STATISTICAL SAND WAVE DYNAMICS IN ONE-DIRECTIONAL WATER FLOWS

Moving sand waves and the overlying tubulent flow were measured on the Wilga River in Poland, and the Tirnava Mica and Buzau Rivers in Roman ia. Bottom elevations and how velocities were measured at six points s imultaneously by multi-channel measuring systems. From these data, the linear and two-dimensional sections of the three-dimensional correlat ion and structure functions and various projections of sand wave three -dimensional spectra were investigated. It was found that the longitud inal wavenumber spectra of the sand waves in the region of large waven umbers followed Hino's -3 law (S(K-x) proportional to K-x(-3)) quite s atisfactorily, confirming the theoretical predictions of Hino (1968) a nd Jain & Kennedy (1974). However, in contrast to Hino (1968), the san d wave frequency spectrum in the high-frequency region was approximate d by a power function with the exponent -2, while in the lower-frequen cy region this exponent is close to -3. A dispersion relation for sand waves has been investigated from analysis of structure functions, fre quency spectra and the cross-correlation functions method. For wavelen gths less than 0.15-0.25 of the flow depth, their propagation velocity C is inversely proportional to the wavelength lambda. When the wavele ngths of spectral components are as large as 3-4 times the flow depth, no dispersion occurs. These results proved to be in good qualitative agreement with the theoretical dispersion relation derived from the po tential-flow-based analytical models (Kennedy 1969; Jain & Kennedy 197 4). We also present another, physically-based, explanation of this phe nomenon, introducing two types of sand movement in the form of sand wa ves. The first type (I) is for the region of large wavenumbers (small wavelengths) and the second one (II) is for the region of small wavenu mbers (large wavelengths). The small sand waves move due to the motion of individual sand particles (type I, C proportional to lambda(-1)) w hile larger sand waves propagate as a result of the motion of smaller waves on their upstream slopes (type II, C proportional to lambda(0)). Like the sand particles in the first type, these smaller waves redist ribute sand from upstream slopes to downstream ones. Both types result in sand wave movement downstream but with a different propagation vel ocity. The main characteristics of turbulence, as well as the quantita tive values characterizing the modulation of turbulence by sand waves, are also presented.