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In this study, the mechanism of sand wave formation is investigated based on inspecting the timevariation of wave number spectra of bed surface. There are three processes in spectral evolution ofsand waves; (1) variance production process based on random repetitions of dislodgement and deposi-tion of bed particles, (2) amplification of favorable wave number range spectra based on bed instabilitymechanism, and (3) variance cascade process based on the phenomenon that individual sand waves areunified on overtaking each other. Particularly, the latter two subprocesses are significant for formingthe characteristics of sand wave spectra, and they are minutely inspected. Furthermore, someexperiments in a rectangular closed conduit are conducted in addition to those in an open channelfor inspections of the mechanism of spectral evolution of sand waves.

In this paper we propose a new evaluation method for the bursting period, on the basis of the phenomenological consideration that the number of the occurrences of interaction-like motions should be removed from those of the ejection or the sweep events in the sorted Reynolds-stress fluctuating signals. Then, it is confirmed by this method that the mean bursting period in open-channel flows may be universally expressed by outer rather than inner parameters, and that its probability distribution becomes log-normal, irrespective of the Reynolds and the Froude numbers, as well as the wall roughness. Next, in order to explain even quantitatively the bursting process or the turbulent structure in the wall region, we propose a simple mathematical model on the basis of the Einstein-Li model and also the knowledge of the bursting-period characteristics obtained above. Though the present model is inherently quasi-two-dimensional and quasi-linear, this model can describe fairly well some distributions of mean-velocity, turbulence intensities and Reynolds stress. In particular, it can satisfactorily explain a sequence of the bursting process.

Many river engineers have hitherto suggested that there might exist cellular secondarycurrents in a straight river which had a pair of counter-rotating streamwise vortices with avortex diameter of about the flow depth. These cellular secondary currents create variousbed configurations such as sand ribbons which are alternating ridges and broad hollows andaligned parallel to the mean flow. Also, they may cause the three-dimensional flow patternsand sediment transportation in an actual river. However, the origin of the cellular secondarycurrent and its physical mechanism are quite unknown at present.In order to reveal the characteristics of the secondary currents and also their interrelationto the bursting phenomena occurring originally in the wall region, the present study hasexamined the turbulent structures in air duct flows with and without the cellular secondarycurrents. Considering that it was very difficult to measure precisely the secondary currentsin water flow because they were only a few percentage of the main flow, they could bemeasured by hot-wire anemomaters in two-dimensional air duct flow which correspondedsimilarly to open-channel flow. By systematically varying the bed configurations in whichthe longitudinal and alternate stripes of smooth and rough beds were set spanwisely, thegeneration and maintenance mechanism of the secondary currents were investigated.As the result, the strongest secondary currents were created when the width of the stripeswas equal to half of the width of the duct which corresponded to the flow deth in open-channel.The effects of the secondary currents on the mean velocity, turbulence intensities andReynolds stress were examined in detail, and then they could be explained well theoreticallyby means of (1) equation of motion, (2) equation of vorticity and (3) equation of turbulentenergy.Next, the effect of the secondary current on the bursting motion was examined by usingthe pattern-recognition method. Although the relative intensity of sweep to ejection motionswas affected by the secondary current, the bursting period was not varied. So, it issuggested that the bursting and cellular secondary current are phenomena different fromeach other and both of them coexist self-consistently.