ANALYTICAL SOLUTION OF ONE-DIMENSIONAL BAY
FORCED BY SEA BREEZE
Nicholas C. Kraus1, M.ASCE, and Adele Militello2
ABSTRACT: This paper introduces a closed-form analytical solution of the
one-dimensional (1D), depth-averaged linearized momentum and continuity
equations that incorporates linear bottom friction and the non-linear wind
stress. The solution describes wind-forced motion in a 1D basin with
horizontal bottom as governed by water depth, basin length, bottom friction
coefficient, wind speed, and fundamental frequency of an oscillatory wind. The
solution displays in compact form general behavior and dependencies of the
physical processes, including generation of wind-induced harmonics of the
forcing motion, damping, and resonance. The solution can serve as a
benchmark test for numerical models of the shallow-water equations, as well as
provide estimates of wind-induced motion in enclosed water bodies.
The water of many bays, estuaries, harbors, lakes, and reservoirs is subjected to forcing
associated with a periodic or quasi-periodic wind. Such forcing can be the sea breeze,
which has solar diurnal periodicity, or the wind associated with passage of seasonal weather
fronts with periods typically varying between 3 and 5 days. The leading-order responses of
an enclosed body to a steady wind set-up, set-down, mean current, and recirculating
current are well known (e.g., Ippen and Harleman 1966). Lesser known are the
harmonics induced to the water body by a periodic wind. Militello and Kraus (2001)
classified these as forced harmonics for motion generated directly by the non-linear wind
stress W W (W = component of wind speed), in contrast to response harmonics generated
within the water body through interactions contained in the various other non-linear terms
in the equations of motion.
1) U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory,
3909 Halls Ferry Road, Vicksburg, MS 39180-6199. Nicholas.C.Kraus@erdc.usace.army.mil.
2) Coastal Analysis, LLC, 4886 Herron Road, Eureka, CA 95503. CoastalAnalysis@home.com.
Kraus & Militello