Morphology of Pits, Channels and Trenches
Part I: Literature Review and Study Approach
L.C. van Rijn and D.J.R. Walstra
January 2002
Rijks-Instituut voor Kust en Zee - RIKZ
Contents
(((
! "#$%&'()$*&# +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++!,!
- ./0(12$*ř&%46*#*#04&5432#'4*#47($)843/)$&%4&549&%$84:/2 +++++++++++++++++++++++++++-,!
)+, -#.%/0$1.2/#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++)3, )+) 42#2#5(%65$7".2/#8+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++)3,
; <&%=8&'>#26*)34&54&5538&%/46*#*#042%/23 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++;,!
9+, :%"#8;/%.(;%/168868("#0(</%;=/7/521"7(6>/7$.2/#++++++++++++++++++++++++++++++++++++++93, 9+) ?$%%6#.8++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++93@
9+9 A">68 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++93,) 9+B C7/;6(2#8."D272.& +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++93,9
? :/'*6/#$4$%2#3=&%$42#'4/)&1&0*)214=%&)/33/34*#462%*#/4)&#'*$* ++++++++++++++++++?,!
B+, C"#0(.%"#8;/%.(;%/168868 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++B3, B+,+, E6F2#2.2/#8("#0(56#6%"7(1="%"1.6%28.218++++++++++++++++++++++++++++++++++++++++++B3, B+,+) G6.("##$"7(8"#0(.%"#8;/%.("7/#5(.=6(E$.1=(1/"8.(D"860(/#
</067(1/<;$.".2/#8 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++B39 B+,+9 G6.("##$"7(8"#0(.%"#8;/%.(06%2>60(F%/<(</%;=/7/521"7(0"."
"7/#5(.=6(E$.1=(1/"8. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++B3H B+) 4$0(.%"#8;/%.(;%/168868("#0(6FF61.(/F(<2#2#5("1.2>2.268 ++++++++++++++++++++++++++++B3I B+9 J1/7/521"7(;%/168868++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++B3,, B+9+, K>6%>26L(/F(;%/168868 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++B3,, B+9+) M$"72.&(/F(L".6%(;="86(2#(066;(;2.8++++++++++++++++++++++++++++++++++++++++++++++B3,H B+9+9 N686"%1=(O$68.2/#8+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++B3,P
@ <2$8/62$*)214'/3)%*=$**#'42A2*12B1/46&'/134&5432#'4$%2#3=&%$42#'
6&%=8&1&0> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@,!
@+, -#.%/0$1.2/#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@3,
@+) Q6#6%"7(<".=6<".21"7(0681%2;.2/#("#0(82<;72F21".2/#8+++++++++++++++++++++++++++++++@3,
@+9 C2<;76(6#52#66%2#5(%$768 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@3)
@+B R#"7&.21"7(</0678(F/%(F7/L(;6%;6#021$7"%(./(1="##67+++++++++++++++++++++++++++++++++@3S
@+@ R#"7&.21"7(</0678(F/%(F7/L(;"%"7767(./(1="##67 +++++++++++++++++++++++++++++++++++++++++++@3I
@+H 4".=6<".21"7(</0678+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@3,*
@+H+, :L/T02<6#82/#"7(>6%.21"7(</067(F/%(/D72O$6(F7/L(1/#02.2/#8U CV:NJG?W(</067++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@3,*
@+H+) :L/T02<6#82/#"7(>6%.21"7(</067(F/%(/D72O$6(L">6(1/#02.2/#8U VG-XJC:T:?(</067++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@3,)
@+H+9 :L/T02<6#82/#"7(</067(F/%(8=/%6;"%"7767(1/#02.2/#8U(YK4KNT
</067 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@3,9
@+H+B :L/T02<6#82/#"7(=/%2Z/#."7("#0(.=%66T02<6#82/#"7(</0678+++++++@3,@
@+H+@ J>"7$".2/#(/F(</0678++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@3,H C 72$243/$342#'48*#')23$43$('*/3 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++C,!
H+, -#.%/0$1.2/#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++H3, H+) C.6"0&("#0(#/#T8.6"0&(F7/L+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++H3) H+)+, E"."(86.8($860(2#(=2#01"8.(8.$0268++++++++++++++++++++++++++++++++++++++++++++++++++H3) H+9 C.6"0&("#0(#/#(8.6"0&(F7/L(L2.=(L">68++++++++++++++++++++++++++++++++++++++++++++++++++++++H39 H+9+, E"."(86.8($860(2#(=2#01"8.(8.$0268++++++++++++++++++++++++++++++++++++++++++++++++++H39 H+9+) E"."(86.8(#/.(&6.($860(2#(=2#01"8.(8.$0268++++++++++++++++++++++++++++++++++++++H3B D <2$8/62$*)2146&'/143$('*/34%/12$/'4$&4=*$34*#49&%$84:/2+++++++++++++++++++++++++++++++++++D,!
S+, -#.%/0$1.2/#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++S3, S+) 4/%;=/7/5&( /F( <2#2#5( ;2.8( "#0( <2#2#5( F%/<( -!T1="##67[
N2\]8L".6%8."".'(,II* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++S3, S+9 4/%;=/7/5&( /F( <2#2#5( F%/<( J$%/T4""8( 1="##67'( E67F.( W&0%"$7218'
,II) +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++S3) S+B 4/%;=/7/5&( /F( 7"%56( 81"76( <2#2#5( ;2.8( #6"%( JVNKT4RRC( 1="##67[
E67F.(W&0%"$7218TR7]&/#'(,IIS +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++S39 S+@ ^7/L(2#(7"%56(81"76(<2#2#5(;2.8[(C>"86]'(,IIP++++++++++++++++++++++++++++++++++++++++++++S39 S+H 4/%;=/7/5&(_)E`a(/F(<2#2#5(;2.8'(W/2.2#]'(V#2>6%82.&(/F(:L6#.6'(,IIS +S3@
S+S 4/%;=/7/5&(_)E`a(/F(<2#2#5(;2.8'(E67F.(W&0%"$7218'(,IIP+++++++++++++++++++++++S3@
S+P ^7/L( "#0( </%;=/7/5&( _)EWa( 2#( 7"%56( 81"76( <2#2#5( ;2.8[( b762#'( E67F.
V#2>6%82.&(/F(:61=#/7/5&'(,III ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++S3I S+I 4/%;=/7/5&( _)EWa( /F( 7"%56( 81"76( <2#2#5( ;2.8'( V#2>6%82.&( /F( :L6#.6'
)**, +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++S3,9
E :(662%>F4)&#)1(3*Ŗ#'4%/)&66/#'2$* +++++++++++++++++++++++++++++++++++++++++++++++++++++E,!
P+, C$<<"%&("#0(1/#17$82/#8+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P3, P+) N61/<<6#0".2/#8(F/%(F$%.=6%(8.$0268 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++P3B P+)+, C.$0&(";;%/"1= +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P3B P+)+) 4/.2>".2/#(F/%(</067(2<;%/>6<6#.("#0(>6%2F21".2/# ++++++++++++++++++++P3@
P+)+9 4/067(2<;%/>6<6#.(D"860(/#(6c28.2#5(=&0%/0&#"<21
dV:4KN(0"."++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P3@
P+)+B 4/067(2<;%/>6<6#.(D"860(/#(F2670(.68.(;2.(2#(G/%.=(C6"++++++++++++++P3H P+)+@ 4/067(2<;%/>6<6#.(D"860(/#(7"%56T81"76(7"D/%"./%&
6c;6%2<6#. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P3H P+)+H b#/L76056(2<;%/>6<6#.(/F(J1/7/521"7(;%/168868++++++++++++++++++++++++P3S G ./5/%/#)/3 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++G,!
