# Dr Matthew Turner

### Biography

I obtained an MMath degree at the UEA in 2002 before completing my PhD in Fluid Dynamics in 2006, also at the UEA, under the supervision of Dr Paul Hammerton. After this, I spent 3 years at the University of Exeter working with Prof. Andrew Gilbert, before moving to the Sir Harry Ricardo Laboratories at the University of Brighton, where I worked with Prof. Sergei Sazhin, Prof. Jonathan Healey (Keele), Dr Renzo Piazzesi (ANSYS UK Ltd) and Dr Cyril Crua.

I started as a Lecturer at Surrey in May 2011 and was promoted to Senior Lecturer in 2016. I'm currently enjoying fruitful research collaborations with Prof. Tom Bridges on sloshing and dynamic coupling of fluid systems and Prof. Ian Roulstone, Dr Bin Cheng and Prof. John Norbury (Oxford) on convection in a moist atmosphere.

For more information, visit my personal web page.

### Areas of specialism

### University roles and responsibilities

- Mathematics PGR Director

### Research

### Research interests

My research interests lie in the field of fluid dynamics, in particular:

- Boundary layer receptivity
- Vortex dynamics
- Jet stability and breakup
- General flow stability
- Sloshing fluids and dynamical coupling
- Moist convection

For more information on my research interests, see the research page of my personal web site.

For more information on my publications, including draft copies of papers, see the publications page of my personal web page.

### My teaching

Currently teaching MAT3041 (Mathematical Fluid Mechanics) and MAT2001 (Numerical and Computational Methods).

### Courses I teach on

## Undergraduate

### My publications

### Publications

*ρ*1 and kinematic viscosity

*ʋ*1 while the lower layer fluid has density

*ρ*2 and kinematic viscosity

*ʋ*2 and the two fluids are assumed to be immiscible. This problem has potentially five independent parameters to investigate, but application of the continuity of the normal stresses at the interface imposes restrictions which reduces the problem to one with three independent parameters, namely a ratio

*σ*of strain rates and the fluid parameter ratios

*ρ*=

*ρ*1/

*ρ*2 and

*ʋ*=

*ʋ*1/

*ʋ*2. Numerical results are presented for selected values of

*ρ*and

*ʋ*for a range of

*σ*and show that stable results exist for all values of

*σ*> 0, and for a range of negative

*σ*values. Sample stable velocity profiles are also presented.

*z*= 0 under the parameter restriction that σ²ρ = 1 where σ is the ratio of the fluid angular velocities at

*z*= ±∞ and ρ is the density ratio of the two fluids. Under this restriction the problem reduces to one with two independent parameters, σ and μ, which is the viscosity ratio of the fluids. Numerical results of the resulting system of ODEs are found for selected values of μ and σ, and it is shown that similarity solutions exist for σ

_{c}(μ)≤ σ ≤ 1 where σ

_{c}(μ) ˂ 0 (i.e. counter-rotating flows). For σ ˂ 0 the lower fluid can become divided into two distinct recirculation regions between which fluid cannot transfer.