But "η" and "Φ" also have to satisfy the dynamic boundary condition, which results in non-trivial (non-zero) values for the wave amplitude "a" only if the linear dispersion relation is satisfied:  with tanh the hyperbolic tangent. So angular frequency "ω" and wavenumber "k" – or equivalently period "T" and wavelength "λ" – cannot be chosen independently, but are related. This means that wave propagation at a fluid surface is an eigenproblem. When "ω" and "k" satisfy the dispersion relation, the wave amplitude "a" can be chosen freely (but small enough for Airy wave theory to be a valid approximation). In the table below, several flow quantities and parameters according to Airy wave theory are given. The given quantities are for a bit more general situation as for the solution given above. Firstly, the waves may propagate in an arbitrary horizontal direction in the x = ("x","y") plane. The wavenumber vector is k, and is perpendicular to the cams of the wave crests. Secondly, allowance is made for a mean flow velocity U, in the horizontal direction and uniform over (independent of) depth "z". This introduces a Doppler shift in the dispersion relations. At an Earth-fixed location, the "observed angular frequency" (or "absolute angular frequency") is "ω". On the other hand, in a frame of reference moving with the mean velocity U (so the mean velocity as observed from this reference frame is zero), the angular frequency is different. It is called the "intrinsic angular frequency" (or "relative angular frequency"), denoted as "σ". So in pure wave motion, with U=0, both frequencies "ω" and "σ" are equal. The wave number "k" (and wavelength "λ") are independent of the frame of reference, and have no Doppler shift (for monochromatic waves). The table only gives the oscillatory parts of flow quantities – velocities, particle excursions and pressure – and not their mean value or drift. The oscillatory particle excursions ξ"x" and "ξ""z" are the time integrals of the oscillatory flow velocities u"x" and "u""z" respectively. Water depth is classified into three regimes:  In the limiting cases of deep and shallow water, simplifying approximations to the solution can be made.