(((((((((
1 Introduction
^/%(86>6%"7(&6"%8(.=6(7"%56T81"76(<2#2#5(/F(8"#0(F%/<(.=6(E$.1=(C61./%(/F(.=6(G/%.=(86"(28(2#
0281$882/#(%67".60(./(.=6(#660(/F(8"#0(F/%(8=/%6F"16'(D6"1=("#0(0$#6(#/$%28=<6#.("#0(7"%56T 81"76(6#52#66%2#5(L/%]8(".(86"(_4""8>7"].6(6c.6#82/#'("2%;/%.(".(86"a+(:=6(<2#2#5(<6.=/08 1/#8206%60( D"821"77&( F"77( 2#./( .L/( 1".65/%268U( L206'( 8="77/L( /%( 8<"77'( 066;( <2#2#5( ;2.8+
d%686#.7&'( 8="77/L( ;2.8( #/.( 066;6%( .="#( "D/$.( )( <( "%6( 6c1">".60( D6&/#0( .=6( )*( <( 06;.=
1/#./$%(./( /D."2#( 8"#0( F/%(D6"1=(#/$%28=<6#.8+(E66;(<2#2#5(;2.8(=">6(#/.(&6.(D66#(<"06 6c.6#82>67&+(R(.6<;/%"%&(;2.(L2.=("(06;.=(/F("D/$.()*(<(_D67/L(8$%%/$#02#5(D60(8$%F"16a(="8 D66#(6c1">".60(17/86(./(.=6(8=/%6(2#("(L".6%(06;.=(/F("D/$.(,*(<'(D$.(.=28(;2.(L"8(%6F27760 8=/%.7&(_"(F6L(</#.=8a("F.6%(1/#8.%$1.2/#(./(;%6>6#.(0"<"56(./(.=6(1/"8."7(8&8.6<(_d$#"286
;%/\61.a+
:=6(<2#2#5(/F(86"(8"#0(L277("FF61.(D/.=(.=6(61/7/5&("#0(</%;=/7/5&(/F(.=6(1/"8."7(8&8.6<+
:=6(61/7/5&(28("FF61.60(2#(.=6(86#86(.=".(.=6(F7/%"("#0(F"$#"(/F(.=6(8&8.6<(28(068.%/&60(D&(.=6
<2#2#5("1.2>2.268'(L=6%6"8("78/(.=6(%676"86(/F(>6%&(F2#6(8602<6#.8(_827.("#0(17"&a(F%/<(.=6(D60 2#./(.=6(L".6%(1/7$<#(<"&(=">6("(02%61.(2#F7$6#16(/#(.=6(61/7/521"7(8&8.6<+(:=6(7/1"7(D60 F"$#"(28("7</8.(1/<;76.67&(068.%/&60(D&(.=6(<2#2#5("1.2>2.268+(:=28("78/(="8("(02%61.(#65".2>6 6FF61.( /#( "77( 72>2#5( 1%6".$%68( L=21=( "%6( F/%( .=62%( F//0( 06;6#06#.( /#( .=6( D60( F"$#"+( :=6
%61/>6%&(;6%2/0(/F(8="77/L(<2#2#5("%6"8(28(/F(.=6(/%06%(/F(@(&6"%8'(D$.(.=6(%61/>6%&(;6%2/0
<"&(2#1%6"86(1/#8206%"D7&(L2.=(2#1%6"82#5(6c1">".2/#(06;.=(_06"0(L".6%(Z/#6(".(D/../<(/F 066;(;2.a+(R002.2/#"7(#65".2>6(6FF61.8(<"&(/11$%(0$6(./(2#1%6"86(/F(.=6(.$%D202.&(/F(.=6(L".6%
;="86("D/>6(.=6(D60( 0$6(./( F2#68(F%/<( .=6( D60(7"&6%8( D%/$5=.( 2#./( .=6( L".6%(;="86( D&(.=6
<2#2#5("1.2>2.268(_8.2%%2#5a+
:=6(</%;=/7/5&(28("FF61.60(2#(.=6(86#86(.=".(7/1"77&(.=6(D60(76>67(28(7/L6%60(8$D8."#.2"77&(2#
.=6(F/%<(/F("(D/%%/L(;2.(_/%(1="##67a'(L=21=(<"&(2#F7$6#16(.=6(7/1"7(F7/L("#0(L">6(F26708
"#0(=6#16(.=6(8"#0(.%"#8;/%.(%".68(0$6(./(</02F21".2/#(/F(8=/"72#5'(%6F%"1.2/#("#0(%6F761.2/#
;"..6%#8+(:=6(;2.("%6"(_87/;68a(<"&(<25%".6(./L"%08(.=6(8=/%6(/>6%(.2<6("#0e/%(<"&("1.("8("
82#](_.%";;2#5a(F/%(8602<6#.8(F%/<(.=6(#6"%8=/%6(8&8.6<+(K#(7/#5(.6%<(_,**(&6"%8a(.=6("%6"
/F(2#F7$6#16(<"&(6c.6#0(/>6%(.6#8(/F(]<f8(/$.8206(.=6(/%252#"7(<2#2#5("%6"+(^$%.=6%</%6'(.=6 8<"77T81"76("#0(7"%56T81"76(D60(F/%<8(_F%/<(<65"%2;;768(./(8"#0(L">68a(<"&(D6( 068.%/&60 7/1"77&'( L=21=( <"&( "78/( =">6( "#( 6FF61.( /#( .=6( =&0%/0&#"<21( 8&8.6<( _7688( F%21.2/#( "#0 .$%D$76#16a+( `"%2/$8( 8.$0268( /F( .=6( </%;=/7/521"7( 1/#86O$6#168( /F( 86"( 8"#0( <2#2#5( =">6 D66#(;6%F/%<60'(D$.(</8.(/F(.=686(1/#86O$6#168(1"#(#/.(&6.(D6(F$77&( />6%866#( "#0( F$%.=6%
8.$0268("%6(%6O$2%60(./(72#6($;(.=6(;/82.2>6("#0(#65".2>6(6FF61.8(/F(86"(8"#0(<2#2#5'(8/(.=".("
%".2/#"7( 061282/#( L2.=( %68;61.( ./( 7/1".2/#( "#0( O$"#.2.&( /F( F$.$%6( 86"( 8"#0( <2#2#5( 1"#( D6
<"06+(:=28(72.6%".$%6(%6>26L(;%686#.8("#(/>6%>26L("#0(2#>6#./%&(/F(.=6(</8.(%676>"#.(8.$0268
;6%F/%<60($;(./(#/L'(1/>6%2#5U
!" %65$7".2/#8(/#(86"(8"#0(<2#2#5(_?=";.6%()a'
!" </%;=/0&#"<218(/F(/FF8=/%6(<2#2#5("%6"8(_?=";.6%(9a'
!" 8602<6#.(.%"#8;/%.("#0(61/7/521"7(;%/168868(2#(<"%2#6(1/#02.2/#8(_?=";.6%(Ba'
!" <".=6<".21"7(0681%2;.2/#(/F(8602<6#.(.%"#8;/%.("#0(">"27"D76(</0678(_?=";.6%(@a'
!" 0"."(86.8("#0(=2#01"8.(8.$0268(_?=";.6%(Ha'
!" <".=6<".21"7(8.$0268(%67".60(./(;2.8(2#(.=6(G/%.=(C6"(_?=";.6%(Sa+
^2#"77&'(%61/<<6#0".2/#8(F/%("002.2/#"7(%686"%1=(6FF/%.8("%6(52>6#("#0(0281$8860(2#(?=";.6%
P+(:=28(1=";.6%("78/(1/#."2#8("#(/$.72#6(/F(.=6(8.$0&(";;%/"1=(F/%(.=6(8$D86O$6#.(;="868(/F .=6(;%686#.(;%/\61.(2#(C61.2/#(P+)+
:=6(8.$0&(="8(D66#(0/#6( L2.=2#( .=6( ?//;6%".2/#( ^%"<6L/%]( /F( N2\]8L".6%8."".eN-bg( "#0 E67F.eW&0%"$7218(F/%(?/"8."7(N686"%1=(_`Kd(d%/\61.()a+
2 Regulations for mining of sand in Dutch sector of North Sea
2.1 Introduction
?/#16882/#8(F/%(.=6(<2#2#5(/F(86"(8"#0(2#(.=6(G/%.=(C6"("%6(D/$#0(./(%65$7".2/#8+(d/2#.8(/F
"..6#.2/#(2#(F/%<$7".2#5(.=686(%65$7".2/#8("%6U
!" 61/7/5&(_D/../<(F"$#"'("75"6'(D2%0(="D2.".a
!" 028;6%82/#(/F(<$0'
!" </%;=/7/5&(/F(8=/%6F"16("#0(1/"8.72#6'
!" </%;=/7/521"7(2#.6%"1.2/#(L2.=(6c28.2#5("#0(F$.$%6(6#52#66%2#5(L/%]8(_#">25".2/#
1="##678(./(;/%.8(/F(N/..6%0"<("#0(R<8.6%0"<'(;2;672#68'(4""8>7"].6(6c.6#82/#'("2%;/%.
2#(86"'(6.1+a+
2.2 Mining regulations
N65$7".2/#8( /#( <2#2#5( "1.2>2.268( 2#( .=6( E$.1=( C61./%( /F( .=6( G/%.=( C6"( "%6( F/%<$7".60( 2#U hN652/#""7( K#.5%/#02#58;7"#( G//%0Z66i( )( _NKG( )a+( :=686( %65$7".2/#8( <"2#7&( 1/#16%#
<2#2#5( 06;.=( "#0( <2#2#5( "%6"( 2#( %67".2/#( ./( .=6( L".6%( 06;.=( /#( .=6( <2#2#5( 7/1".2/#+( :=6
<"c2<$<(<2#2#5(06;.=(F/%(.=6(;%686#.(<2#2#5("1.2>2.268(28()(<+(-#(.=6(;%686#.(%6;/%.'(/#7&
.=6(%65$7".2/#8(F/%(066;(8"#0(<2#2#5(;2.8(_066;6%(.="#()(<a("%6(1/#8206%60+(^/%(.=686(066;
;2.8'(.=6(F/77/L2#5(%65$7".2/#8("%6(52>6#(_;+(BP("#0(BI(/F(NKG()aU
!" 8"#0(<2#2#5(2#(066;(;2.8'(/$.8206(.=6(GRd(T()*(<(06;.=(1/#./$%(28(1/#02.2/#"77&("77/L60 2F(.=6(;%686#16(/F(8$FF2126#.("</$#.8(/F(1/$%86(8"#0(28(<"06(;7"$82D76(F2%8.+
!" R.(5%"#.2#5("(;6%<2.'("(</#2./%2#5(;%/5%"<'("2<60(".(.=6(6FF61.8(/F(.=6(<2#2#5("1.2>2.268
<"&(D6(%6O$2%60[
!" 2#>6#./%&(/F(.=6(6#>2%/#<6#."7(6FF61.8(/F(.=6(;%/;/860(<2#2#5("1.2>2.268!_J-Ra+
G/(8;612F21(%65$7".2/#8(L2.=(%65"%0(./(.=6(<"c2<$<(<2#2#5(06;.=("%6(52>6#(2#(.=6(NKG() 0/1$<6#.+(:=6(<"c2<$<(06;.=(28(%68.%21.60(2#(.=6(86#86(.=".(2%%6>6%82D76(#65".2>6(6FF61.8(/#
.=6(6#>2%/#<6#.("%6(#/.("77/L60+(C/<6(1%2.6%2"(52>6#(F/%(.=6(<"c2<$<(06;.='("%6U
!" .=6(#6L(8$%F"16(8602<6#.8(8=/$70(#/.(06>2".6(.//(<$1=(F%/<(.=6(/%252#"7(/#68[
!" ".(.=6(D/../<(/F(.=6(;2.(#/(%60$1.2/#(/F(.=6(L".6%(6c1="#56(28("77/L60'(2#(/%06%(./(;%6>6#.
