Do hyperpycnal-plume deposits record river-flood dynamics?

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Aldous Hawkins
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1 GSA DATA REPOSITORY Do hyerycnl-lume eosits recor river-floo ynmics? Michel P. Lmb * Dvi Mohrig Jckson School of Geosciences niversity of Texs 1 niversity Sttion C1100 Austin Texs SA *Now t Division of Geologicl n Plnetry Sciences Cliforni Institute of Technology MC E. Cliforni Blv. Psen CA 9115 SA MODEL DEVELOPMENT Grully Vrie Flow strem of the lunge oint flow is moele using the bckwter eution (Henerson 1966) h x Sb CfF 1 F (1) where h is the flow eth x is the istnce from the shoreline S b is the besloe C f is friction fctor n F is the Froue number F. () 3 gh The ischrge of wter er unit with is given by h (3) where is the eth verge velocity. Eutions (1-3) re solve for subcriticl inlet flow (F < 1) subject to bounry conition n n inut fluvil ischrge ( 0 ) using numericl finite-ifference scheme. The bounry conition is foun by setting the wter surfce elevtion to men se level t the ownstrem limit of the moeling omin (x 100 km). The coefficient of friction is set to 10-3 (Prker 1991). Becuse we neglect 1

2 erosion n eosition the eth verge seiment concentrtion in the fluvil zone is eul to tht secifie t the inlet ( c 0 ). Plunging lume The conition for lunging is function of the ensimetric Froue number (F ) (Akiym n Stefn 1984; Prker n Toniolo 007) where F (4) 3 gh n is the ensity excess of the current bove the mbient flui ensity. For the cse of fresh turbi lume entering sline ocen where w(1 Rc) 1 (5) w is the ensity of fresh wter R is the submerge secific ensity of seiment s w ( R n s is the ensity of seiment) n c is the eth verge volumetric w concentrtion of seiment. Prker n Toniolo (007) showe tht the ensimetric Froue number t the lunge oint (F ) n the ensimetric Froue number of the turbiity current just ownstrem of lunging (F ) re function only of coefficient of mixing 1 (6) where is the ischrge just ownstrem of lunging (x = x ) n is the ischrge t the lunge oint (x = x ). Flume exeriments hve shown tht 0.17 (Lee n Yu

3 1997). sing this vlue the moel of Prker n Toniolo (008) inictes tht F = 0.5 F = 1.0 n the rtio of the ownstrem flow thickness to tht t the lunge oint is h / h = Thus the lume is execte to occuy the entire wter column until the ensitmetric Froue number ros below bout 0.5. At this oint the wter column collses to flow eth bout three urters s thick n to ensimetric Froune number ner criticl (F = 1). sing these vlues the inut seiment concentrtion ( c 0 ) n ischrge from the ivergence zone ( 0 ) eutions (3-6) cn be solve for the flow eth eth verge velocity n eth verge seiment concentrtion t the lunge oint ( h c c 0 ) n ownstrem of the collse ( h c ). From continuity c c /( 1 ). The istnce over which lunging occurs hs been shown to scle with the lunge eth ( L A1 h ) where A 10 (Lee n Yu 1997). For simlicity we ssume tht the flow 1 eth n flow velocity chnge linerly between x n x. Turbiity current zone lunging ( h The vlues of flow eth velocity n seiment concentrtion ownstrem of c ) shoul serve s the bounry conitions for turbiity current moel to route flow n seiment further sewr (Prker 198). Becuse our emhsis is on the trnsitionl bckwter eth-limite n lunging regions we ssume stey n uniform flow in the turbiity current zone for simlicity. Thus conservtion of mss n momentum for the turbiity current yiels h = h = n c = c. 3

4 STEADY STATE APPROXIMATION ner most conitions it is resonble to ssume tht the stey stte rofiles clculte herein cn reresent ifferent time erios uring single floo event. This is becuse the timescle ( t ) for the lunge oint to move in resonse to chnge in ischrge or seiment concentrtion is smll comre to the tyicl urtion of floo event. For exmle the time for the lunge oint to move istnce shoul be inversely roortionl to the flow velocity t the lunge oint so tht t / h. For the rofiles T1-T4 shown in Fig. 3 ~ 10 km n / h ~ 1 m/s. Thus t ~ 10 4 s or bout.8 hours which is smll comre the urtion of river floos which cn lst for ys or longer. VELOCITY-DISCHARGE SCALING h In the norml flow zone = 0 n therefore eutions (1) n () cn be x reuce to gs C f 1/ 3 illustrting tht velocity is execte to scle with ischrge to the one-thir ower. At the shoreline flow velocity scles with ischrge nerly linerly becuse / hs n h s is only wekly eenent on ischrge. In the turbiity current zone the velocity scles with ischrge n seiment concentrtion to the one-thir ower becuse rerrnging eution (4) results in scles linerly with c 0 (eution 5). ( 1 ) F g0 1/ 3 n 4

5 REFERENCES CITED Akiym J. n Stefn H.G Plunging Flow into Reservoir - Theory: Journl of Hyrulic Engineering v Henerson F.M Oen Chnnel Flow: New York Mcmilln 5. Lee H.Y. n Yu W.S Exerimentl stuy of reservoir turbiity current: Journl of Hyrulic Engineering v Prker G. 198 Conitions for the ctstrohiclly erosive turbiity currents: Mrine Geology v Selective sorting n brsion of river grvel. II: Alictions: Journl of Hyrulic Engineering v Prker G. n Toniolo H. 007 Note on the nlysis of lunging of ensity flows: Journl of Hyrulic Engineering-Asce v DOI: /(ASCE) (007)133:6(690). 5

Submitted to the Journal of Hydraulic Engineering, ASCE, January, 2006 NOTE ON THE ANALYSIS OF PLUNGING OF DENSITY FLOWS

Submitted to the Journal of Hydraulic Engineering, ASCE, January, 2006 NOTE ON THE ANALYSIS OF PLUNGING OF DENSITY FLOWS Submitte to the Journal of Hyraulic Engineering, ASCE, January, 006 NOTE ON THE ANALYSIS OF PLUNGING OF DENSITY FLOWS Gary Parker 1, Member, ASCE an Horacio Toniolo ABSTRACT This note is evote to the correction