Periodic Reporting for period 4 - STAMP (Stratified turbulence and mixing processes)
Reporting period: 2022-04-01 to 2024-03-31
The project investigates turbulence and mixing in stably stratified fluid. Mixing is central to a wide range of questions from the heat uptake in the global ocean, the transport and dilution of pollutants in the atmosphere, the efficient cooling of buildings, to the homogenising of products in the food industry. However, the mechanisms that are responsible and their physical and dynamical aspects are largely unknown, and it is not possible to predict mixing rates from a knowledge of the overall flow and density fields.
All fluid bodies in nature (the atmosphere, oceans, lakes, the air within a room) have significant regions that are stably stratified, making the study of fluxes and mixing in stratified turbulence essential for applications to a wide range of environmental problems from climate predictions to the design of low-energy buildings. The central question we propose to answer is what determines mixing in stratified flows.
The overall objectives are
I. Identify the structures responsible for mixing turbulent mixing events in a maintained stratified shear at high Reynolds numbers, in particular their connection to classical flow instabilities.
II. Using highly resolved 3D measurements over a volume, study their dynamics and life-cycles.
III. Determine their contributions to mixing in transitional, intermittent and fully turbulent flow, investigating the differences and similarities between these contributions and the equivalent contributions for nonlinear structures in classical unstable initial value problem studies.
IV. Determine the entrainment and relate it to the prevailing dynamical processes.
The Stratified Inclined Duct (SID) has large reservoirs on either side of a long rectangular duct to sustain a long-lived exchange flow. Importantly, the apparatus can be tilted at a small angle θ to force the denser layer to accelerate as it flows downslope and vice versa. The originality of SID is that the simple, natural forcing of gravity through θ sustains vigorous interfacial stratified turbulence that long seemed out of reach of either laboratory or numerical experiments. SID can be seen as a natural extension of Reynolds classic pipe flow experiment. Pipe flow has a single control parameter the Reynolds number. SID, on the other hand, has two control parameters: Re, which is set by the density difference between the two reservoirs and θ. This additional control parameter provides a wealth of new flow phenomena associated with the stratification and allows us to achieve the objectives above.
All fluid bodies in nature (the atmosphere, oceans, lakes, the air within a room) have significant regions that are stably stratified, making the study of fluxes and mixing in stratified turbulence essential for applications to a wide range of environmental problems from climate predictions to the design of low-energy buildings. The central question we propose to answer is what determines mixing in stratified flows.
The overall objectives are
I. Identify the structures responsible for mixing turbulent mixing events in a maintained stratified shear at high Reynolds numbers, in particular their connection to classical flow instabilities.
II. Using highly resolved 3D measurements over a volume, study their dynamics and life-cycles.
III. Determine their contributions to mixing in transitional, intermittent and fully turbulent flow, investigating the differences and similarities between these contributions and the equivalent contributions for nonlinear structures in classical unstable initial value problem studies.
IV. Determine the entrainment and relate it to the prevailing dynamical processes.
The Stratified Inclined Duct (SID) has large reservoirs on either side of a long rectangular duct to sustain a long-lived exchange flow. Importantly, the apparatus can be tilted at a small angle θ to force the denser layer to accelerate as it flows downslope and vice versa. The originality of SID is that the simple, natural forcing of gravity through θ sustains vigorous interfacial stratified turbulence that long seemed out of reach of either laboratory or numerical experiments. SID can be seen as a natural extension of Reynolds classic pipe flow experiment. Pipe flow has a single control parameter the Reynolds number. SID, on the other hand, has two control parameters: Re, which is set by the density difference between the two reservoirs and θ. This additional control parameter provides a wealth of new flow phenomena associated with the stratification and allows us to achieve the objectives above.
The work performed has been to conduct experiments in a stratified inclined duct (SID) and to measure the structures involved in the mixing processes. To do so, we employed state-of-the-art simultaneous volumetric measurements of the density field and the three-component velocity field, and analysed these experimental data using time- and volume-averaged potential and kinetic energy budgets. We showed that regime transitions are caused by an increase in the kinetic energy dissipation within the duct. As the power input is increased above zero, the two-dimensional, parallel-flow dissipation (power output) increases through an increase in the magnitude of the exchange flow, triggering waves above a certain threshold in interfacial shear. However, once the hydraulic limit of two-layer exchange flows is reached, three-dimensional dissipation at small scales (turbulence) takes over, at first intermittently, and then steadily. This general understanding of regime transitions and energetics in the SID experiment provides a basis for the study of more complex sustained stratified shear flows found in the natural environment.
The structures responsible for mixing are identified, and found to be intense elongated rotating structures called ‘rortices’ which are characterised by rapid rotation about an axis inclined to the horizontal. We showed that these structures can be traced back to an initial linear instability on the interface between the two layers in the flow.
