3
suspension concentration gradients on the turbulence structure, c) bed armoring,
d) bed-form generation and bottom stress partitioning, e) multiple grain sizes, f)
both suspended and bed load sediment transport, and g) fully coupled
morphological changes.
The M3D model resulting from the combined M2D and SLICE models
contains specialized methods and elements to provide accurate and efficient
numerical solutions. The two most characteristic features of M3D are a highly
refined mesh near the bed and the incorporation of surface wave properties in
the turbulence model.
This approach allows detailed and continuous
representation of currents and sediment transport through the near-bed wave-
current boundary layer. The M3D model resolves the horizontal and vertical
directions and is based on a numerical solution to the Reynolds-Averaged
Navier-Stokes equations (RANS) with the shallow water assumptions (i.e.
hydrostatic pressure). The basic hydrodynamic equations solved are, in
standard notation:
∂u ∂u 2 ∂uv ∂uw 1 ∂p ∂
∂u ∂
∂u ∂
∂u
+
+
+
+
=
+
+ Kz
+ fv
(1)
Kx
Ky
ρ ∂x ∂x
∂t
∂x
∂x
∂z
∂x ∂y
∂y ∂z
∂z
∂v ∂uv ∂v 2 ∂vw 1 ∂p
∂v ∂
∂v
∂v ∂
∂
- fu
+
+
=
+
+
+
+
(2)
Kz
Ky
Kx
ρ ∂y ∂x
∂y ∂z
∂z
∂x ∂y
∂z
∂y
∂x
∂t
∂p
∂u ∂v ∂w
= - ρg
+ +
=0,
(3)
∂z
∂x ∂y ∂z
Turbulence processes are described by a k - l turbulence closure scheme.
The k - l model is based on a differential equation for the turbulent kinetic
energy k and an algebraic description of the turbulent length scale l . The
turbulence model is coupled to the sediment transport model to represent density
stabilization of turbulence mixing due to variation in the vertical density field
(salinity or suspended sediment).
The transport model (sediment, salinity or any other scalar transport) is
based on the basic time-dependent scalar transport equation (conservation of
mass, advection, and diffusion) with enhancements to represent sediment
settling, erosion and deposition. Erosion is determined as a function of the
hydrodynamic stress at the bed. The calculated hydrodynamic stress is based on
the total bed roughness, which may include the effects of ripples and other
bedforms. A separate module predicts the bedforms based on wave and current
conditions. If bedforms are present, the hydrodynamic bed stress is partitioned
Previous Page
