In warm climates in particular, sea breeze can induce substantial diurnal motion in

water bodies. Because wind forcing is a quadratic function of its speed, response

the fundamental forcing frequency (Zetler 1971). Nonlinear interactions within the water

body also transfer energy into harmonic frequencies, as shown in numerous studies of tidal

motion. In two-dimensional, depth-averaged horizontal flow, the quadratic bottom stress,

advection, and nonlinear continuity terms generate response harmonics because they are

nonlinear with respect to the current velocity, water-surface elevation, or both.

A central consideration in understanding wind-induced water motion and its harmonics

is that a water body is locally forced over its entire surface. In contrast, the tide must

propagate from a connection to the ocean and is damped by friction as it traverses the bay

or estuary. Thus, a distinction between wind and tide is that wind is a *local *forcing whereas

the tide is a *boundary *forcing. The relative strength of terms in the equations of motion is,

therefore, different.

The sea breeze fluctuates with a frequency of 1 cpd (cycle per day) that is close to

frequencies of the diurnal tidal constituents (K1 O1, S1, and others). Similarly, higher

harmonics of the water motion induced by sea breeze (wind harmonics) lie at frequencies

near the higher harmonics of the diurnal tidal frequencies. Thus, wind harmonics can be

obscured by tidal motion and not easily detected. Conversely, tidal constituents must be

calculated carefully if wind harmonics are present because they introduce similar motion

not of gravitational origin. In embayments where the tidal amplitude is small, the sea

breeze can contribute significantly to the diurnal variance of the water surface and current.

This situation is common along the coast of Texas, where the strong predominant southeast

wind and sea breeze can dominate the tide in producing setup and setdown in its numerous

shallow estuaries and bays (Collier and Hedgpeth 1950). Militello (2000) and Militello and

Kraus (2001) examined sea-breeze-induced motion at Baffin Bay, Texas, a large, non-tidal

water body. Kraus and Militello (1999) document along-axis oscillations in water level

exceeding 0.6 m in response to periodic fronts passing East Matagorda Bay, Texas.

This paper introduces a new 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 analytic solution describes

linearized 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

the oscillatory wind.

For focus of discussion and development of the analytic solution, a spatially uniform

oscillatory wind blowing parallel to the *x*-axis is specified. The wind speed is then given as

(1)

where *w*0 = speed of the steady wind, *w *= amplitude of the oscillatory wind, and σ =2π/*T *,

in which *T *= period of the oscillatory wind. A sinusoidal representation for the wind with

2

Kraus & Militello