURRENTS II (WAVEINDUCED LONGSHORE CURRENT)

NEARSHORE CURRENTS II (WAVE-INDUCED LONGSHORE CURRENT) Wave-Induced Longshore Current Governing Equations for Nearshore Currents Vertically integrated, time-averaged momentum equations: U U  V  g  Fbx  Lx  Rbx  Rsx x y x V V  U V  g  Fby  Ly  Rby  Rsy x y y U Fb: bottom friction L: lateral mixing + continuity equation Rb: wave forcing Rs: wind forcing Wave Forcing  S xx S xy     d  x y   S xy S yy  Rby      d  x y  Rbx   1  S xx  gH  n(cos   1)   2  n Cg C 1  S yy  gH  n(sin   1)   2  S xy  ngH sin 2 16 Wind Forcing General formulation:   CD aW CD a W W cos  d C  Rsy   D a W W sin  d Rsx   Lateral Mixing U         xy d  y    y  1   V    V   Ly     yx d  yy d   d  x  x  y  y   Lx  1   U    xx d d  x  x Mixing coefficient:   u m H Bottom Friction General expression: bx  c f  u  v u by  c f  u  v v Total instantaneous velocity: u  U  ub v  V  vb Oscillatory wave motion:  2t  ub  um cos   cos   T   t  vb  um cos   sin   T  Velocity amplitude: um  gHT  2d  L cosh    L  Driving terms: Fbx   Fby   cf d cf d u2  v2u u2  v2 v (triangular brackets denote time-averaging over a wave period) Longshore Current and Wave Setup/Set-down Momentum equation, x-direction (setup/setdown): gd d dS   xx  C D a W W cos  dx dx Momentum equation, y-direction (longshore current): fby   Fby d d  dV  d dx  dx dS xy    CD a W W sin    f by   dx   Evaluation of bottom friction: 1/    2t   t  fby  c f  um2 cos2    V  2Vum cos   sin    T   T       t  V  u m cos  T  sin       Approximations: c f umV  fby  c f umV 1  sin    fby  fby  c f V V weak current strong current Square-wave approximation:   w2 fby  c f  Z  sin  V Z   V  w2  2wV sin   V  w2  2wV sin  2 w  um  Z   Evaluation of Wind Drag Coefficient Duck data (outside surf zone) CD/cf about 1.2 Estimation of Wind Drag Coefficient WAMDI Group (1988): CD (W )  1.2875103 W  7.5 m/s CD (W )   0.8  0.065 W 103 W  7.5 m/s Validation of Longshore Current Model Data sets: • Visser laboratory data • Kraus-Sasaki field data • Thornton and Guza field data Comparison with wave height, mean water elevation, and longshore current Monte-Carlo simulation for random waves Visser Data Case No wave height and current setup/setdown Hin=0.089 m, T=1.00 sec,  in=15.4 deg Visser Data Case No wave height and current setup/setdown Hin=0.078 m, T=1.02 sec,  in=15.4 deg Kraus-Sasaki Data Shelf-type profile Hsb=1.0 m, T=4.1 sec,  b=9 deg Thornton-Guza Data Case Feb wave height current Hrms,in=0.56 m, T=14.3 sec,  in=7.8 deg Thornton-Guza Data Case Feb wave height current Hrms,in=0.45 m, T=12.8 sec,  in=9.0 deg Parameter Values Laboratory data: cf = 0.01 – 0.02,   0.5 cf = 0.005 – 0.015,   0.3 linear model nonlinear model Field data: cf = 0.004 – 0.006,   0.5 linear model cf = 0.003 – 0.005,   0.3 nonlinear model ... period) Longshore Current and Wave Setup/Set-down Momentum equation, x-direction (setup/setdown): gd d dS   xx  C D a W W cos  dx dx Momentum equation, y-direction (longshore current): ... Validation of Longshore Current Model Data sets: • Visser laboratory data • Kraus-Sasaki field data • Thornton and Guza field data Comparison with wave height, mean water elevation, and longshore