Information about the Vertical Velocity Profile

Information about the Vertical Velocity Profile

This applet displays a vertical and logarithmical profile of current velocity in an infinitely wide channel. A watercolumn is divided into several horizontal layers. The applet calculates for each layer a horizontal velocity v which is a function of z, the height of each layer relative to the bottom.

Input measures

Bottom Gradient and Water Depth do not need any explanation.

• The Strickler Value defines the bottom shear stress. A higher value stands for a lower stress.

Examples:

sand (Elbe and Weser Estuary): approx. 48 m**(1/3) s**(-1/2)

wild creek with rubble: approx. 20 m**(1/3) s**(-1/2)

• deltaZ: The watercolumn is divided into several horizontal layers. The user specifies the vertical distance between neighboured layers via the input field deltaZ. For a correct graphical display deltaZ should be smaller than the Log Law's Z0 value.

Output measures

• In this model there is a layer directly above the bottom where the velocity is zero. Log Law's Z0 is the height of this layer. Log Law's Z0 depends on Water Depth and Strickler Value.
• V(H) shows the velocity at the water surface.
• V DepthAveraged stands for the depth-averaged velocity. The calculation of the average includes the layers with v=0 m/s as well as the layers with v>0 m/s. The calculation is more accurate by using smaller values of deltaZ.
• The result field at the lower right corner of the applet displays a line with pairs (velocity v and height relative to the bottom z)

Physics

Calculation of the horizontal velocity v

v = sqrt(g * WaterDepth * BottomGradient) / Kappa * ln(z/z0)

g = 9.81 m/s: gravity Kappa = 0.41: Karman constant z0 : zero Level of the logarithmic law with

z0 = (12./30.*WaterDepth) / 10**(StricklerValue * WaterDepth**(1/6) / 18))

The user should consider that this profile is only an approximation. Especially near the bottom the formula simplifies a little bit.