%60$1.2/#(/F(.=6(/c&56#(1/#.6#.[
!" 61/7/521"7(%61/>6%&(/F(.=6(<2#2#5(%652/#(L2.=2#("(%6"8/#"D76("</$#.(/F(.2<6(_8"&(,*
&6"%8a+
3 Morphodynamics of offshore mining areas
3.1 Transport processes and morphological evolution
!"#$%&''&()*+,-#.//
:=6( </%;=/7/521"7( D6=">2/$%( /F( "( 066;6#60( <2#2#5( "%6"( _;2.'( 1="##67'( .%6#1=a( 2#( 1/"8."7 F7/L( _L2.=( /%( L2.=/$.( L">68a( 8=/L8( .=6( F/77/L2#5( D"821( F6".$%68'( 06;6#02#5( /#( .=6 /%26#.".2/#(/F(.=6(;2.(./(.=6(F7/L(02%61.2/#+
:=6(F/77/L2#5(.=%66(1"868("%6(=6%62#(028.2#5$28=60(_^25$%6(9+,+,aU
!" H#*'*%/)$*友&I4=/%=/#'*)(12%4&%4&B1*J(/4$&4$8/462*#4)82##/1K=*$42L*3M(06;/82.2/#
".( .=6( $;8.%6"<( 87/;68( "#0( 6%/82/#( /F( .=6( 0/L#8.%6"<( 87/;68( /F( .=6( ;2.( %68$7.2#5( 2#
<25%".2/#(/F( .=6( 066;6#60("%6"( 2#( .=6( 02%61.2/#( /F( .=6( 0/<2#"#.( F7/L(_<"2#7&( D60( 7/"0 .%"#8;/%.a[( 06;/82.2/#( 2#( .=6( 066;6%( "%6"( /F( .=6( ;2.( D&( %60$1.2/#( /F( .=6( 8"#0( .%"#8;/%.
1";"12.&(_<"2#7&(8$8;6#060((7/"0(.%"#8;/%.a[
!" N*'21451&I4=/%=/#'*)(12%4&%4&B1*J(/4$&4$8/462*#4)82##/1K=*$42L*3M(6%/82/#(/F(D/.=(8206 87/;68(0$6(./(D2T02%61.2/#"7(F7/L[(06;/82.2/#(2#(.=6(066;6%("%6"(/F(.=6(;2.(D&(%60$1.2/#(/F .=6(8"#0(.%"#8;/%.(1";"12.&(_<"2#7&(8$8;6#060((7/"0(.%"#8;/%.a[
!" N*'21451&I4=2%211/14$&4$8/462*#4)82##/1K=*$42L*3M(F7"..6#2#5(/F(.=6(87/;68(D&(.%"#8;/%.(/F 8602<6#.( F%/<( .=6( 87/;68( 2#./( .=6( 066;6%( "%6"( /F( .=6( ;2.( D&( 5%">2.".2/#"7( 87/;6( 6FF61.8 _<"2#7&(D60(7/"0(.%"#8;/%.(2#(;"%"7767(F7/La+
UNIDIRECTIONAL FLOW
TIDAL FLOW Bed level at tim e T
PARALLEL TIDAL FLOW
O*0(%/4;+!+! "#$%&#'#()*+'!,-.-'#%/-01!#2!*&+00-'
3#%4 ")($+1)#0!)0!50),)$-*1)#0+'!2'#6!%-$%-0,)*5'+$!1#!/+)0!+7)8
"),,'-4 9-%#8)1)#0!+0,!-$#8)#0!)0!1),+'!2'#6!%-$%-0,)*5'+$!1#!/+)0!+7)8 :#11#/4 ;'+11-0)0(!#2!8'#%-8!)0!1),+'!2'#6!%+$+''-'!1#!/+)0!+7)8
A=6#("(1$%%6#.(;"8868("(;2.(/%(1="##67'(.=6(1$%%6#.(>67/12.268(061%6"86(0$6(./(.=6(2#1%6"86(/F .=6(L".6%(06;.=8(2#(.=6(;2.(/%(1="##67("#0(=6#16(.=6(8602<6#.(.%"#8;/%.(1";"12.&(061%6"868+
R8("(%68$7.(.=6(D60T7/"0(;"%.21768("#0("(16%."2#("</$#.(/F(.=6(8$8;6#060(8602<6#.(;"%.21768 L277(D6(06;/82.60(2#(.=6(;2.+(:=6(86..72#5(/F(8602<6#.(;"%.21768(28(.=6(0/<2#"#.(;%/1688(2#(.=6 0/L#87/;2#5(_061676%".2/#a("#0(2#(.=6(<20076(861.2/#("#0(/F(.=6(;2.+(-#(.=6(1"86(/F("(8.66;T 82060(;2.(L2.=(F7/L(86;"%".2/#(%68$7.2#5(2#(.=6(56#6%".2/#(/F("002.2/#"7(.$%D$76#16(6#6%5&'(.=6 86..72#5(;%/1688(<"&(D6(%60$160(1/#8206%"D7&+(-#(.=6($;87/;2#5(_0/L#8.%6"<a(861.2/#(/F(.=6
;2.( .=6( 0/<2#"#.( ;%/1688( 28( 8602<6#.( ;21]T$;( F%/<( .=6( D60( 2#./( .=6( "11676%".2#5( F7/L'
%68$7.2#5( 2#( "#( 2#1%6"86( /F( .=6( 8$8;6#060( 8602<6#.( 1/#16#.%".2/#8+( :=6( </8.( %676>"#.
;%/168868(2#(.=6(06;/82.2/#("#0(6%/82/#(%652/#8("%6U(1/#>61.2/#(/F(8602<6#.(;"%.21768(D&(.=6
=/%2Z/#."7("#0(>6%.21"7(F7$20(>67/12.268'(<2c2#5(/F(8602<6#.(;"%.21768(D&(.$%D$76#.("#0(/%D2."7
</.2/#8'(86..72#5(/F(.=6(;"%.21768(0$6(./(5%">2.&("#0(;21]T$;(/F(.=6(;"%.21768(F%/<(.=6(D60(D&
1$%%6#.("#0(L">6T2#0$160(D60T8=6"%(8.%68868+(:=6(6FF61.(/F(.=6(L">68(28(.=".(/F("#(2#.6#82F260 8.2%%2#5("1.2/#(2#(.=6(#6"%TD60(%652/#(%68$7.2#5(2#(7"%56%(8602<6#.(1/#16#.%".2/#8'(L=276(.=6 1$%%6#.(28(%68;/#82D76(F/%(.=6(.%"#8;/%.".2/#(/F(.=6(8602<6#.+( :=6(8.2%%2#5(6FF61.(02<2#28=68 L2.=( 2#1%6"82#5( L".6%( 06;.=+( :=$8'( .=28( 6FF61.( 28( 7688( 2<;/%."#.( 2#( .=6( ;2.( 2.867F+( :=686
;%/168868( "%6( 81=6<".21"77&( 8=/L#( F/%( 1%/88( F7/L( />6%( "( 7/#5'( #"%%/L( 1="##67( 2#( ^25$%6 9+,+)+
O*0(%/4;+!+- <-,)/-01!1$+08%#$1!%$#*-88-8!)0!+!*&+00-'!%-$%-0,)*5'+$!1#!1&-!2'#6
-#( 1"86( /F(/D72O$6(F7/L( />6%( "(1="##67e;2.( .=6( 8602<6#.( .%"#8;/%.( 2#( 7/#52.$02#"7( 02%61.2/#
<"&(2#1%6"86(1/#8206%"D7&(L2.=(%68;61.(./(.=6($#028.$%D60(7/#52.$02#"7(.%"#8;/%.(/$.8206(.=6 1="##67+(!6#86#(6.("7+(_,IIIa(%6;/%.8("#(2#1%6"86(/F("(F"1./%()(F/%("#(";;%/"1=("#576(/F(B@/+ -#(1"86(/F(F7/L(;"%"7767(L2.=(.=6(1="##67("c28'(.=6(8206(87/;68(/F(.=6(1="##67("%6(F7"..6#60("#0 8<//.=60(0$6(./(5%">2.".2/#"7(6FF61.8+(A=6#("(8602<6#.(;"%.2176(%68.2#5(/#("(8206(87/;6(28(86.
2#./(</.2/#(D&(L">68(/%(1$%%6#.8'(.=6(%68$7.2#5(</>6<6#.(/F(.=6(;"%.2176(L277'(0$6(./(5%">2.&'
=">6( "( 1/<;/#6#.( 2#( 0/L#L"%08( 02%61.2/#+( X&( .=28( <61="#28<( 8602<6#.( <".6%2"7( L277
"7L"&8( D6( .%"#8;/%.60( ./( .=6( 066;6%( ;"%.( /F( .=6( 1="##67( &26702#5( %60$160( 06;.=8( "#0 8<//.=60(8206(87/;68+(:=686(6FF61.8("%6(;"%.21$7"%7&(2<;/%."#.(2#(1/#02.2/#8(L2.=("(%67".2>67&
#"%%/L(1="##67("#0(F7/L(;"%"7767(./(.=6(7/#568.("c28(/F(.=6(1="##67+
:=6( ;%6021.2/#( /F( 8602<6#.".2/#( 2#( <2#2#5( ;2.8( _D"1]F2772#5a( D"821"77&( 1/#828.8( /F( .L/
676<6#.8U
!" 8602<6#.(.%"#8;/%.(1"%%260(D&(.=6(";;%/"1=2#5(F7/L(./(.=6(1="##67'(06;6#02#5(/#(F7/L' L">6("#0(8602<6#.(;%/;6%.268[
!" .%";;2#5( 6FF2126#1&( /F( .=6( ;2.'( 06;6#02#5( /#( ;2.( 02<6#82/#8'( 1="##67( /%26#.".2/#( "#0 8602<6#.(1="%"1.6%28.218+
0%%.#1*-%*/"(2*3"4./
C"#0(L">68(1"#("FF61.(.=6(D6=">2/$%(/F(#">25".2/#(1="##678(2#(.L/(L"&8U
!" 56#6%".2/#(/F(8"#0(L">68(2#8206(.=6(1="##67(.=6%6D&(%60$12#5(.=6(06;.=[
!" 8"#0( L">68( "#0( 8=/"78( /#( D60( \$8.( /$.8206( 1="##67( "#0( <25%".2#5( ./L"%08( .=6( ;2.
