Turbidity Currents Comparing Theory and Observation in the Lab

PURPOSE OF ACTIVITY The goal of this exercise is to enable students to explore some of the controls on fluid flow by having them simulate turbidity currents using lock-gate exchange tanks while varying the bed slope and the turbidity. Observational data are compared with theoretical relationships known from the scientific literature. The exercise promotes collaborative/peer learning and critical thinking while using a physical model and analyzing results.


PURPOSE OF ACTIVITY
The goal of this exercise is to enable students to explore some of the controls on fluid flow by having them simulate turbidity currents using lock-gate exchange tanks while varying the bed slope and the turbidity.Observational data are compared with theoretical relationships known from the scientific literature.The exercise promotes collaborative/peer learning and critical thinking while using a physical model and analyzing results.

WHAT THE ACTIVITY ENTAILS
During two lab periods of two and half hours duration, students use a physical model to simulate turbidity currents flowing over differing bottom slopes.They are given a Plexiglas tank and gate, a wooden stand to change the bottom slope, a drill with a paint stirring attachment to generate turbulence, sediment, rulers, and other equipment as described below.They determine how much sediment to add to vary the density of the flow.The tank is filled with water of a known temperature (and thus known density and viscosity).The gate is inserted into the tank to provide a known volume of water in the lock behind the gate.While the drill is used to generate turbulence in the lock, a known mass of sand is poured into the lock.The lock gate and drill are then removed, allowing the simulated turbidity current to flow down the tank.Students use smart phones or cameras to videotape and record the duration of the flow during the simulation.They record data needed to characterize the flows using sediment transport and basic fluid dynamics equations, and they write group reports of their findings.The simulations are conducted during the first lab period.The group analyzes the data during the second lab period and outside of class.The instructor and the teaching assistant are available to support the group learning experience during the lab periods, providing assistance with the calculations and background on dimensional scaling.

Turbidity Currents
Comparing Theory and Observation in the Lab By Joseph D. Ortiz and Adiël A. Klompmaker

DIMENSIONAL SCALING AS A MEANS OF COMPARING FLUID FLOWS
We can employ dimensional scaling to compare the properties of various fluid flows.These provide a means of characterizing the flow from a theoretical standpoint.When the assumptions underlying these simple theories are met, the results match empirical observations.A current can pick up sediment off the bottom when the boundary shear stress (the force acting on the particle in the direction of the current) exceeds the drag on the particle.How the particle is transported depends on its density, size, and the properties of the fluid flow.Larger particles are transported as bed load, rolling or scraping along the bottom.Smaller, less dense particles saltate (bounce along the bottom), and finer grains are transported by suspension.The finest particles remain in suspension the longest and are referred to as the wash load.The Rouse number relates the settling velocity of the particle to the boundary shear stress to estimate the manner of transport.The Reynolds number, the Froude number, and the Richardson number define the characteristics of the fluid flow.The Reynolds number can be used to determine the relative importance of turbulence and laminar flow.The Froude number is used to determine if the flow is rapid or tranquil, and the Richardson number provides an estimate of the stability of the flow, which in this context relates to how effectively the turbulence can be damped by the flow.