The effects of molecular diffusivity were initially noticed from qualitative observations of flows stratified with heat. Most of our experiments used salt stratification that has a very low diffusivity and exhibited sharp density contrasts as a result. Using heat, which diffuses 100 times faster than salt in water, produced broader density contrasts and exhibited different transitions to turbulence. This is explored via direct numerical simulations with parameter values the same as in the heat-stratified experiments.
In addition to achieving the original objectives we made further discoveries about exchange flows. The first discovery is that the flow is intrinsically hydraulically controlled. Simulations showed there was a pressure minimum in the centre of the duct that caused a retrograde pressure gradient in each layer after it flowed past the midpoint, causing separation and initiating a jump. It was also shown that this process could be analysed in terms of interactions of long interfacial waves propagating in in opposite directions in each layer. In addition we showed that using a physically-informed neural network (PINN) we could reduce the noise and improve the resolution of the experimental data, and use the output to infer new features of the dynamics. In particular, we showed that the flow exhibits ‘self-organised criticality’.
From a technological standpoint we constructed a new experiment with many improved features: higher resolution data from better optical access, higher resolution cameras; long run times from large reservoirs; dynamic tilt control using a mechanical lift; enhancements to the image analysis software DigiFlow that provided new diagnostic capabilities to identify flow structures. We also developed the first direct numerical simulation of SID flow with an exact match of all aspects of the experiment: geometry, fluid properties, and flow parameters.
The structures responsible for mixing are identified, and found to be intense elongated rotating structures called ‘rortices’ which are characterised by rapid rotation about an axis inclined to the horizontal. We showed that these structures can be traced back to an initial linear instability on the interface between the two layers in the flow.
The effects of molecular diffusivity were initially noticed from qualitative observations of flows stratified with heat. Most of our experiments used salt stratification that has a very low diffusivity and exhibited sharp density contrasts as a result. Using heat, which diffuses 100 times faster than salt in water, produced broader density contrasts and exhibited different transitions to turbulence. This is explored via direct numerical simulations with parameter values the same as in the heat-stratified experiments.
In addition to achieving the original objectives we made further discoveries about exchange flows. The first discovery is that the flow is intrinsically hydraulically controlled. Simulations showed there was a pressure minimum in the centre of the duct that caused a retrograde pressure gradient in each layer after it flowed past the midpoint, causing separation and initiating a jump. It was also shown that this process could be analysed in terms of interactions of long interfacial waves propagating in in opposite directions in each layer. In addition we showed that using a physically-informed neural network (PINN) we could reduce the noise and improve the resolution of the experimental data, and use the output to infer new features of the dynamics. In particular, we showed that the flow exhibits ‘self-organised criticality’.
From a technological standpoint we constructed a new experiment with many improved features: higher resolution data from better optical access, higher resolution cameras; long run times from large reservoirs; dynamic tilt control using a mechanical lift; enhancements to the image analysis software DigiFlow that provided new diagnostic capabilities to identify flow structures. We also developed the first direct numerical simulation of SID flow with an exact match of all aspects of the experiment: geometry, fluid properties, and flow parameters.
The most significant breakthrough is the direct numerical simulation of the experiments, exactly matching every detail. This is the first time that this has been achieved for stratified turbulence in confined geometry. Usually some compromises are needed, either in representing the fluid properties or only approximating the boundary conditions or for different values of the flow parameters.
This was unexpected and due mainly to the skill in the postdoc who we employed to carry out the computations. As mentioned above the DNS provide the pressure field, but they also provide data along the whole duct while the experimental data are limited to a section illuminated by the laser sheet. Consequently, we were able to use the DNS data to examine the hydraulics of the system that has turned out to reveal new interactions between long and short waves and new routes to turbulence. While the original focus was on mixing rates, these new routes to transition have wide implications in environmental and industrial flows.
In the past few months of the grant we collected a new data set covering a wide range of Reynolds numbers and more vigorous turbulence. These data are still undergoing analysis and we expect to write at least two papers on the results of this analysis. We also have a paper under review on a further analysis of flow structures and their role in dissipation and mixing, and a paper in preparation on hydraulics in a three-layer flow that extends the two-layer analysis to the onset of intermittent trubulence.
This was unexpected and due mainly to the skill in the postdoc who we employed to carry out the computations. As mentioned above the DNS provide the pressure field, but they also provide data along the whole duct while the experimental data are limited to a section illuminated by the laser sheet. Consequently, we were able to use the DNS data to examine the hydraulics of the system that has turned out to reveal new interactions between long and short waves and new routes to turbulence. While the original focus was on mixing rates, these new routes to transition have wide implications in environmental and industrial flows.
In the past few months of the grant we collected a new data set covering a wide range of Reynolds numbers and more vigorous turbulence. These data are still undergoing analysis and we expect to write at least two papers on the results of this analysis. We also have a paper under review on a further analysis of flow structures and their role in dissipation and mixing, and a paper in preparation on hydraulics in a three-layer flow that extends the two-layer analysis to the onset of intermittent trubulence.