Shallow water hydraulics

Flood Modeller 2D solver, and many other models of its type, represent shallow water hydraulics. These can be described by the shallow water equations:

u and v - two components of the horizontal velocity

h - flow depth

z - bed elevation

x and y - horizontal distances in the x and y directions

t - time

g - acceleration due to gravity

n - Manning's coefficient of roughness

ν - the kinematic eddy viscosity used to parameterise horizontal turbulent momentum transport, with a value between 0 and 1. The default value in the interface for this parameter is zero, meaning that viscosity is excluded from the Shallow Water equations. This can improve model run times, but a better solution would be obtained using a value of 0.15 or higher (can be much higher for open sea).

These equations describe the motion of water in terms of a depth-averaged 2D velocity and the water depth, in response to the forces of gravity and friction. These equations typically represent situations where flow is approximately horizontal, is uniform with depth, and where vertical accelerations are small. The velocity components represent the water velocity averaged:

• Over the depth of the water column, ignoring variations in flow direction and magnitude with depth

• Over time, ignoring short-term turbulent velocity variations

One important property of shallow water flows is the different behaviours of subcritical and supercritical flows. Supercritical flows have a tendency to develop jumps (sudden changes in velocity and water level), which are difficult to represent in the model without causing instability. The difficulty of modelling these jumps is the reason 2D solver has the TVD solver as well as the more commonly used ADI solver (described in the following sections).