1"$82#5(2#F277(/F(.=6(;2.+
b"./=(6.("7+(_,IIPa(8.$0260(.=6(56#6%".2/#("#0(<25%".2/#(/F(8"#0(L">68(/>6%("(8=/"7(2#8206("
#">25".2/#(1="##67(_X28"#86./(1="##67'(!";"#a+(:=6(8"#0(L">68(="0("(=625=.(/F("D/$.(@(<
"#0("(76#5.=(/F("D/$.(,**(<("#0(L6%6(</8.(;%/#/$#160("#0(</D276(2#(06;.=8(/F("D/$.(,@(./
)@( <+( :=6( 1%68.72#68( /F( .=6( 8"#0( L">68( "%6( 6886#.2"77&( #/%<"7( ./( .=6( 02%61.2/#( /F( .=6
;%60/<2#"#.(.20"7(1$%%6#.8+(:=6(D60(1/#828.60(/F(8"#0(2#(.=6(%"#56(/F(*+@(./()(<<+(:=6(8"#0 L">6(1%68.8(L6%6(%6</>60(2#(.=6(;6%2/0(,IP,T,IP9(D&(0%6052#5(./(/D."2#("(7"%56%(06;.=(F/%
#">25".2/#( _0%60560( >/7$<6( /F( "D/$.( )( <2772/#( <9a+( E$%2#5( "( ;6%2/0( /F( ,*( &6"%8( "F.6%
0%6052#5( .=6( 8"#0( L">6( ;"..6%#( L"8( %68./%60( 82<27"%( ./( .=6( 2#2.2"7( 82.$".2/#+( X"860( /#
"#"7&828(/F(%65$7"%(8/$#02#5(0"."'(.=6(F/77/L2#5(/D86%>".2/#8(L6%6(06%2>60U
!" 5%"0$"7(%60$1.2/#(/F(.=6(<6"#(06;.=(_8;".2"77&(">6%"560a(2#(.=6(</8.(8="77/L("%6"(/F(.=6 8=/"7(_06;.=8(/F(,@(./()*(<a(D&("D/$.( *+S(<( />6%( ,*(&6"%8( />6%( "#( "%6"( /F( "D/$.(F2>6 L">6(76#5.=8(0$6(./(8"#0(.%"#8;/%.(./L"%08(.=6(8="77/L(;"%.(/F(.=6(8=/"7[
!" 5%"0$"7( 2#1%6"86( /F( .=6( 8"#0( L">6( =625=.( D&( "D/$.( 9( <( />6%( "( ;6%2/0( /F( ,*( &6"%8 _%60$1.2/#(/F(<2#2<$<(06;.=a[
!" 8"#0(L">6(<25%".2/#(_"D/$.(@(<e&%(2#(06;.=8(/F()@(./(9*(<($;(./(,@(<e&%(2#(06;.=8(/F(,@
./()@(<a(F%/<(D/.=(82068(/F(.=6(8=/"7(./L"%08(.=6(</8.(8="77/L(;"%.(/F(.=6(8=/"7(2#(.=6 02%61.2/#(/F(.=6(;%60/<2#"#.(1$%%6#.8+
b"./=( ( 6.( "7+( 8$5568.( ./( ;6%F/%<( ;/1]6.( 0%6052#5( ".( 2#.6%<602".6( 06;.=8( ./( 2#.6%16;.( .=6 .%"#8;/%.(/F(8"#08(./(.=6(8="77/L(;"%.(/F(.=6(8=/"7+
0%%.#1*-%*562
-#( <$00&( 1/#02.2/#8'( =25=( 1/#16#.%".2/#8( /F( <$0( 2#( 8$8;6#82/#( L2.=( "11/<;"#&2#5( =25=
86..72#5(%".68("#0(%67".2>67&(.=21](06;/82.8(<"&(6c28.("7/#5(.=6(D60+(:=686(06;/82.8(";;6"%(./
D6(0$6(./(.=6(06;/82.2/#(/F(F7$20(<$0(F7/18(1/#>61.60(2#./(.=6(%652/#(F%/<(D/.=($;8.%6"<("#0 0/L#8.%6"<( "8( "( %68$7.( /F( 0%2F.8( #6"%( .=6( D60+( :=686( 0%2F.8( 1"#( D6( 86.( $;( D&( L">6T0%2>6#
F/%168'( "#0e/%( =/%2Z/#."7( 06#82.&( 5%"026#.8( 2#0$160( D&( 02FF6%6#168( 2#( 8"72#2.&( D6.L66#( .=6 F%68=(L".6%(F7/L("#0(86"(L".6%+(:=6(>6%.21"7(028.%2D$.2/#(/F(.=6(8602<6#.(1/#16#.%".2/#8(1"#
D6(1="%"1.6%2Z60( "8( "( .=%66T7"&6%( 8&8.6<( L2.=( 176"%( 2#.6%F"168( _7$./172#68a'( "8( F/77/L8( _`"#
N2\#'(,II9aU
!" 1/#8/720".60(<$0(".(.=6(D/../<(L2.=(1/#16#.%".2/#8(7"%5D6%(.="#("D/$.(9**(]5e<9[(F7/18
"#0( ;"%.21768( "%6( 8$;;/%.60( D&( 0%"5( F/%168( 6c6%.60( D&( .=6( 681";2#5( F7$20( _=2#06%60 86..72#5(6FF61.8a[
!" </D276( _F7$20a( <$0( 8$8;6#82/#( 7"&6%( _*+,( ./( ,( <a( L2.=( 1/#16#.%".2/#8( 2#( .=6( %"#56 D6.L66#(,*("#0(9**(]5e<9[(.=6(F7$20(<$0(1"#(D6(.%"#8;/%.60(D&(.206T'(L2#0T'(L">6T("#0 5%">2.&T0%2>6#(F/%168(_#6"%TD60(0%2F.(>67/12.268(/F(*+*@(./(*+@(<e8a[
!" </D276( 027$.6( <$0( 8$8;6#82/#( _$;( ./( L".6%( 8$%F"16a( L2.=( 1/#16#.%".2/#8( 2#( .=6( %"#56 D6.L66#(*+,("#0(,*(]5e<9[(.=6(F7/18("#0(;"%.21768("%6(8$;;/%.60(D&(.$%D$76#16T2#0$160 F/%168[( .=6( <$0( 8$8;6#82/#( 1"#( D6( .%"#8;/%.60( D&( .206T'( L2#0T'( L">6T0%2>6#( F/%168 _>67/12.268(/F(*+9(./(,(<e8a
A=6#( .=6( 86"( D60( 1/#."2#8( %67".2>67&( 7"%56( <$00&( "#0( 827.&( 8602<6#.( F%"1.2/#8'( 1/=682>6 F/%168( D61/<6( 2<;/%."#.+( Q6#6%"77&'( .=6( 8.%6#5.=( /F( .=6( 1/#8/720".60( 8/27( "5"2#8.( 6%/82/#
2#1%6"868(06;6#02#5(/#(.=6(.&;6(/F(17"&(<2#6%"78'(.=6(;%686#16(/F(/%5"#21(<".6%2"78'(.=6(8."56 /F(1/#8/720".2/#'(6.1+(^7$<6(6c;6%2<6#.8(8=/L(.=".(.=6(8"#0(1/#16#.%".2/#8("%6(825#2F21"#.7&
%60$160(_F"1./%(9*a(2#(1/#02.2/#8(L2.=(L">6(</.2/#(/>6%("(D60(1/#828.2#5(/F()@j(<$0("#0 S@j(8"#0(1/<;"%60(./(.=6(8"#0(1/#16#.%".2/#8("D/>6("(,**j(8"#0( D60( _`"#( N2\#'( ,II9a+
:=6(8."56(/F(1/#8/720".2/#(/F(.=6(<$0(D60(28("#(2<;/%."#.(F"1./%(2#(.=6(6%/02D272.&(/F(.=6(D60
<".6%2"7+(^%68=(<$0(06;/82.8(=">6("(>6%&(7//86(.6c.$%6(/F(<$0( F7/18(L=21=( "7%6"0&( =">6( "
7/L(06#82.&(.=6<867>68+(:=6(L6.(D$7](06#82.&(/F(F%68=(<$0(06;/82.8(28(2#(.=6(%"#56(/F(,*@*
./(,,**(]5e<9(_I@j(L".6%a+(:=6(1/=682>6(F/%168(2#(F%68=(06;/82.8("%6(8.277(>6%&(7/L("#0(.=6
<".6%2"7(1"#(6"827&(D6(6%/060+(:=6(06#82.&(/F(F%68=(06;/82.8(5%"0$"77&(2#1%6"868("8(2#.6%8.2.2"7 L".6%(28(;%688680(/$.(D&(5%">2.&(F/%168+(:=28(;%/1688(/F(1/#8/720".2/#(2#2.2"77&(5/68(%67".2>67&
F"8.'( D$.( 5%"0$"77&( 87/L8( 0/L#+( :=6( 8.%6#5.=( "5"2#8.( 6%/82/#( 2#1%6"868( L2.=( 2#1%6"82#5 1/#8/720".2/#("#0(06#82.&+
A">6("1.2/#(/>6%("(<$00&(D60(<"&(56#6%".6("(=25=T1/#16#.%".2/#(F7$20(<$0(7"&6%(17/86(./
.=6(D60+(:=6(8602<6#.(1/#16#.%".2/#8(2#(.=28(7"&6%(<"&(D6(/F(.=6(/%06%(/F(,**(./(9**(]5e<9+ :=6(8602<6#.(1/#16#.%".2/#8("D/>6(.=28( 7"&6%(56#6%"77&( "%6("#( /%06%( /F( <"5#2.$06( 8<"776%+
:206T0%2>6#'( L">6T0%2>6#'( L2#0T0%2>6#( /%( 5%">2.&T0%2>6#( _/#( 87/;68a( 1$%%6#.8( "%6( "D76( ./
.%"#8;/%.(.=6(F7$20(<$0(7"&6%8(./L"%08(.=6(1="##67(%68$7.2#5(2#(6c16882>6(06;/82.2/#(/#(8=/%.
