Direct-adjoint-looping methods for generalised stability problems
Lead Research Organisation:
University of Cambridge
Department Name: Applied Maths and Theoretical Physics
Abstract
It is of great practical importance to understand how flows undergo the transition to turbulence, as turbulence typically hugely increases mixing, transport and dissipation within flows of environmental and industrial interest. It is commonly believed that `normal' mode flow instabilities play a central role in such transition processes, and the conventional argument is that the `most unstable' normal mode will dominate the nonlinear evolution of the flow, and hence lead the flow to transition. However, the underlying linearized operator is non-normal, and so it is possible for substantial transient growth of perturbations to occur. A particularly attractive method to consider such transient growth problems is the so-called `direct-adjoint looping' method, which can be generalised to consider fully nonlinear perturbations, where the developing perturbations can reach a sufficiently large amplitude to nontrivially modify the `base flow'. This method is particularly well-suited to consider generalised stability problems, where the measure which is being extremised is not necessarily the `energy' of the developing perturbation. Indeed, there are several interesting mathematical issues about the most appropriate measures to use, and this project will approach the general issue of perturbation `growth' in a range of environmentally and industrially important flows from a variety of mathematical and computational directions.
Organisations
People |
ORCID iD |
Colm-Cille Caulfield (Primary Supervisor) | |
Jeremy Parker (Student) |
Publications
Parker J
(2020)
The viscous Holmboe instability for smooth shear and density profiles
in Journal of Fluid Mechanics
Parker J
(2021)
Optimal perturbation growth on a breaking internal gravity wave
in Journal of Fluid Mechanics
Parker J
(2020)
Linear and nonlinear dynamics in stratified shear flows
Parker J
(2020)
Koopman analysis of isolated fronts and solitons
Parker J
(2020)
Koopman Analysis of Isolated Fronts and Solitons
in SIAM Journal on Applied Dynamical Systems
Parker J
(2019)
Kelvin-Helmholtz billows above Richardson number 1/4
Parker J
(2019)
Kelvin-Helmholtz billows above Richardson number
in Journal of Fluid Mechanics
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N509620/1 | 01/10/2016 | 30/09/2022 | |||
1940773 | Studentship | EP/N509620/1 | 01/10/2017 | 31/03/2021 | Jeremy Parker |
Description | Through applying existing computational methods, with particular new modifications relevant to our studies, we have studied in detail the dynamics of flows which are relevant to important geophysical processes in both the oceans and the atmosphere. Deep ocean mixing is a particularly poorly understood area which is extremely important to long term predictions of the climate. Here we have pushed understanding by examining new parameter regimes in greater detail, through which we have raised new questions about widely held beliefs in this field. |
Exploitation Route | This work paves the way for greater interpretation and understanding of the results of simulations and observations in atmospheric and oceanic sciences, and in particular should encourage researchers to put less faith in widely used "rules-of-thumb" which are not supported by our evidence. |
Sectors | Environment |
Title | Stratiflow |
Description | A new code for direct numerical simulation of stratified shear flows and stratified turbulence. |
Type Of Technology | Software |
Year Produced | 2018 |
Open Source License? | Yes |
Impact | Used for the publications on this award. |