BACKGROUND
Turbidity currents form one class of sediment gravity flows (e.g., Middleton, 1993).They are an important mechanism of sediment transport in fluid environments (lakes and the ocean) as they move coarse-grained material from the margins to the interiors of basins.The ocean's broad, flat abyssal plains are formed in part by the action of turbidity currents.Submarine canyons are carved by their repeated flow into the deep sea (Figure 1a).
Turbidity currents can be triggered by submarine failures such as a slumps and slides or by earthquakes or other disturbances such as storm-induced waves (e.g., Meiburg and Kneller, 2009).The supporting mechanism for the flow is turbulence.The current consists of sediment-laden, turbid water that travels downslope.As the sediment gravity flow accelerates downslope, it scours the bottom, entraining fluid from above and sediment from below.The flow consists of a well-defined head, body, and tail.
A turbidite deposit forms as the sediment drops out of suspension or bedload transport ceases.Turbidites are composite graded beds that include a variety of sedimentary structures related to differences in the flow regime (Pickering et al., 1986).Turbidites are capped by thin drapes of silt or clay.Coarse, proximal turbidites, which are deposited near the initiation points of turbidity currents, consist of thick beds of coarse-grained material over scoured bases.Intermediategrained, medial turbidites are often expressed in the classic Bouma sequence (Figure 1b), consisting of scoured bases and several graded crossbeds sandwiched between thick basal  sand and thinner silt or clay caps (Bouma, 1964;Bouma and Brouwer, 1964).Fine-grained, distal turbidite deposits exhibit smaller grain sizes and may lack high energy, cross-bedded features, making them difficult to differentiate from hemipelagic or pelagic sedimentation.
This laboratory exercise allows students to generate turbidity currents under controlled conditions using finegrained sediment to create the turbidity that drives the transport (Figure 2).This activity provides a more concrete connection to the actual sediment transport and deposition of the flows observed in nature than simulations using water of differing densities or colored with dye, or fluids of different densities or viscosities (such as milk) to generate the turbid flow.
We can measure the velocity of the flow empirically if we know the distance traveled per unit time: Considerable theoretical work has evaluated the factors that contribute to flow velocity (e.g., Middleton, 1993;Meiburg and Kneller, 2009;An, 2010).As the mass of sediment suspended in the flow increases, so does the density of the turbid flow relative to that of the ambient low-density water above it, and thus its velocity increases.We can estimate the flow velocity of the head using the theoretical relationship Notice that the flow velocity of the head is proportional to the density difference between the higher density, turbid, sediment-laden water in the flow (ρ t in kg/m 3 ) and the lower density, ambient water (ρ) multiplied by the acceleration of gravity (g in m/s 2 ) and the height of the turbidity current (h in m).Prior research indicates the Froude number for the flow (F r )-the ratio of inertial to gravitational forces acting on the flow-yields the proper coefficient of proportionality to relate the flow velocity to the density contrast (e.g., Kneller and Buckee, 2000).
The Froude number for a turbidity current is defined as where U head is the mean velocity of the turbid flow (in m s -1 ).When F r is greater than 1, the flow is rapid, while for values less than 1, the flow is tranquil.Studies suggest that appropriate Froude numbers for turbidity currents range between F r = 2 -1/2 to 1 for turbulent flow in deep water, while flows in finite water depth follow a relationship in which F r h/H, where h is the height of the turbulent flow, and H is the water depth (e.g., Middleton, 1993;Meiburg and Kneller, 2009).In addition to the Froude number, the properties of turbidity currents can be described using three additional dimensionless numbers, the Reynolds number, the Rouse number, and the Richardson number.
The Reynolds (R e ) is a dimensionless number, which relates the turbulent forces driving the flow (numerator term) to the dissipative, frictional forces that diminish it (denominator term).For R e greater than 2000, the flow is turbulent.For values less than 2000, the flow is laminar.The R e number is defined as where ρ t is the density of the turbid fluid (in kg/m 3 ), U head is the mean velocity of the head of the turbidity current (in m/s), h is the height of the turbidity current head, and µ is the dynamic (or molecular) viscosity of the water (in kg/ms), which depends on the temperature of the water.The viscosity and density of freshwater based on its temperature can be taken from a plot (Figure 3) or calculated from an  online form (http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop/airprop.html).Given a measure of the water temperature, the form can be used to look up the density and viscosity of the freshwater in the tank.To calculate the density of the turbid, sediment-laden water, students need to account for the mass and volume of sediment added to the freshwater, which increases the density of the turbid mixture.The Richardson number, which determines the stability of the flow, is defined as where C is the volume concentration of sediment in the flow (the ratio of the sediment volume to the volume of water in the lock), u * is the shear velocity of the flow (in m/s), and the other variables are as defined above.The shear velocity in this context is a measure of the rate of change of the velocity of the flow with distance from the bottom boundary, where friction causes the velocity to go to zero.This is the so-called "no slip" constraint.The shear velocity (u * ) is defined as in which τ is the bottom boundary shear stress, a measure of the force acting on the sediment particles; ρ t is the fluid density of the turbulent flow (in kg/m 3 ); μ is the dynamic viscosity of water (in kg/ms); and ∂u/∂z is the vertical velocity gradient, the rate of change of velocity with depth (in s -1 ).Without sophisticated equipment, measurements of ∂u/∂z and u * are difficult to quantify, but they can be measured with acceptable error.We can use the "no slip" assumption-which states that the velocity must be zero at the bottom boundary of the flow-in conjunction with the observed estimate of U to approximate ∂u.This will provide a crude, two-point estimate of the vertical velocity gradient from zero at the base of the flow to U, the observed mean velocity of the head.That provides the numerator, ∂u, for the vertical velocity gradient.We will have to make an estimate of the depth where the velocity profile reaches the mean flow value.We will assume that it is equal to the flow height as it rides up over the clear water in front of the turbidity current to estimate ∂z based on our observation of the height of the leading edge of the head of the turbidity current, which we define as z.Thus, we can estimate R i and plot R i vs. slope to see how they are related.With a description of the these flow characteristics, we also can determine the manner in which sediment is transported by the turbid flow using the Rouse number, which relates the settling velocity of a grain to the shear boundary stress acting on it.The Rouse number P is defined as where w s is the settling velocity of particles, κ is the von Kármán constant (generally taken as 0.41, see Gaudio et al., 2010) (Dade and Friend, 1998;Udo and Mano, 2011).
For the settling velocity (w s in m/s), we will use the Impact Law, defined as where C d , is a drag coefficient, ρ t is the density of the turbulent flow (in kg/m 3 ), ρ is the density of the fluid (in kg/m 3 ), g is the acceleration of gravity (in m/s 2 ), and d is the diameter of an average spherical sediment particle (in m).To estimate C d , we need to calculate a particle Reynolds number (Re p ) in which the density and length scale are based on the properties of the grain: We can then determine the drag coefficient C d for particles of specific shape from an empirical curve of Re p vs. C d .This poses an immediate problem, however, because we see from Equation 9 that the Re p itself depends on w s , but we need to know C d to determine w s using Equation 8.One solution to this problem is to iteratively solve for Re p by using initial estimates of C d and w s and then to replace values of C d and w s iteratively until the relationship converges on a solution with minimal errors in C d .For operational purposes, we will define the convergence as a <10 -4 difference in the initial and revised estimates of C d .Once students know C d and w s , they can determine the Rouse number using Equation 7 (see also Figure 4).

