# Computer modelling of laboratory experiments

#### Met Office / Oxford Rotating Annulus Laboratory Simulation (MORALS)

This is a direct numerical simulation of the rotating annulus experiment. It solves the Navier-Stokes equations in annular geometry using the Boussinesq approximation. It is mostly used to study the thermally-driven rotating annulus but has also been used to study boundary currents by adding a vertical boundary, and large vortices on the giant planets by internal heating of the fluid. More information about this model can be found by following the link in the bar on the left.

#### QUAsi-Geostrophic Model for Investigating Rotating fluids Experiments (QUAGMIRE)

This is a quasi-geostrophic model of the rotating annulus designed by Paul Williams (now at Reading). It was designed to simulate a system with two immiscible fluid layers, but has more recently been extended to multiple layers and the latest version (v1.4) features fully stratified flow.

#### Imperial College Ocean Model (ICOM)

This is a next-generation fluid dynamics model used primarily for ocean simulations. It is a finite-element model whose major features are (1) the ability to adapt the model grid in real-time, which allows regions of the flow which are more interesting to be assigned higher resolution, at the expense of other regions, and (2) great flexibility in the choice of domain in which the fluid is simulated (customised domains an be built from scratch if required). We have recently started work on using this to model our rotating fluids experiments, in particular the thermally-driven annulus.

#### Current projects:

### Predictability of the rotating annulus (Roland Young)

We have built a forecasting framework for the thermally-driven rotating annulus laboratory experiment using MORALS and well-established weather prediction techniques for ensemble generation (breeding vectors) and data assimilation (analysis correction). These methods were studied in isolation and then used to forecast the laboratory experiment and measure its predictability.

### Finite-dimensional dynamics in baroclinic chaos (Judy Simpson)

For many purposes, atmospheric flow may be dominated by the non-linear interaction of relatively few independent wave modes, leading to dynamics which may be steady, periodic or exhibiting finite-dimensional chaos. Under these circumstances it should be possible, at least in principle, to model and predict the behaviour of the flow using a relatively simple model with just a few degrees of freedom. But how many degrees of freedom are needed, and how can we formulate such a model? We use the QUAGMIRE simulation to model moderately complex flows which we can study and measure in the laboratory.

Annulus flow produced by QUAGMIRE v1.4:

### Next-generation adaptive mesh modelling of laboratory experiments (James Maddison)

We have configured the Imperial College Ocean Model to simulate the thermally driven rotating annulus. The novel technologies implemented in this model, in particular the use of general unstructured meshes and dynamic mesh adaptivity, enable the simulation of previously challenging flows. We are comparing ICOM simulations of the thermally driven annulus against data collected in our laboratory, and are using this to identify strengths and weaknesses of the dynamic mesh adaptive methods in geophysical applications. We are also using ICOM to simulate domains with topography and at high rotation rate.

### The annulus as a test bed for meteorological techniques (Roland Young)

We can use the annulus to study methods in current use or in development for weather prediction using a real fluid with a non-idealised model under laboratory conditions. The laboratory is a bridge between analytical systems, where new methods are first tested, and large atmospheric models, where they are eventually applied. With colleagues at the Centre for the Analysis of Time Series at the London School of Economics, we have used MORALS to test shadowing techniques using the gradient descent method for state estimation, and intend to compare this with other methods in current use and development like 4D-Var, the ensemble Kalman filter, and the particle filter.

#### MORALS temperature time series at a single point at the start and after 8 steps of the gradient descent method: