Laminar and Turbulent Flow

Fluids in motion display two fundamentally different modes of flow depending upon the flow velocity, fluid viscosity, and roughness of the bed over which flow takes place. ^[1] These two modes are laminar flow and turbulent flow, and distinguishing them is essential for understanding how sediment is eroded, transported, and deposited. Most natural fluid flows are turbulent, but the distinction matters because laminar and turbulent flow behave very differently in their interaction with a sediment bed.

Laminar Flow

In laminar flow, a thin stream of dye injected into a slowly moving, unidirectional fluid persists as a straight, coherent stream of nearly constant width. ^[1] Laminar flow can be visualised as a series of parallel sheets or filaments called streamlines, in which movement occurs on a molecular scale owing to constant vibration and translation of the fluid molecules. ^[1] The streamlines may curve over an object, but they never intertwine. ^[1]

Laminar flow takes place only at very low fluid velocities over smooth beds. ^[1] This restriction to low velocities and smooth surfaces means laminar flow is the exception rather than the rule in natural environments. Most natural rivers, ocean currents, and wind flows move fast enough and over rough enough surfaces to be turbulent. Laminar flow of geological significance is largely confined to the slow creep of ice within glaciers and to the flow of extremely viscous debris.

Turbulent Flow

If flow velocity increases or viscosity of the fluid decreases, the dye stream is no longer maintained as a coherent stream but breaks up and becomes highly distorted. ^[1] It moves as a series of constantly changing and deforming masses in which there is sizable transport of fluid perpendicular to the mean direction of flow - the streamlines are intertwined in a very complicated way. ^[1] This type of flow is called turbulent flow because of the transverse movement of these masses of fluid. ^[1]

Turbulence is thus an irregular or random component of fluid motion. ^[1] Highly turbulent water masses are referred to as eddies. ^[1] Most flow of water and air under natural conditions is turbulent, although flow of ice and mud flows are essentially laminar. ^[1]

This pervasive turbulence in natural systems has a direct consequence for sediment transport: the random upward and downward components of fluid velocity that turbulence generates are capable of lifting particles off the bed and keeping them in suspension. Without turbulence, particles in a current would settle immediately at their Stokes settling velocity; turbulence allows particles far heavier than that settling rate would suggest to be carried in suspension for long distances.

Turbulence and Settling Velocity

The upward motion of water particles in turbulent water masses slows the fall rate of settling particles and decreases their settling velocity. ^[1] Fluid turbulence also tends to increase the effectiveness of fluid masses in eroding and entraining particles from a sediment bed. ^[1] These two effects - slower settling and greater erosion - make turbulence central to all aspects of the sediment transport budget.

Velocity in Turbulent vs. Laminar Flow

Velocity measured over a period of time at a particular point in a laminar flow is constant. ^[1] By contrast, velocity measured at a point in turbulent flow tends toward an average value when measured over a long period of time, but it varies from instant to instant about this average value. ^[1] This instantaneous variability is the signature of turbulence and is also why turbulent flow transports sediment more effectively: the instantaneous peaks in velocity and shear stress periodically exceed the threshold needed to lift and move particles, even when the time-averaged flow would not.

Turbulent flow resists distortion to a much greater degree than does laminar flow, so a fluid undergoing turbulent flow appears to have a higher viscosity than the same fluid undergoing laminar flow. ^[1]

Eddy Viscosity

This apparent increased viscosity in turbulent flow is called eddy viscosity, which varies with the character of the turbulence and results from turbulent momentum. ^[1] Eddy viscosity is commonly several orders of magnitude higher than dynamic viscosity. ^[1] This is why turbulent flows behave so differently from laminar flows at similar velocities - the effective resistance to shear is orders of magnitude larger, which alters the entire velocity profile within the flow.

Velocity Profiles

Because of the greater shear stress required to maintain a particular velocity gradient in turbulent flow, turbulent flow-velocity profiles have different shapes than laminar flow-velocity profiles. ^[1] Under conditions of turbulent flow, laminar or near-laminar flow occurs only very near the bed. ^[1]

For smooth beds, there is a thin layer close to the bed boundary where molecular viscous forces dominate - molecular adhesion causes the fluid immediately at the boundary to remain stationary, and successive overlying layers slide relative to those beneath at a rate dependent upon fluid viscosity. ^[1] This thin near-bed zone, called the viscous sublayer or laminar sublayer, is technically not truly laminar - it is characterised by streaks of faster and slower moving fluid - but viscous forces dominate within it.

The shape of the turbulent velocity profile above the viscous sublayer is determined by time-averaged values of velocity and depends upon the nature of the bed over which the flow takes place. ^[1] A turbulent velocity profile is more blunt near the bed and more uniform in the upper part of the flow compared to the linear gradient of a laminar profile - a distinction that has important consequences for predicting sediment transport rates at different heights above the bed.

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