.6%<(.2<6(81"768(_8./%<8'(</#8//#(L">68a+(R(F7$20(<$0(7"&6%(L2.=("(.=21]#688(/F(*+,(<'("
1/#16#.%".2/#(/F(,**(]5e<9("#0("(=/%2Z/#."7(>67/12.&(/F(*+,(<e8'(&26708("(.%"#8;/%.(%".6(/F(, ]5e<e8(/%(*+**)(<9e<e8(_"88$<2#5("(0%&(D$7](06#82.&(/F(@**(]5e<9a'(L=21=(28(6O$2>"76#.(./
"D/$.(,S@(<9e<e0"&+(:=$8'("(1="##67(L2.=("(1%/88T861.2/#(/F(,***(<9e<(L277(D6(1/<;76.67&
F27760(2#("D/$.(@(./(H(0"&8(_8./%<(.2<6(81"76a(D&(F7$20(<$0(1"%%260(2#./(.=6(1="##67+
-#F/%<".2/#( /#( </06772#5( /F( F7$20( <$0( .%"#8;/%.( 28( 52>6#( D&( K00( "#0( ?//;6%( _,IPIa' b%"#6#D$%5("#0(A2#.6%L6%;(_,IISa'(R72(6.("7+'(_,IISa("#0(A2#.6%L6%;(6.("7+(_)**)a+
N616#.(8.$0268(_A2#.6%L6%;'(,III'()**,'()**)a(8$5568.(.=".(.=6(F/%<".2/#(/F(F7$20(<$0(F%/<
8$8;6#82/#8( /F( 1/=682>6( 8602<6#.8( 2#( 06;%6882/#8( 2#( .=6( 86"( D60( _1="##678( /%( ;2.8a( /%( 2#
="%D/$%( D"82#8( 28( .=6( %68$7.( /F( 8$;6%8".$%".2/#( /F( .=6( 8$8;6#82/#'( .=".( 28( .=".( .=6( .%"#8;/%.
1";"12.&(/F(.=6(F7/L(28(6c166060+(:=686(8.$0268("78/(8$5568.(.=".(.=6(56#6%".2/#(/F(F7$20(<$0
"7%6"0&(."]68(;7"16(".(%67".2>67&(8<"77(1/#16#.%".2/#8(_k(,(]5e<9a+(A2#.6%L6%;(6.("7+(_)**,a 68.2<".6(.=".(.=6(8".$%".2/#(1/#16#.%".2/#(2#(.=6(E$.1=(1/"8."7(Z/#6("</$#.8(./("(>"7$6(2#(.=6
%"#56(/F(*+,(./(*+@(]5e<9+(:=6(8".$%".2/#(1/#16#.%".2/#(?8(81"768(</%6(/%(7688(L2.=U
?8(#($(V9e__8T,a5(=(L8a(L=6%6($l(L".6%(06#82.&'(8T,l(%67".2>6(8602<6#.(06#82.&'(5l(5%">2.&
"11676%".2/#'(Vl(F7/L(>67/12.&'(=(l(L".6%(06;.=("#0(L8l(86..2#5(>67/12.&+
46"8$%6<6#.8(;6%F/%<60(".("#1=/%(8.".2/#8("(F6L(]<f8(/FF8=/%6(2#(.=6(>212#2.&(/F(.=6(J$%/T 4""8(?="##67'(1"%%260(/$.(2#(.=6(F%"<6L/%](/F(.=6(C-:Y4RG(;%/\61.'(%6>6"760(06;.=T<6"#
8$8;6#060(8602<6#.(1/#16#.%".2/#8($;(./(*+@(]5e<9(0$%2#5(8./%<(1/#02.2/#8'(L2.=(/11"82/#"7
#6"%TD60( 1/#16#.%".2/#8( 0$%2#5( 87"1]( L".6%( 6c16602#5( )*( ]5e<9( _b/]'( )***a+( C2<$7".2/#8 L2.=( "( <".=6<".21"7( ;/2#.( </067( <"06( 2.( ;7"$82D76( .=".( .=686( 8$8;6#82/#8( <"&( 1/77";86
$#06%(16%."2#(1/#02.2/#8'(76"02#5(./(.=6(F/%<".2/#(/F("(.$%D202.&(1$%%6#.("#0(06;/82.8(/F(F7$20
<$0(_A2#.6%L6%;(6.("7+'()**,[(A2#.6%L6%;("#0(>"#(b68867'()**)a+
:=6(.%"#8;/%.(1";"12.&(_/%(8".$%".2/#(1/#16#.%".2/#a(2#("()*(<(066;(8"#0;2.'(7/1".60(".()*(<
L".6%(06;.='(L/$70(061%6"86(D&("(F"1./%(@(./(,*("8("(F2%8.(68.2<".6'("88$<2#5("(061%6"86(2#
>67/12.&(;%/;/%.2/#"7(./(.=6(2#1%6"86(2#(1%/88(861.2/#(_1/#.2#$2.&(1/#8206%".2/#8a+(:=28(L/$70 2<;7&( .=".( F7$20( <$0( <"&( "7%6"0&( D6( F/%<60( 2#( 8$1=( ;2.8( ".( 1/#16#.%".2/#8( /F( "D/$.( *+*@
]5e<9+(R88$<2#5("(F7$20(<$0(1/#16#.%".2/#(/F(,**(]5e<9'(8$1=("(8$8;6#82/#(L/$70(&2670("
F7$20( <$0( .=21]#688( 2#( .=6( %"#56( /F( *+*,( ./( *+*)( <+( W6#16'( .=686( 8602<6#.( 06;/82.8( <"&
D61/<6(825#2F21"#.(0$6(./("11$<$7".2/#(2#(.2<6+(-F(.=6(=&0%/0&#"<21(1/#02.2/#8(F">/$%(.=6 F/%<".2/#(/F(8$1=(F7$20(<$0(7"&6%8'(2.(28(#/.(72]67&(.=".(.=6(.20"7(F7/L(L277(D6("D76(./(%6T6%/06 .=686(06;/82.8+(W/L6>6%'(L">68(<"&(0/(8/3(L=6.=6%(.=28(L277(/11$%(28(#/.(]#/L#(".(;%686#.+
-F(.=686(7"&6%8("%6(#/.(6%/060("#&</%6'(.=6&(L277(1/#8/720".6'(%68$7.2#5(2#(D60(1/#16#.%".2/#8 2#(.=6(%"#56(/F(,**(./(@**(]5e<9+
R.( ;%686#.'( .=6( /11$%%6#16( /F( 8".$%".2/#( 1/#02.2/#8'( "#0( .=6( 8$D86O$6#.( F/%<".2/#( /F( "
.$%D202.&(1$%%6#.("#0(7"&6%8(/F(F7$20(<$0(1"#(D6(82<$7".60(L2.=(.=6(EJY^:9E(</067(8&8.6<
_A2#.6%L6%;("#0(>"#(b68867'()**)a+(R78/(.=6(</>6<6#.8(/F(.=6(F7$20(<$0(7"&6%8(.=6<867>68
"#0(.=62%(;/882D76(6%/82/#(/%(6#.%"2#<6#.(D&(F7/L("#0e/%(L">68(1"#( D6( 1/<;$.60(L2.=( .=6 EJY^:9ETF7$20T<$0(</067+
3.2 Currents
:=6(2#F7$6#16(/F(.=6(066;6#60("%6"(_;2.a(/#(.=6(7/1"7(1$%%6#.(;"..6%#(_.206("#0(L2#0(0%2>6#a(28 06.6%<2#60(D&(.=6U
!" ;2.(02<6#82/#8(_76#5.='(L20.='(06;.=a'
!" "#576(D6.L66#(.=6(<"2#(;2.("c28("#0(02%61.2/#(/F(";;%/"1=2#5(1$%%6#.'
!" 8.%6#5.=(/F(7/1"7(1$%%6#.'
!" D".=&<6.%&(/F(7/1"7("%6"(_8=/"78("%/$#0(;2.a+
Q6#6%"77&'( .=6( 02<6#82/#8( /F( .=6( 066;6#60( "%6"( "%6( 8/( 8<"77( .=".( .=6%6( 28( #/( 825#2F21"#.
2#F7$6#16(/F(.=6(066;6#60("%6"((/#(.=6(<"1%/T81"76(1$%%6#.(;"..6%#+(-#(</8.(1"868(.=6(1$%%6#.
