= Solution
The constant $f=2\Omega\sin\varphi$ is the positive <Coriolis parameter> at northern latitude $\varphi$, $g$ is the <gravitational acceleration>, and $h$ is the undisturbed mean depth of the layer.
The <linearized shallow water equations> assume a homogeneous, incompressible, inviscid layer over a flat bed; a horizontal scale much larger than the depth, so the <shallow-water approximation> and <hydrostatic approximation> apply; depth-independent horizontal velocity; a free-surface displacement $|\eta|\ll h$ and sufficiently small velocity to neglect nonlinear products; and an <f-plane> on which $f$ is constant. The equations also omit viscosity, forcing, and bottom topography.
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