Impact of tidal mixing on shelf sea dynamics under strong tidal influences

Dr Xiaoyan Wei, Bob Marsh, Dr George Nurser

Shelf seas are a critical interface in the Earth System where land-sea exchange of riverine loads (nutrients, sediment, pollutants) and oceanic matter (salt, carbon, biota) strongly affects the health and functioning of marine ecosystems, significantly changing the global carbon cycle and climate. To better predict and mitigate the adverse impacts of these changes on marine ecosystems and the whole Earth System, we need to accurately model the vertical mixing processes which play a key role in water movement and mass distribution in shelf seas.

The empirical K-Profile parameterisation (KPP, Large et al., 1994) and statistical turbulence-closure models (Umlauf & Burchard, 2003) are the most popular vertical mixing parameterisations (VMPs) for the ocean surface boundary layer and shallow estuaries, respectively. However, due to highly variable forcings, shelf seas regularly shift regimes from well-mixed (winter) to strongly stratified (summer), where the dominant vertical mixing processes, such as tides, wind, surface heat fluxes and internal waves, vary greatly. Yet, no existing VMP is accurate for all shelf sea regimes, and it remains one of the greatest challenges for predicting land-sea exchanges in shelf sea models– to capture the realistic vertical mixing variations across different regimes. This challenge will be tackled in this project.


Integrating numerical and semi-analytical modelling, you will improve understanding of shelf sea dynamics under strong tidal influences, and extend KPP into an accurate vertical mixing parameterisation for shelf seas across all regimes, as follows:

  1. Set up a high-resolution NEMO model, considering an idealized weakly-stratified shelf sea forced by constant wind, surface cooling and semi-diurnal tidal forcing.
  2. Derive an empirical formula of the vertical mixing coefficients (vertical eddy viscosity and diffusivity) based on the model results, assuming vertical mixing coefficients to depend on a shape function and large-scale variables (as KPP).
  3. Develop a semi-analytical model with the empirical formula (extending Wei et al., 2021); use model results to partition individual contributions of convective mixing, wind mixing and tidal mixing to stratification and currents.
  4. Extend the empirical formula for strongly and partially stratified regimes by incorporating the contribution of internal waves to mixing (already included in KPP).
  5. Evaluate the performance of the extended KPP by comparing results of the North-West European shelf seas model (NEMO) with different turbulence closures against historical observations in the North-West European shelf seas under different regimes (e.g., summer, winter); quantify the contribution of tidal mixing to currents and stratification for each regime.


NOC Liverpool

The INSPIRE DTP programme provides comprehensive personal and professional development training alongside extensive opportunities for students to expand their multi-disciplinary outlook through interactions with a wide network of academic, research and industrial/policy partners. The student will be registered at the University of Southampton and hosted at the National Oceanography Centre (NOC), Liverpool.

Specific training will include: 

  1. Discipline-based training –relevant seminars and journal clubs; selected SOES modules (e.g., SOES3009, Shelf Seas and Shelf Edge Dynamics).
  2. Professional skills for research leadership – training workshops for making good presentations, time management, and paper/proposal writing.
  3. Research methods training – modelling workshops (including the use of HPC (High Performance Computing) systems and JASMIN, the UK data analysis facility for environmental science), programming courses/webinars (Fortran, Python), and summer schools.
  4. Career Development and Transferable Skills Training – presenting at domestic and international conferences, annual training programme organised by the University of Liverpool (Making an Impact).  


Eligibility & Funding Details: 

Please see for details.

Background Reading: 

Large, W. G., McWilliams, J. C., & Doney, S. C. (1994). Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Reviews of geophysics, 32(4), 363-403.

Umlauf, L., & Burchard, H. (2003). A generic length-scale equation for geophysical turbulence models. Journal of Marine Research, 61(2), 235-265.

Wei, X., Schuttelaars, H. M., Williams, M. E., Brown, J. M., Thorne, P. D., & Amoudry, L. O. (2021). Unraveling interactions between asymmetric tidal turbulence, residual circulation, and salinity dynamics in short, periodically weakly stratified estuaries. Journal of Physical Oceanography, 51(5), 1395-1416.