;"..6%#(28(/#7&(1="#560(2#(.=6(02%61.(>212#2.&(/F(.=6("%6"(1/#16%#60+
X"821"77&'(.=%66(82.$".2/#8(1"#(D6(028.2#5$28=60U
!+44 <2*#4)82##/1K=*$42L*34=2%211/14$&4)(%%/#$
A=6#(.=6(066;6#60("%6"(28(82.$".60(;"%"7767(./(.=6(7/1"7(1$%%6#.'(.=6(>67/12.268(2#(.=6(066;6%
Z/#6(<"&(2#1%6"86(1/#8206%"D7&(0$6(./(.=6(061%6"86(/F(.=6(D/../<(F%21.2/#'(06;6#02#5(/#(.=6 76#5.=( "#0( L20.=( /F( .=6( 066;6%( Z/#6+( !$8.( $;8.%6"<( /F( .=6( 1="##67'( F7/L( 1/#.%"1.2/#( L277 /11$%(/>6%("(8=/%.(028."#16(&26702#5("(7/1"7(2#1%6"86("#0(061%6"86(/F(.=6(F7/L(>67/12.&(_/%06%
/F( ,*j( ./( )*j'( 06;6#02#5( /#( 1="##67( L20.=( A( "#0( $;8.%6"<( F7/L( 06;.=( =/a+( ^7/L
1/#.%"1.2/#(L277(D6(<2#2<$<(F/%(Amm=/+(:=6(F7/L(>67/12.&(2#(.=6(1/#.%"1.2/#(861.2/#(1"#(D6 68.2<".60(F%/<(_=,m=/aU
$1/#ln)=/e_=/o=,ap$/( _9+)+,a
:=6(76#5.=(/F(.=6(1/#.%"1.2/#(861.2/#(28(/F(.=6(/%06%(/F(.=6(1="##67(L20.=(A+(C2<27"%7&'(F7/L 1/#.%"1.2/#( L277( /11$%( \$8.( D6F/%6( .=6( 0/L#8.%6"<( 6#0( /F( .=6( 1="##67+( :=6( F7/L( >67/12.&
028.%2D$.2/#("7/#5(.=6(<"2#("c28(/F(.=6(1="##67(28(8=/L#(81=6<".21"77&(2#(^25+(9+)+,+
COAST Velocity Ux
channel or pit
Flow lines
U1 Uo
Length L
width W
O*0(%/4;+-+! "+)0!*&+00-'=%)1!+7)8!%+$+''-'!1#!*5$$-01
R88$<2#5( .=6( L".6%( 8$%F"16( 87/;6( ./( D6( 1/#8."#.'( .=6( 6O$272D%2$<( F7/L( _$,a( 2#8206( .=6 1="##67(1"#(D6(0681%2D60(D&(.=6(?=qZ&(6O$".2/#'(&26702#5(.=6(F/77/L2#5(F"%TF2670(6c;%6882/#
_=,m=/aU
$,l$/_?,e?/a_=,e=/a*+@( _9+)+)a
L2.=( $,l6O$272D%2$<( F7/L( >67/12.&( 2#8206( 1="##67( "#0( $/l( 6O$272D%2$<( F7/L( >67/12.&
$;8.%6"<(/F(1="##67'(=,l(L".6%(06;.=(2#(1="##67+(Q6#6%"77&'(.=6(F7/L(2#8206(.=6(1="##67(28 8/<6L=".(7"%56%(.="#(/$.8206(.=6(1="##67(_$,m$/a'(6c16;.(L=6#(.=6(76#5.=(/F(.=6(1="##67(28
%67".2>67&(8<"77(_Yk)Aa+(:=6("0\$8.<6#.(76#5.=(%(/F(.=6(F7/L(./(.=6(#6L(6O$272D%2$<(>"7$6 2#8206(.=6(1="##67(28( /F(.=6(/%06%( /F( ?,)=,e_)5a'( &26702#5( >"7$68( /F( 9( ./( B( ]<( _E6( `%26#0' ,IIHa+(:=6(6c;/#6#.2"7(("0\$8.<6#.(;%/1688(1"#(D6(6c;%68860("8U
$c)l$,)o_$/)T$,)a6Tce%( _9+)+9a Q6#6%"77&'( .=6( #6L( 6O$272D%2$<( F7/L( >67/12.&( 2#( .=6( 1="##67( 28( %6"1=60( F/%( Ym,*A( "#0 Amm=/+
-+4 <2*#4)82##/1K=*$42L*34=/%=/#'*)(12%4$&4)(%%/#$
A=6#(.=6(066;6#60("%6"(28(82.$".60((;6%;6#021$7"%(./(.=6(7/1"7(1$%%6#.'(.=6(>67/12.268(2#(.=6 066;6%(Z/#6("%6(%60$160(0$6(./(.=6(2#1%6"860(L".6%(06;.=+(:=28(2#F7$6#16(28(</8.(825#2F21"#.
2#(.=6(#6"%TD60(7"&6%(/F(.=6(061676%".2/#(Z/#6(L=6%6("0>6%86(;%688$%6(5%"026#.8("%6( "1.2#5' 1"$82#5( "( 8.%/#5( %60$1.2/#( /F( .=6( F7/L+( -#( 1"86( 8.66;( 8206( 87/;68( _,U@( "#0( 8.66;6%a( F7/L 86;"%".2/#( "#0( %6>6%8"7( L277( /11$%( 2#.%/0$12#5( "( %".=6%( 1/<;721".60( F7/L( ;"..6%#+( :=6
>67/12.268(2#(.=6(%612%1$7".2/#(Z/#6("%6(8<"77(1/<;"%60(L2.=(.=/86(2#(.=6(<"2#(F7/L+(:=6(F7/L
>67/12.268( 2#( .=6( #6"%TL".6%( 8$%F"16( 7"&6%8( "%6( ="%07&( 2#F7$6#160( D&( .=6( ;%686#16( /F( .=6 1="##67(_2#6%.2"7(6FF61.a+
:=6( 06;.=T">6%"560( F7/L( >67/12.&( 2#8206( .=6( 1="##67( _$,a( 1"#( D6( 06.6%<2#60( F%/<( .=6 1/#.2#$2.&(6O$".2/#(_O(28(1/#8."#.aU
$,l$/_=/e=,a _9+)+Ba
:=6( 7"&6%( D6.L66#( .=6( #6"%( 8$%F"16( %652/#( "#0( .=6( %612%1$7".2/#( %652/#( 28( 0/<2#".60( D&
;%/0$1.2/#(/F(.$%D$76#16(6#6%5&(_<2c2#5(7"&6%a+(A=6#(.=6(066;6#60("%6"(28(L206(6#/$5='(.=6 F7/L(L277(%6".."1=(".(.=6(6#0(/F(.=6(0/L#87/;2#5(8206'("8(8=/L#(2#(^25+(9+)+)+(4/%6($#2F/%<
>67/12.&(;%/F2768(L277(D6(;%686#.(".(.=6($;87/;2#5(_0/L#8.%6"<a(8206(/F(.=6(1="##67+(-#(1"86(/F
"(#"%%/L(1="##67(.=6(F7/L(;"..6%#(L277(D6(1/<;76.67&(0/<2#".60(D&(F7/L(86;"%".2/#("#0(F7/L
%6>6%8"7(;=6#/<6#"+(4/8.(;%/D"D7&'("(7"%56( >/%.6c(L277(56#6%".60( 2#(.=6( 1="##67+(E6."2760
<".=6<".21"7(8.$0268(=">6(D66#(0/#6(D&(R7F%2#]("#0(`"#(N2\#(_,IP9a("#0(%616#.7&(D&(!6#86#
6.( "7+( _,IIIa+( :=6( 7"..6%( 8.$0260( .=6( </%;=/7/521"7( D6=">2/$%( /F( 8<"77( 81"76'( 8.66;T82060
;2;672#6(1="##678($82#5("(F$77(9E(</067(F/%(/D72O$6(F7/L(1/#02.2/#8+(:=6(F7/L(2#(.=686(.&;68 /F( 1="##678( 1"#( /#7&( D6( 0681%2D60( D&( "( 06."2760( 9E( </067( "8( .=6( F7/L( ;"..6%#( 28( 8.%/#57&
0/<2#".60(D&(.=6(F7/L(86;"%".2/#(Z/#6(2#(.=6(8.66;T82060(1="##67'(/F.6#(6c.6#02#5(/#./(.=6 0/L#8.%6"<( 8206( 87/;6+( :=6( 86;"%".2/#( Z/#6( 28( 7"%568.( F/%( "#( ";;%/"1=( "#576( /F( I*/( D$.
D61/<68(L6"]6%(F/%(8<"776%("#5768+
O*0(%/4;+-+- >&+00-'!%-$%-0,)*5'+$!1#!*5$$-01
;+4 <2*#4)82##/1K=*$42L*34&B1*J(/4$&4)(%%/#$
A=6#(.=6(066;6#60("%6"(28(82.$".60(/D72O$6(./(.=6(7/1"7(1$%%6#.'(.=6(6FF61.8(/F(;"%"7767("#0
;6%;6#021$7"%( F7/L( ;"..6%#8( "%6( /11$%%2#5( 82<$7."#6/$87&+( :=6( >67/12.&( 1/<;/#6#.
;6%;6#021$7"%( ./( .=6( 1="##67( 28( 2#>6%867&( ;%/;/%.2/#"7( ./( .=6( 7/1"7( L".6%( 06;.='( L=276( .=6
>67/12.&( 1/<;/#6#.( ;"%"7767( ./( .=6( 1="##67( <"&( 2#1%6"86( 0$6( ./( "( %60$1.2/#( /F( D/../<
F%21.2/#+(R8("(%68$7.'(.=6(8.%6"<72#68(8=/L("(%6F%"1.2/#T.&;6(;"..6%#(2#(.=6(1="##67(_866(^25+
9+)+9a+( :=28( 6FF61.( 28( </%6( ;%/#/$#160( 2#( .=6( D/../<( %652/#( L=6%6( .=6( >67/12.268( "%6
%67".2>67&(8<"77+(V8$"77&'(.=6%6(28("#(/>6%"77(2#1%6"86(/F(.=6(>67/12.268(2#(.=6(1="##67(L=6#(.=6
"#576(&/(D6.L66#(.=6(";;%/"1=2#5(1$%%6#.("#0(.=6(1="##67("c28(28(8<"776%(.="#("D/$.()*/(./
9*/'(06;6#02#5(/#(1="##67(02<6#82/#8("#0(D/../<(%/$5=#688+
:=6(6O$272D%2$<(_06;.=T">6%"560a(F7/L(>67/12.&(>61./%(2#(.=6(1="##67(>,(1"#(D6(68.2<".60("8 _!6#86#(6.("7+'(,IIIaU
>,l>/(n_=/(82#&/ae_=,(82#&,ap _9+)+@a
L2.=( >/l6O$272D%2$<( ";;%/"1=2#5( F7/L( >67/12.&'( =/lL".6%( 06;.=( $;8.%6"<( /F( 1="##67'
=,lL".6%(06;.=(2#(1="##67'(&/l";;%/"1=("#576'(&,l(6O$272D%2$#("#576(2#(1="##67(_!6#86#(6.
