Hydrodynamic analysis of fully developed turbidity currents over plane beds based on self‐preserving velocity and concentration distributions

Abstract

This paper presents a hydrodynamic analysis for the fully developed turbidity currents over a plane bed stemming from the classical three‐equation model (depth‐averaged fluid continuity, sediment continuity, and fluid momentum equations). The streamwise velocity and the concentration distributions preserve self‐similarity characteristics and are expressed as single functions of vertical distance over the turbidity current layer. Using the experimental data of turbidity and salinity currents, the undetermined coefficients and exponents are approximated. The proposed relationships for velocity and concentration distributions exhibit self‐preserving characteristics for turbidity currents. The depth‐averaged velocity, momentum, and energy coefficients are thus obtained using the proposed expression for velocity law. Also, from the expressions for velocity and concentration, the turbulent diffusivity and the Reynolds shear stress distributions are deduced with the aid of the diffusion equation of sediment concentration and the Boussinesq hypothesis. The generalized equation of unsteady nonuniform turbidity current is developed by using the velocity and concentration distributions in the moments of the integral scales over the turbidity current layer. Then, the equation is applied to analyze the gradually varied turbidity currents considering closure relationships for boundary interaction and shear velocity. The streamwise variations of current depth, velocity, concentration, reduced sediment flux, and Richardson number are presented. Further, the self‐accelerating and depositional characteristics of turbidity currents including the transitional feature from erosional to depositional modes are addressed. The effects of the streamwise bed slope are also accounted for in the mathematical derivations. The results obtained from the present model are compared with those from the classical model.

Destructiveness of pyroclastic surges controlled by turbulent fluctuations

“…2a ). This characteristic form of vertical velocity profiles is well-fitted by earlier empirical models developed for dilute turbidity currents 33 , 34 . Integrating these studies on particle-laden gravity currents with recent studies on volcanic plumes 35 , 36 , we here propose a continuous power-Gaussian mathematical form of the mean vertical velocity profile as where the dimensionless height , with being the height of the wall region where the velocity maximum occurs; is the wall layer exponent; is the jet region exponent; and where and are fitted variables.…”

“…2b ). In the jet region, the density profiles are well described by current empirical models developed for dilute gravity currents 34 . However, in the wall region, vertical density gradients are strongly enhanced due to the fast settling of mesoscale turbulent particle clusters 32 , 37 , 38 and neither instantaneous nor time-integrated concentration profiles are well described by existing empirical models 34 .…”

“…Equation ( 2 ) is a differentiable version of the profile proposed by ref. 34 who proposed a power law in the boundary layer and a Gaussian profile in the outer layer.

Fig.

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“…b typical example of the flow’s solid mass fraction as a function of height (solid blue line) at a given time at a static observer location of 3.12 m. The green line shows the fit to the measured data by the empirical model of ref. 34 developed for dilute turbidity currents, which is defined as , where is solid mass fraction, is non-dimensional height, and and are free fitting parameters. In the wall region, the empirical model deviates from the experimental data due to fast settling mesoscale turbulence clusters that occur in our experimental pyroclastic surges 11 , 28 , 32 , but not in dilute turbidity currents.…”

A theoretical framework and the experimental dataset for benchmarking numerical models of dilute pyroclastic density currents

“…We simplify both the temperature and mass fraction profiles by neglecting their temporal variability, and give their time-average profile. Data are fitted with the theoretical exponential profile proposed by Cantero-Chinchilla et al (2015) for 3) and the parameters reported in legend and in Tab. 6.…”