MATERIALS
• Turbidity current tank (1.20 m long, 0.30 m tall, and 0.12 m wide) • Gate (0.35 m tall by 0.12 m wide) • Grease pens or erasable whiteboard markers to mark the sides of the tanks • Stand to change the slope of the tank from 0° to 2°, 4°, and 6° • Sediment with a known size distribution (i.e., determined using sieve analysis or an automated tool, such as a Malvern Mastersizer 2000) • Scoop • Plastic bag to hold sediment while measuring mass • Drill equipped with a stirring apparatus to power the current • Rulers, protractors, and meter sticks • Scale • Buckets for sand and water • Thermometer • Stopwatch (or phone with timer function) • Still and video cameras

FIGURE 1 .
FIGURE 1.(a) Schematic of the marginal environment in marine and lacustrine settings where turbidity currents arise and turbidites are deposited (Source:Meiburg and Kneller, 2009).(b) Definition of the classic Bouma Sequence, one of several classification schemes that have been proposed for turbidite deposits.Note that proximal turbidites will exhibit coarser beds than distal turbidites, and not all beds in the Bouma sequence are present in all turbidite deposits (Source:Middleton, 1993). b

FIGURE 2 .
FIGURE 2. Lab handout documenting tank geometry and variables to measure.

FIGURE 4 .
FIGURE 4. (a) The relationship between w s and grain size under the Impact law with pure and turbid water and under Stokes law.(b) The relationship between the log 10 -transformed drag coefficient (C d ) and the log 10 -transformed particle Reynolds number (Re p ) plotted as blue-filled squares.The red-filled squares depict an approximation for the drag coefficient applicable for Stokes settling law, Re p ~ 24 /C d .The black curve provides a fourth-order, least-squares polynomial fit between the log-transformed C d and Re p data: y = -4.56x 10 -3 (x 4 ) + 4.24 x 10 -2 (x 3 ) + 2.59 x 10 -2 (x 2 ) -9.54 x 10 -1 (x) + 1.49.