Forced plumes

Abstract

This paper describes an investigation of the turbulent forced plumes generated by steady release of mass, momentum and buoyancy from a source situated in an extensive region of uniform or stably stratified fluid. The treatment, which is an extension of earlier work on buoyant plumes, also brings out the relationship between the jet and the Plume as special cases of forced plumes.The analysis shows that the behaviour of a forced plume from a source of finite size which delivers buoyancy, mass and momentum can in a uniform environment be related to that from a virtual point source of buoyancy and momentum only, and a treatment is given for the latter type of forced plume. When the environment is weakly stratified it is inferred that forced plumes can be related to point definitely; but when the environment is stably stratified, increasing the release of mass and momentum from a given source of buoyancy has the effect at first of reducing the total height of the plume, and only for very large flux of momentum does the height increase again, without limit. A description is given for the behaviour of vertical jets in a stably stratified environment, and for forced plumes of fluid with negative buoyancy.

Generalised unsteady plume theory

“…For further details regarding the physical interpretation of the first three terms on the right-hand side of (2.21), the reader is referred to Craske & van Reeuwijk (2015a), as they also appear in the equations describing an unsteady jet. The final contribution in (2.21) is only found in plumes and is proportional to the flux-balance parameter Γ of Morton (1959). If θ m > 1, the buoyancy provides slightly more forcing in the energy equation (2.10) than one would expect from identically distributed b and w. Noting that the area Q 2 /M is inversely proportional to the momentum flux M, the effect of θ m > 1 is to reduce the entrainment coefficient.…”

“…Due to the fact that F s = θ g F/θ m , (2.22) can also be expressed in terms of the mean buoyancy flux F. Noting that the use of the total source buoyancy flux F s , rather than the effective source buoyancy flux F E , would lead to an over-estimation of Q and M, the solutions (2.22) might be useful to experimentalists who wish to compare data to theory using a known source buoyancy flux F s . Comparison of the system (2.22) to the classical plume solutions of Morton et al (1956) shows that the flux-balance parameter of Morton (1959) is 25) which characterises the relative importance of buoyancy compared with inertia in the flow. When 0 < Γ < 1, the plume is dominated by inertia and referred to as being 'forced'; when 1 < Γ the plume is dominated by buoyancy and is referred to as being 'lazy'.…”

Particle recycling and oscillations of volcanic eruption columns

“…Finally, in section 6, we discuss the implications of these results in the context of eruption columns. We adopt the top-hat model [Morton, 1959] We make the Boussinesq approximation and use the entrainment hypothesis that the uprising buoyant plume entrains ambient fluid at the radial speed ue(z) = •w(z) across the outer surface r = b(z) [Morton et al, 1956;Turner, 1986]. We assume that for buoyant plumes with low particle concentration the presence of the particles does not affect the nature of the turbulence and that we may use the standard assumption that the entrainment parameter • is a constant; as we describe later in the paper, this simplification is borne out by our experimental results.…”

A simple integral model of buoyancy‐generating plumes and its application to volcanic eruption columns

“…Thermal expansion of entrained air increases the buoyancy flux to change its value to positive at the upper part. This indicates that eruption columns should be classified as the flow illustrated in Figure 1b rather than a forced plume, which was proposed by Morton [1959] to describe a flow that includes a transition from a turbulent jet to a turbulent plume with a constant buoyancy flux. If this is true, the terminal height of an eruption column would be a function of the volume expansion, as derived in equation (27).…”

“…[27] As discussed by Morton [1959], the transition from a turbulent jet to a turbulent plume with a constant buoyancy flux occurs over a length scale of…”