“…For the updated wall‐bounded melt plume parameterization (panel (b)), we also use a smaller entrainment coefficient α = 0.068 (based on Parker et al. (2021)) and much larger consistent with wall‐bounded melt plumes, commonly‐used turbulent heat and salinity transfer constants of Γ T = 0.022 and Γ S = 6.2 × 10 −4 (based on Jenkins et al. (2010)), and the horizontal velocity using a value of 0.2 m/s from Jackson et al.…”
Section: Application Of Theory To Observations At Leconte Glacier Alaskamentioning
Buoyancy fluxes and submarine melt rates at vertical ice‐ocean interfaces are commonly parameterized using theories derived for unbounded free plumes. A Large Eddy Simulation is used to analyze the disparate dynamics of free plumes and wall‐bounded plumes; the distinctions between the two are supported by recent theoretical and experimental results. Modifications to parameterizations consistent with these simulations are tested and compared to results from numerical and laboratory experiments of meltwater plumes. These modifications include 50% weaker entrainment and a distinct plume‐driven friction velocity in the shear boundary layer up to 8 times greater than the externally‐driven friction velocity. Using these updated plume parameter modifications leads to 40 times the ambient melt rate predicted by commonly used parameterizations at vertical glacier faces, which is consistent with observed melt rates at LeConte Glacier, Alaska.
“…For the updated wall‐bounded melt plume parameterization (panel (b)), we also use a smaller entrainment coefficient α = 0.068 (based on Parker et al. (2021)) and much larger consistent with wall‐bounded melt plumes, commonly‐used turbulent heat and salinity transfer constants of Γ T = 0.022 and Γ S = 6.2 × 10 −4 (based on Jenkins et al. (2010)), and the horizontal velocity using a value of 0.2 m/s from Jackson et al.…”
Section: Application Of Theory To Observations At Leconte Glacier Alaskamentioning
Buoyancy fluxes and submarine melt rates at vertical ice‐ocean interfaces are commonly parameterized using theories derived for unbounded free plumes. A Large Eddy Simulation is used to analyze the disparate dynamics of free plumes and wall‐bounded plumes; the distinctions between the two are supported by recent theoretical and experimental results. Modifications to parameterizations consistent with these simulations are tested and compared to results from numerical and laboratory experiments of meltwater plumes. These modifications include 50% weaker entrainment and a distinct plume‐driven friction velocity in the shear boundary layer up to 8 times greater than the externally‐driven friction velocity. Using these updated plume parameter modifications leads to 40 times the ambient melt rate predicted by commonly used parameterizations at vertical glacier faces, which is consistent with observed melt rates at LeConte Glacier, Alaska.
“…While both and the vertical plume velocity are assumed to adopt ‘top-hat’ cross-stream profiles so that either quantity is uniform within a lateral boundary and zero outside, the interfaces at which they become zero are defined as and , respectively, where is a constant. Due to the wall-shear resistance, the value of is significantly below unity, see § 1 and the supporting data in Parker et al (2021). Figure 1.Schematic of a simultaneously entraining and detraining wall plume with top-hat cross-stream profiles in a stably stratified quiescent environment with natural, or buoyancy, frequency .…”
Section: Plume Model With Simultaneous Entrainment and Detrainmentmentioning
confidence: 54%
“… for line plumes (Paillat & Kaminski 2014). However, this ratio substantially drops to , as evaluated from figure 7 of Parker et al (2021), for a wall plume generated by a plane vertically distributed buoyancy source. Clearly, this reduced ratio of thicknesses is due to the wall-shear resistance which results in significantly flatter vertical velocity profiles relative to those of free plumes.…”
This article presents a theoretical modelling framework for the previously unconsidered case of turbulent wall plumes that detrain continually with height in stably stratified environments. Built upon the classic turbulent plume model, our approach incorporates turbulent detrainment with a variable coefficient of detrainment. Based on a linear constitutive relationship between the ratio of the detrainment to entrainment coefficients and the ambient buoyancy gradient, it is found that for linear ambient stratifications, a dynamic quasi-equilibrium region, characterised by a near invariant local plume Richardson number, is achieved, downstream of which this equilibrium rapidly breaks down. With increasing ambient buoyancy gradient, while the plume becomes increasingly slender with weaker vertical motions, the level at which the plume breaks down to form a horizontal intrusion first decreases and then increases. Moreover, distinct from classic purely entraining plumes, a detraining wall plume can swell within the pre-equilibrium adjustment stage provided the local Richardson number is sufficiently low
$({Ri\ll 6})$
, behaviour which is in accordance with observations made in filling-box experiments.
“…In Part 1 (Parker et al. 2021) of this work we considered a distributed wall-source plume in an unconfined environment by creating a uniform vertical wall source of buoyancy by forcing relatively dense salt water through a porous wall. Here we enclose the apparatus used in Part 1 and perform density measurements to investigate the resulting ambient buoyancy stratification that develops as a result of a distributed wall-source plume in both a confined unventilated environment and a confined ventilated environment.…”
Section: Introductionmentioning
confidence: 99%
“…The rate of descent of the first front must balance the plume volume flux entering the stratified region and the additional source volume flux within the stratified region, i.e. dh/dt = −(Q p + q(H − h))L −1 , where we assume that the plume width is much smaller than L. (Parker et al 2021) of this work we considered a distributed wall-source plume in an unconfined environment by creating a uniform vertical wall source of buoyancy by forcing relatively dense salt water through a porous wall. Here we enclose the apparatus used in Part 1 and perform density measurements to investigate the resulting ambient buoyancy stratification that develops as a result of a distributed wall-source plume in both a confined unventilated environment and a confined ventilated environment.…”
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