"7+'(,IIIa+(:=6(6O$272D%2$<(>"7$68(L277(D6(%6"1=60(2F(.=6(1%/88(1="##67(L20.=(A(28(7"%56%(.="#
";;%/c2<".67&( @**=/'(_Am@**=/a+(:=6(6O$272D%2$<( F7/L( >67/12.&( L277( 6c1660( .=6( $;8.%6"<
>67/12.&( 2F( .=6( 1="##67( 06;.=( 28( %67".2>67&( 7"%56( "#0( .=6( ";;%/"1=( "#576( 28( %67".2>67&( 8<"77 _k9*/a+
O*0(%/4;+-+; >&+00-'!%+$+''-'!1#!*5$$-01
d=&821"7(</067(8.$0268(=">6(D66#(;6%F/%<60(".(.=6(W&0%"$721(N686"%1=(C.".2/#(A"772#5F/%0 _WN(A"772#5F/%0'(,IS9a("#0(".(E67F.(W&0%"$7218(_X/6%'(,IP@a+(:=6(.68.8(".(WNC(A"772#5F/%0 L6%6(1/#0$1.60(2#(%67".2>67&(L206(1="##678(2#172#60(./(.=6(1$%%6#.(".("#5768(/F(*/(./(9*/+(:=6 L".6%( 06;.=( /#( .=6( D"#]8( %"#560( F%/<( *+*,@( ./( *+,( <( "#0( .=6( 02FF6%6#16( 2#( .=6( 06;.=
D6.L66#(.=6(1="##67("#0(.=6(D"#]8(L"8(*+*)(<+(X"860(/#(.=686(%68$7.8'(2.(1"#(D6(1/#17$060 .=".( F/%( "#5768( 8<"776%( .="#( 9*/'( .=6( >67/12.&( 2#( .=6( 1="##67( 28( 56#6%"77&( 7"%56%( .="#( .=".
/$.8206(.=6(1="##67+
:=6(.68.8(".(E67F.(W&0%"$7218(L6%6(1/#0$1.60(2#(%67".2>67&(L206(1="##678(2#172#60(./(.=6(F7/L
".("#5768(/F(B@/(./(I*/+(:=6(L".6%(06;.=(/$.8206(.=6(1="##67(%"#560(F%/<(*+,(./(*+)(<+(:=6
02FF6%6#16(2#(06;.=(D6.L66#(.=6(1="##67("#0(.=6(D"#]8(L"8(*+,(<+(-#("77(1"868'(.=6(<6"8$%60
>67/12.268(2#8206(.=6(1="##67(L6%6(8<"776%(.="#(.=/86(/$.8206(.=6(1="##67+(X/6%(_,IP@a(="8 8=/L#( .=".( .=6( 06;.=T">6%"560( >67/12.&( 2#( "#( /D72O$6( 1="##67( /F( 2#F2#2.6( 76#5.=( 1"#( D6 1/<;$.60(D&(.=6(F/77/L2#5(%67".2>67&(82<;76(<".=6<".21"7(</067+
?/#.2#$2.&U '_=$ae'cl* ((((((_9+)+Ha
4/.2/#U $'$e'c(o((D'ce_$=a(o(5'_=oZDae'cl* ((((((_9+)+Sa
$'>e'c(o((D'&e_$=a(o(5'_=oZDae'&l* ((((((_9+)+Pa
L2.=U($'(>l(06;.=T">6%"560(>67/12.268(2#(c'(&(02%61.2/#8'(=l(L".6%(06;.='(ZDl D60( 76>67( ./(0".$<'((Dl( D60( 8=6"%( 8.%688'( cl( 1//%02#".6( #/%<"7( ./( 1="##67
"c28'(&l(1//%02#".6(;"%"7767(./(1="##67("c28'($l(F7$20(06#82.&+
X"860(/#("(#$<6%21"7(8/7$.2/#(/F(.=28(86.(/F(6O$".2/#8'(X/6%(="8(;%686#.60(06825#(5%";=8(F/%
.=6(1$%%6#.(>67/12.&("#0(06F761.2/#("#576(2#(.=6(<20076(/F("(1="##67(/D72O$6(./(.=6(F7/L(_^25+
9+)+Ba+( :=6( L".6%( 06;.=( /$.8206( .=6( 1="##67( 28( 2#( .=6( %"#56( D6.L66#( )+@( "#0( ,*( <+( :=6 1="##67(06;.=(L2.=(%68;61.(./(.=6(8$%%/$#02#5(D/../<(28(@(<+(:=6(8206(87/;68(/F(.=6(1="##678
"%6(,(./(,*+(:=6(D/../<(L20.=(28()**(<+(:=6(";;%/"1=(>67/12.&(28()(<e8+(:=6(D60(%/$5=#688 28(]8l(*+,(<+((^25$%6(9+)+B(8=/L8(.=".($,m$*(F/%(";;%/"1=("#5768(k(,@/+
!6#86#(6.("7+(_,IIIa(="8(8.$0260(.=6(/D72O$6(F7/L(/>6%("(1="##67( $82#5("( 9E(<".=6<".21"7
</067( _%2520( 720( ";;%/"1=a'( 2#17$02#5( "( 9E( .$%D$76#16( </067( _bTJ;827/#( </067a+( :=6 6O$".2/#8("%6(.%"#8F/%<60(/#./("(1$%>272#6"%(1//%02#".6(8&8.6<( "#0( 8/7>60($82#5(.=6( F2#2.6
>/7$<6(<6.=/0+(:=6(</067(L"8(>6%2F260($82#5(.=6(6c;6%2<6#."7(%68$7.8(/F(WN(A"772#5F/%0 _,IS9a+( :=6(</067( L"8( F/$#0( ./( 8".28F"1./%27&( %6;%686#.( .=6( 6FF61.( /F( %6F%"1.2/#( 2#1%6"82#5 ./L"%08(.=6(D/../<+
^25$%6(9+)+@(8=/L8(.=6(%6F%"1.60(8.%6"<72#68(F/%(.L/(82.$".2/#8+(:=6(8.%6"<72#68(%6;%686#.(.=6
;".=8(/F(.=%66(F7$20(;"%.21768(%676"860(".(.=%66(02FF6%6#.(=625=.8("D/>6(.=6(D60(_\$8.("D/>6(.=6 D60'(".(<20T06;.=(("#0(#6"%(.=6(L".6%(8$%F"16a+(:=6(8.%6"<72#6(#6"%(.=6(D60(="8(.=6(7"%568.
06F761.2/#+(:=6(>"%2".2/#(/F(.=6(1$%%6#.(%6F%"1.2/#(_06F761.2/#a(/>6%(.=6(>6%.21"7(<"&(D6(866#
"8( "( 861/#0"%&( </.2/#( 1/6c28.2#5( L2.=( .=6( 06;.=T">6%"560( F7/L+( :=6( 8.%/#568.( 861/#0"%&
</.2/#(_8.%/#568.(F%"1.2/#(6FF61.a(/11$%8(F/%(";;%/"1=("#5768(2#(.=6(%"#56(/F(H*/(./( P*/+(-#
.=".( 1"86( .=6( 02FF6%6#16( D6.L66#( .=6( 06;.=T">6%"560( F7/L( "#576( "#0( .=6( "#576( /F( .=6( D60T 8=6"%(8.%688(%6"1=68(>"7$68($;(./(9*/+
-#(^25$%6(9+)+@("( F/$%.=(8.%6"<72#6(28(8=/L#(F/%( "( F7$20( ;"%.2176( 2#8206( .=6( F7/L( 86;"%".2/#
Z/#6+(:=6(87/;6(/F(.=6(1="##67(28(%67".2>67&(8.66;[(.=$8("(7"%56(86;"%".2/#(Z/#6(28(56#6%".60+
:=6( F7$20( ;"%.2176(2#8206(.=6( 86;"%".2/#( Z/#6( 28( 1"%%260( 2#( .=6( 7/#52.$02#"7( 02%61.2/#( /F( .=6 1="##67+
0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4 1 . 6 1 . 8 2
0 . 3 0 . 4 0 . 5 0 . 6 0 . 7
D e p t h r a t io ( h o / h 1 )
Velocity ratio (u1/uo)
ang le = 8 5 ang le = 8 0 ang le = 7 5 ang le = 6 0 ang le = 4 5 ang le = 3 0 ang le = 1 5 ang le = 1 0 ang le = 5
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
0 . 3 0 . 4 0 . 5 0 . 6 0 . 7
D e p t h r a t io ( h o / h 1 )
Deflection angle in channel (degrees)
ang le = 5 ang le = 1 0 ang le = 1 5 ang le = 3 0 ang le = 4 5 ang le = 6 0 ang le = 7 5 ang le = 8 0 ang le = 8 5
h1 ho
slopes 1 to 10 Flow
O*0(%/4;+-+? ?-'#*)1@!+0,!,-2'-*1)#0!+0('-!)0!/),,'-!#2!*&+00-'!2#$!#A')B5-!2'#6
&CD6+1-$!,-%1&!#518),-!*&+00-'E!&FD!6+1-$!,-%1&!)08),-!*&+00-'E 5CD,-%1&G+.-$+(-,!.-'#*)1@!#518),-!*&+00-'E
5FD,-%1&G+.-$+(-,!.-'#*)1@!)0!/),,'-!#2!*&+00-'
O*0(%/4;+-+@ ?)85+')8+1)#0!#2!$-2$+*1-,!81$-+/')0-8E
H+1)#!#2!,-%1&!)0!*&+00-'!I9FJ!+0,!,-%1&!#518),-!*&+00-'!I9CJDKE H+1)#!#2!*&+00-'!6),1&!ILJ!+0,!,-%1&!#518),-!*&+00-'!I9CJ!DKM N-214 O%%$#+*&!+0('-DMC#
H)(&14 O%%$#+*&!+0('-DPC#
3.3 Waves
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
.=6( ;%686#16( /F( .=6( 1/"8.( .=6( F7/L( 2#( .=6( 1="##67( L277( D6( 06F761.60( 2#( /FF8=/%6( 02%61.2/#
