Internal hydraulic jumps in two-layer systems

2015 ◽  
Vol 787 ◽  
pp. 1-15 ◽  
Author(s):  
Peter G. Baines
Keyword(s):  
Energy Loss ◽  
Single Layer ◽  
Boussinesq Approximation ◽  
Maximum Speed ◽  
Hydraulic Jumps ◽  
Zero Energy ◽  
Layer Model ◽  
Two Fluids ◽  
Conjugate State ◽  
Two Layer Model

This paper describes a new model of internal hydraulic jumps in two-layer systems that places no restrictions (such as the Boussinesq approximation) on the densities of the two fluids. The model is based on that of Borden and Meiburg (J. Fluid Mech., vol. 276, 2013, R1) for Boussinesq jumps, and has the appropriate behaviour in various limits (single-layer, small amplitude, Boussinesq, infinite depth). The energy flux loss in each layer across the jump is positive for all realistic jumps, reaching a maximum for the jump with maximum speed. Larger-amplitude jumps are possible, with decreasing energy loss, down to the ‘conjugate state’ of zero energy loss. However, it is argued that such states may be difficult to realise in practice, and if formed, will tend to the jump with maximum speed. The energy loss is mostly in the contracting layer unless the density there is small. The two-layer model is extended to incorporate mixing between the layers within the jump, with mixing based on the Richardson number.

Two-layer Model for Electroabsorption and Built-in Potential Measurements on a-Si:H pin Solar Cells

1996 ◽  
Vol 420 ◽  
Author(s):  
Lin Jiang ◽  
E. A. Schiff
Keyword(s):  
Solar Cells ◽  
Amorphous Silicon ◽  
Second Harmonic ◽  
Semiconductor Devices ◽  
Single Layer ◽  
Experimental Results ◽  
Layer Model ◽  
Two Layer Model ◽  
Organic Devices

AbstractModulated Electroabsorption (EA) measurements have been widely used to estimate built-in potentials (Vbi) in semiconductor devices. The method is particularly simple in devices for which the built-in potential is dropped in a single layer of the device. However, experimental results in amorphous silicon and organic devices can involve at least 2 layers. In the present paper we consider the information which can be obtained about 2-layer semiconductor devices from electroabsorption measurements. In particular we describe a 2-layer EA model appropriate to a-Si:H based pin solar cells, for which both the p+ and i layers contribute to the EA signal. We present an analysis of capacitance and second harmonic measurements which yields the EA coefficient for the p+ layer of the device, and we present measurements on a-Si:H pin devices which appear consistent with this analysis. Wavelength dependent EA then yields the built-in potential across the 2-layer device.

Internal bores: an improved model via a detailed analysis of the energy budget

2012 ◽  
Vol 703 ◽  
pp. 279-314 ◽  
Author(s):  
Zachary Borden ◽  
Eckart Meiburg ◽  
George Constantinescu
Keyword(s):  
Propagation Velocity ◽  
Single Layer ◽  
Propagation Speed ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Net Energy ◽  
Layer Model ◽  
Viscous Effects ◽  
Two Layer Model ◽  
Internal Bores

AbstractInternal bores, or internal hydraulic jumps, arise in many atmospheric and oceanographic phenomena. The classic single-layer hydraulic jump model accurately predicts the bore height and propagation velocity when the difference between the densities of the expanding and contracting layers is large (i.e. water and air), but fails in the Boussinesq limit. A two-layer model, which conserves mass separately in each layer and momentum globally is more accurate in the Boussinesq limit, but it requires for closure an assumption about the loss of energy across a bore. It is widely believed that bounds on the bore speed can be found by restricting the energy loss entirely to one of the two layers, but under some circumstances, both bounds overpredict the propagation speed. A front velocity slower than both bounds implies that, somehow, the expanding layer is gaining energy. We directly examine the flux of energy within internal bores using two- and three-dimensional direct numerical simulations and find that although there is a global loss of energy across a bore, a transfer of energy from the contracting to the expanding layer causes a net energy gain in the expanding layer. The energy transfer is largely the result of turbulent mixing at the interface. Within the parameter regime investigated, the effect of mixing is much larger than non-hydrostatic and viscous effects, both of which are neglected in the two-layer analytical models. Based on our results, we propose an improved two-layer model that provides an accurate propagation velocity as a function of the geometrical parameters, the Reynolds number, and the Schmidt number.

