- Linear wave calculations (wavenumber and orbital velocity)
- Particle settling velocity and critical shear stress
- Ripple height and wavelength (for wave-generated orbital and anorbital ripples)
- Wave-current boundary-layers (current shear velocity and apparent roughness, and total bed shear stress)
- Water properties (density, viscosity, heat capacity, freezing point, sound velocity)
- Wave height and period for fetch-limited, depth-limited waves.
- Wind stress from wind speed and elevation

This applet calculates angular wave frequency, wavenumber, and
near-bottom horizontal orbital velocity for monochromatic linear
gravity waves (c.f. Komar, 1976). The
wavenumber *k* = 2 pi/*L*, where *L* is wavelength, is
determined from the dispersion equation. Because *k* is implicit
in the dispersion equation, this is normally an iterative calculation
with asymptotic solutions for shallow and deepwater cases. This
applet uses the explicit approximation suggested by Hunt (1979), which (according to my limited
tests) is accurate to within about 0.2%.

This applet calculates particle settling velocities according to three standard equations: the Stokes settling equation (e.g., Neilsen 1992, p.165), the Gibbs equation (also in Neilsen, 1992, p. 165), and the empirical equation developed by Dietrich (1982), which incorporates values of the Powers roundness factor and the Corey shape factor. It also calculates critical shear stress for non-cohesive well-sorted particles using a non-dimensional Sheilds curve ( White, 1970; Gelfenbaum and Smith, 1986. Water properties must be specified in order to calculate water density and viscosity...these routines are the same as the ones in the water properties applet.

This program calculates equilibrium height, wavelength, and steepness of wave-formed ripples on a sandy bottom using the empirical formulations of Wiberg and Harris (1994). Required input is wave height, wave period, water depth, and sand grain diameter. Linear-wave calculations are used to calculate near-bottom orbital velocity and orbital diameter. The ripple geometries are valid only for sand-sized sediments (-1 to 4 phi; 2 to 0.0625 mm), and only when the critical shear stress has been exceeded, but the material is not in suspension. At this point the program does not check the transport criteria carefully...it only suggests that there may be no transport when orbital velocity is less than 0.13 cm/s.

This applet calculates properties of a neutrally stratified wave-current bottom boundary layer using the approach of Madsen (1994). In the absence of waves, the current profile near the bottom is generally logarithmic, taking the form:

*u = u*c/*kappa * ln( *z/zo* )

where
*u* is speed at elevation *z*, *u*c* is current shear
velocity, kappa is von Karmans constant (0.41) and *zo* is the
bottom roughness length. The effect of wave-induced turbulence (which
is confined to a thin sublayer within the current boundary layer) is
to increase coupling between the currents and the bottom. Assuming
that the current velocity at some reference elevation (usually 1 m
above the bed) is held constant, the effect of adding waves is to
increase drag, as evidenced by a larger "apparent" *zoa* (or,
equivalently, an enhanced bottom-drag coefficient *Cde*. The
shear in the current boundary layer is increased (higher *u*c*).
In addition, the calculations estimate the friction velocity
associated with the wave motion (*u*w*) and the maximum friction
velocity of the combined waves and currents *u*wc*. The
calculations presented here assume constant linear eddy viscosities
in the current and wave boundary layers, connected by a region of
uniform eddy viscosity. A critical assumption is that a single length
scale exists, and the solution is formally restricted to the range of
roughness indicated in Madsen's Eqn. 32 and 33. Watch for error
messages at the bottom of the output.

This applet implements Eqns. 3-39 and 3-40 from the *Shore Protection Manual*. Input is
the 10-m wind speed *u* [m s-1], the fetch *f* [km], and the
water depth *h* [m]. The applet adjusts wind speed to adjusted
wind speed *Ua* according to Eqn. 3-28a before being used. The
calculations assume a flat bottom with depth *h*. No checks are
made to ensure that reasonable values are entered or that the
calculations are within the applicable range.

- Compatibility - I wrote these in Java 1.0, and some of the code has been deprecated. My Java programming tools, which were never sharp, are now also rusty, but I may someday revamp these in a more modern version of Java.
- Formatting - As you can see, the formatting of numbers leaves something
to be desired. Java 1.0 had no standard formatting capabilities, and Java
1.1 had a very clunky one. The formatting varies with each browser. If I come
across a good implementation of
`printf`

or similar, I will use that. - Math Libraries - Java doesnt have hyperbolic functions or
`log10`

functions, so I pulled out my CRC Math Handbook and kludged some together. I am sure that approach will come back to haunt me later. Watch this space.

The applets in the **sedx** package have not been completely tested and
are not warranted in any way. Please do not use them for any application that
involves money, or the welfare of people, animals, or sediment particles.

Development of the **sedx** package was supported by the Division
of Marine Research, Commonwealth Scientific and Research Organisation (CSIRO)
in Hobart, Australia. Maintainence is now supported by the USGS, but any errors
are the sole responsibility of Chris Sherwood.

If you find errors, please sent email to csherwood@usgs.gov