_82<27"%(./(%2;(1$%%6#.8'(866(^25+(9+9+,a+
:=%66(82.$".2/#8(/F(L">6(;%/;"5".2/#(/>6%(.=6(1="##67("%6(=6%62#(028.2#5$28=60U
!+4 <2*#4)82##/1K=*$42L*34=2%211/14$&4I2A/3
A=6#(.=6(L">68( "%6( ;%/;"5".2#5( ;"%"7767( ./(.=6(<"2#( "c28( /F( .=6( 066;6#60("%6"'(.=6( L">6
=625=.(2#(.=6(066;6%("%6"(L277(D6(%60$160(8/<6L=".(0$6(./(.=6(2#1%6"860(L".6%(06;.=+(:=6 L">6(1676%2.&(L277(2#1%6"86(2#(.=6(066;6%("%6"(&26702#5(1$%>60(L">6(1%68.8+(A">6(6#6%5&(/#
.=6(8206(87/;68(L277(D6(%60$160(D&(02FF%"1.2/#"7(6FF61.8+( A">68( L2.=("(>6%&( 8<"77( ";;%/"1=
"#576(6#.6%2#5(.=6(066;6%("%6"(L277(D6(%6F%"1.60(/$.(/F(.=6("%6"'(866(^25$%6(9+9+,+
-+4 <2*#4)82##/1K=*$42L*34=/%=/#'*)(12%4$&4I2A/3
A=6#(.=6(L">68("%6(;%/;"5".2#5( ;6%;6#021$7"%( ./( .=6(<"2#("c28( /F( .=6( 066;6#60( "%6"'( .=6 L">6(=625=.(2#(.=6(066;6%(Z/#6(L277(%60$16(0$6(./(.=6(2#1%6"860(06;.=+(C61/#0"%&(6FF61.8("%6
%6F761.2/#( ;=6#/<6#"( ".( .=6( 60568( /F( .=6( 8206( 87/;68+( :=28( 6FF61.8( "%6( =/L6>6%( /F( <2#/%
2<;/%."#16(F/%(56#.76(8206(87/;68(_7688(.="#(,USa+
;+4 <2*#4)82##/1K=*$42L*34&B1*J(/4I2A/3
A=6#(.=6(L">68("%6(;%/;"5".2#5(/D72O$6(./(.=6(<"2#("c28(/F(.=6(066;6#60("%6"'(8=/"72#5("#0
%6F%"1.2/#(6FF61.8(L277(/11$%("#0("(%".=6%(028.$%D60(L">6(;"..6%#(<"&(D6(56#6%".60("D/>6(.=6 066;6%(Z/#6(06;6#02#5(/#(.=6(06;.=("#0(L">6(";;%/"1=("#576+(-#(1"86(/F("(%67".2>67&(8<"77
";;%/"1=("#576'(.=6(2#1/<2#5(L">68(<"&(D6(.%";;60(_%6F%"1.60e%6F761.60(D"1]L"%08a(/#(.=6 87/;6(/F(.=6(066;6#60("%6"(%68$7.2#5(2#("(825#2F21"#.7&(8<"776%(L">6(=625=.(2#(.=6(066;6#60
"%6"'(866(^25$%6(9+9+,+((R(1%/88(L">6(;"..6%#(1/#828.2#5(/F(2#1/<2#5("#0(/$.5/2#5(L">68(L277 D6( 56#6%".60( /$.8206( .=6( 1="##67+( :=6( 1%2.21"7( L">6( ";;%/"1=( "#576( _L2.=( %68;61.( ./( .=6 1="##67("c28a(28("D/$.()@/(./( 9*/(F/%( L">6( ;6%2/08( /F( S( ./( I(8'( 06;.=8( /F( ,@( ./()*( <'(8206 87/;68(/F(,(./(S("#0(1="##67(06;.=(/F(@(./(,*(<+(-#1/<2#5(L">68(L2.=("#( ";;%/"1=("#576 7"%56%( .="#( .=6( 1%2.21"7( >"7$6( L277( 1%/88( .=6( 066;6%( "%6"[( .=6( L">6( 02%61.2/#( /F( .=6( L">68 76">2#5( .=6( 1="##67( L277( </%6( /%( 7688( .=6( 8"<6( "8( .=".( /F( .=6( 2#1/<2#5( L">68( 0$6( ./
1/<;6#8".2#5(%6F%"1.2/#"7(6FF61.8(/#(D/.=(8206(87/;68(_2#(1"86(/F("(%67".2>67&(#"%%/L(1="##67'
^25+(9+9+,a+(Y2#6"%(/%(L6"]7&(#/#T72#6"%(L">6(.=6/%&(1"#(D6($860(./(68.2<".6(.=686(6FF61.8(F/%
6"1=(;"%.21$7"%(1"86+
Crossing waves Reflecting waves
Waves refracting from channel
COAST
Channel
cr. angle
Wave breaking Offshore
currents
O*0(%/4;+;+! Q22-*1!#2!,--%-$!+$-+!I*&+00-'J!#0!6+.-!%$#%+(+1)#0
3.4 Slope instability
:=6(8206(87/;68(/F("(0%60560(;2.'(1="##67(/%(.%6#1=(8=/$70(%6<"2#(8."D76("F.6%(1/#8.%$1.2/#+
X"860( /#( %686"%1=( ".( E67F.( W&0%"$7218'( 2.( 28( 1/#17$060( .=".( .=%66( <61="#28<8( /F( 87/;6 2#8."D272.&(1"#(/11$%'(06;6#02#5(/#(7/1"7(1/#02.2/#8(_^25$%6(9+B+,aU
!" 87/;6(1/77";86'
!" 72O$6F"1.2/#("#0(8$116882>6(F7/L(87206'
!" D%6"1=2#5("#0(%6.%/5%6882>6(87/;6(6%/82/#
:=6(<"c2<$<(87/;6(28("(F$#1.2/#(/F(06;.=(/%(87/;6(=625=.'(5%"2#(82Z6("#0(06#82.&(/%(;/%/82.&
D$.("78/(./(/;6%".2/#"7("8;61.8(1/#16%#2#5(F/%(2#8."#16(.=6(0%6052#5("1.2>2.&+
C7/;6( 1/77";86( 1"#( /#7&( /11$%( ".( >6%&( 8.66;( 87/;68( _k,U)( ./( 9a+( Y2O$6F"1.2/#( 1"#( /11$%( 2#
7//867&(;"1]60(8"#0(7"&6%8(/#7&'("#0(<"&(%68$7.(2#("(2#8."#."#6/$8(<"88(F7/L(1%6".2#5(>6%&
56#.76(87/;68(_m(,U,*(./(,@a+(-F(8$FF2126#.(56/.61=#21"7(0"."("%6(">"27"D76'(.=6(%28](F/%(87/;6 2#8."D272.&(1"#(D6(1/<;$.60((_Q6/067F.'(,IIBa+(N6.%/5%6882>6(D%6"1=2#5(28(L677(]#/L#(2#(.=6 0%6052#5(;%"1.216'("8(<6#.2/#60(2#(%67".2/#(./(066;(8$1.2/#(0%6052#5'(D$.("8("(<61="#28<(/F
87/;6(2#8."D272.&(2#(06#867&(;"1]60(8"#0(2.(28(#/.(1/<</#7&(%61/5#2860(8/(F"%(_`"#(06#(X6%5 6.("7+'()**)a+
X%6"1=2#5("78/(/11$%8(".(0"<(D$%8.8(_gL2#;%/6F'( ,IIB'( E67F.( V#2>6%82.&( /F(:61=#/7/5&a'("
%686"%1=(;%/5%"<(28(1"%%260(/$.(/#(.=28(./;21("7%6"0&'(D$.(.=6(D%6"1=2#5(<61="#28<(="8(D66#
2#1/%;/%".60(%616#.7&(2#(/%06%(./(2<;%/>6(</0678(_E67F.(W&0%"$7218'()***Da+
X%6"1=68( $#06%( L".6%( ;%/0$16( "( O$"82T8.6"0&( .$%D202.&( 1$%%6#.'( .=".( <"&( D6( .=6( /%252#( /F
<"882>6( 8"#08( 06;/82.60( 2#( 1="##678( "#0( 2#( 8/<6( 066;( <"%2#6( 6#>2%/#<6#.8'( 8/<6.2<68 />6%( </%6( .="#( 9( ]<+( ( ?="%"1.6%28.21( ;%/F276( 2#( .=6( 1"86( /F( D%6"1=2#5( 28( "( 8.66;( ./;( "#0 8$116882>6(56#.76%(87/;68(061%6"82#5(L2.=(87/;6(=625=.+
N28]( /#( 87/;6( 2#8."D272.&( "#0( 87/;6( 06>67/;<6#.( 0$6( ./( D%6"1=2#5'( L=21=( <"&( D6( /F 2<;/%."#16(F/%(<2#2#5( /F(8"#0(2#(066;( ;2.8'( 1"#( D6( 82<$7".60( L2.=( "( ,E( 8.".2/#"%&( </067 _4"8.D6%56#(6#(`"#(06#(X6%5'()**)a+
C$<<"%282#5'(2.(1"#(D6(1/#17$060(.=".(8206(87/;6(2#8."D272.&(06;6#08(/#U(_2a(0%6052#5(<6.=/0
";;7260'(_22a(6c1">".2/#(06;.=("#0(_222a(8602<6#.(;%/;6%.268(/F(.=6(066;6%(7"&6%8+
Bed profile before collapse
Bed profile after collapse
Retrogressive erosion length L
Gradual slope retreat Water surface
Channel
Water surface
Channel
Instantaneous mass slide due to liquefaction
O*0(%/4;+?+! <'#%-!2+)'5$-!/-*&+0)8/8 3#%4 <'#%-!*#''+%8-
"),,'-4 <'#%-!A$-+*&)0(!+0,!$-1$#($-88).-!-$#8)#0 :#11#/4 <'#%-!')B5-2+*1)#0!+0,!/+88!8'),-