A two-layer approach to modelling the transformation of dilute pyroclastic currents into dense pyroclastic flows

2010 ◽  
Vol 467 (2129) ◽  
pp. 1348-1371 ◽  
Author(s):  
Emma E. Doyle ◽  
Andrew J. Hogg ◽  
Heidy M. Mader
Keyword(s):  
Single Layer ◽  
Pyroclastic Flows ◽  
Constant Density ◽  
Particle Collisions ◽  
Layer Model ◽  
Fluid Turbulence ◽  
Naturally Occurring ◽  
Dense Granular Flow ◽  
Two Layer Model ◽  
End Members

Most models of volcanic ash flows assume that the flow is either dilute or dense, with dynamics dominated by fluid turbulence or particle collisions, respectively. However, most naturally occurring flows feature both of these end members. To this end, a two-layer model for the formation of dense pyroclastic basal flows from dilute, collapsing volcanic eruption columns is presented. Depth-averaged, constant temperature, continuum conservation equations to describe the collapsing dilute current are derived. A dense basal flow is then considered to form at the base of this current owing to sedimentation of particles and is modelled as a granular avalanche of constant density. We present results which show that the two-layer model can predict much larger maximum runouts than would be expected from single-layer models, based on either dilute or dense conditions, as the dilute surge can outrun the dense granular flow, or vice versa, depending on conditions.

Coherent structures of nonlinear barotropic-baroclinic interaction in unequal depth two-layer model

2021 ◽  
Vol 408 ◽  
pp. 126347
Author(s):  
Jiaqi Zhang ◽  
Ruigang Zhang ◽  
Liangui Yang ◽  
Quansheng Liu ◽  
Liguo Chen
Keyword(s):  
Coherent Structures ◽  
Layer Model ◽  
Two Layer Model

Propagation and localization of Rossby waves over random topography (two-layer model)

Wave Motion ◽  
1998 ◽  
Vol 28 (4) ◽  
pp. 333-352 ◽  
Author(s):  
V.I. Klyatskin ◽  
N.V. Gryanik ◽  
D. Gurarie
Keyword(s):  
Rossby Waves ◽  
Layer Model ◽  
Two Layer Model

Permafrost mapping by audiofrequency magnetotellurics

1978 ◽  
Vol 15 (10) ◽  
pp. 1539-1546 ◽  
Author(s):  
A. Koziar ◽  
D. W. Strangway
Keyword(s):  
Mackenzie Delta ◽  
Conductive Layer ◽  
Frequency Range ◽  
Layer Model ◽  
Resistive Layer ◽  
Asymptotic Models ◽  
Two Layer Model ◽  
Electrical Methods ◽  
Permafrost Mapping ◽  
Lateral Variations

The audiofrequency magnetotelluric (AMT) method has been used to study permafrost thickness near Tuktoyaktuk, N.W.T. in the Mackenzie Delta. In the frequency range of 10 Hz–10 kHz the permafrost behaves as a simple resistive layer over a conductive layer. This simple two-layer model can be inverted by asymptotic models to give a unique value for the thickness of the highly resistive frozen layer. In areas of simple layering, these results correlate well with drilling. In areas of sharp lateral variations in resistivity, depths tend to be underestimated. Unlike other electrical methods, AMT is not hampered by the presence of a surface melt layer in the summer if the conductivity–thickness product of this 'active layer' is less than about 0.03 mho (0.03 S).

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