CHAPTER 5 INTRODUCTION TO OCEANIC TURBIDITY CURRENTS 5.1 INTRODUCTION

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1 CHAPTER 5 INTRODCTION TO OCEANIC TRBIDITY CRRENTS 5.1 INTRODCTION Trbidity rrents are the ndersea eqivalents of sediment-laden river flows. They onsist of density-driven bottom rrents for whih the agent of the density differene is sediment. Trbidity rrents or in the oean and lakes. They an be sffiiently powerfl to erode spetalar sbmarine anyons. On lower slopes in the deep oean they are responsible for the deposition of hge sbmarine fans that are orsed by some of the largest meandering hannels in the world. Trbidity rrents, while very similar to sbaerial sediment-laden river flows, are different in one fndamental aspet. Even in the absene of sediment river flow ontines, bease gravity plls the water down the slope. In the ase of trbidity rrents in deep water, however, a hydrostati pressre distribtion with the absene of flow is maintained when sediment is not present. Gravity mst at on sspended sediment to pll it down the slope; it in trn drags the flid with it. In the absene of trblene, however, the sediment mst settle ot, bringing the flow to a halt. It will be seen that trbidity rrents have the apaity to self-aelerate or self-deelerate, a featre that is not seen in river flows. 5. GOVERNING EQATIONS A trbidity rrent is shematized in Figre 5.1. A formal derivation of the layeraveraged governing eqations an be fond in Parker et al. (1986). A brief smmary is given here. The trbidity rrent is assmed to onsist of a dilte sspension of sediment. It is taken to be a sstained event with a head, a long body and the tail. A two-dimensional trbidity rrent is onsidered here for simpliity. The streamwise oordinate x and the pward normal oordinate z are assmed to be bondary-attahed oordinates along the oean bed. The bed slope S is assmed to be small. The Bossinesq assmption is invoked for the eqations of momentm balane. The volme onentration of sspended sediment and streamwise flow veloity, bothaveraged over trblene, are taken to be fntions of x, z and t. Layer thikness H GP Letre Notes: Sediment Transport 39

2 of the nderflow along with layer-averaged onentration C and streamwise veloity are defined as H = CH = H = dz dz dz (5.1a,b,) Figre 5.1 Definition diagram for trbidity rrents. Approximate similarity is assmed in the veloity and onentration profiles; z ς = (3.) C H These are frther simplified sing the rde bt sefl top-hat assmption; 1 for ς 1 f = (3.3) for ς > 1 The governing eqations an then be simplified sing the bondary layer approximations and integrated to layer-averaged form sing the same methods as employed in Chapter 1. The reslting layer-averaged eqations an be written as follows. Water mass balane takes the form H + (H) = e t x w (3.4) GP Letre Notes: Sediment Transport 4

3 where e w is a dimensionless oeffiient of entrainment of ambient water from above. In general it is a fntion of the blk Rihardson nmber Ri b, defined as RgCH Ri b = (3.5) The vale Ri b = yields the highest vale of e w and orresponds to jet flow; for Ri b > 1 the flow beomes sbritial in the Rihardson sense and e w beomes very small. Sediment mass balane takes the form (CH) + (CH) = vs (E roc) t x (3.6) where E is again a dimensionless oeffiient of entrainment of bed sediment and b ro = (3.7) C Flow momentm balane takes the form (H) + t 1 ( H) = x x R g (CH ) + RgCHS Cf (3.8) Note that the driving term for the flow, RgCHS is linearly proportional to onentration, whereas the resistive term ontains an spproximately qadrati dependene on veloity. Likewise, in the eqation of sediment mass balane, the term E, whih being dependent on bondary shear stress τ b is in trn dependent on, adds sediment to the sspension as inreases. The term r o C orresponds to inreased settling, or loss of sediment from the rrent as C inreases. These terms allow for some fasinating interations that are best seen in the ontext of a simpler set of model eqations. The model eqations are written as C m = C t = C t (3.9a,b) The first of these eqations models sediment mass balane, with m modeling the entrainment of bed sediment into sspension and C modeling the settling of sspended sediment onto the bed. The seond of these eqations models flow momentm balane, GP Letre Notes: Sediment Transport 41

4 with C modeling the downstream pll of gravity on the sediment and the resistive fore of drag. The model eqations have a fixed point (, C) = (1, 1) orresponding to an eqilibrim flow similar to the normal state of open hannel flow. If m >, however, it is easily shown that this eqilibrim is nstable. nless initial onditions ( i, C i ) fall preisely at the fixed point, the flow eventally either aelerates or deelerates away from the fixed point. The proess is shematized in Figre 5., whih shows igniting (selfaelerating) and sbsiding (self-deelerating) fields and a onvergene line. Figre 5. Behavior of the model trbidity rrent. The essential featre of Figre 5. is a galloping instability. If the initial flow veloity and onentration are high enogh, the flow an entrain more sediment from the bed, making it heavier. This in trn inreases the downstream pll of gravity,, aelerating the flow. Aeleration and entrainment an feed into eah other leading to ever-swifter flow. On the other hand, if the initial vales of and C are too low sediment is lost, the pll of gravity dereases, more sediment is lost et. as the flow deelerates. While a fll modeling of the above phenomenon sing the governing eqations of trbidity rrents is rather more diffilt, the essential reslt remains nmodified. At high slopes it is fond that onditions for ignition are relatively easily obtained. At lower and lower slopes the sbsiding zone beomes larger and larger, ntil a slope is reahed at whih all trbidity rrents die ot. A sample phase diagram allated from the fll model of Fkshima et al. (1985) is shown in Figre 5.3. The simlation is for Sripps Sbmarine Canyon, a site where self- GP Letre Notes: Sediment Transport 4

5 aelerative trbidity rrents are known to or with some freqeny. The flow is assmed to be steady in time bt developing in the downslope diretion. The pstream vale of rrent thikness H is assmed to be 3 m, and C f is taken to be.4. In the plot and Ψ= CH denote pstream vales. The igniting and sbsiding fields are learly evident in the diagram. Figre 5.3 Phase diagram ompted for Sripps Sbmarine Canyon Analyses of the above type an explain the genesis of highly erosive trbidity rrents apable of exavating sbmarine anyons. As slope delines, they an explain the deposition of sbmarine fans. An extension of the above analysis to two dimensions an explain the maintenane of hannels demarated by high levees even in a prely depositional environment. GP Letre Notes: Sediment Transport 43