The bed forms generated by liquid flows over loose-grain boundaries assume only two orientations relative to flow, being either transverse or longitudinal, but range enormously in physical scale. Two types of bed form, current ripples and parting lineations, take a characteristic length (2) which is independent of boundary conditions as expressed by flow depth (d). We have that:

λL≤ 0.025 m (parting lineations)

λR≤ 0.60 m (ripples).

The characteristic length of other kinds of bed form is correlated with flow depth, according to the equations:

λD= 1.16D1.1.55 (dunes)

λA 6.3d (antidunes, Fr = 1.0)

λSR= 1.35d1.31 (sand ribbons)

λM - 672d1.11 (meander bars)

λT= 116d2 (tidal current ridges)

From these relationships can be deduced the compositions of theoretical hierarchies of bed forms, where a hierarchy is defined as a series of bed forms graded as to size which in combination are adapted to a single overall flow condition. The compositions of these hierarchies, which are closely matched by naturally occurring hierarchies, are broadly related to available flow depth, general flow conditions (lower or upper regime), and availability of sediment.

Bed forms are considered to be due to unstable interactions between the bed material and the over-bed flow, of liquid or grains or both.

Hierarchies of bed forms arise because the quantities determining the flow are suficiently numerous that several mutually unstable combinations can exist, each combination being expressed in terms of a bed form of a characteristic physical scale and orientation relative to flow.