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3.14.4 Model parameters


Table 3.2: Model parameters used in the gravity plume experiment.
$ g$ $ 9.81$ m s$ ^{-2}$ acceleration due to gravity
$ \rho_o$ $ 999.8$ kg m$ ^{-3}$ reference density
$ \alpha $ $ 2 \times 10^{-4}$ K$ ^{-1}$ expansion coefficient
$ A_h$ $ 1 \times 10^{-2}$ m$ ^2$s$ ^{-1}$ horizontal viscosity
$ A_v$ $ 1 \times 10^{-3}$ m$ ^2$s$ ^{-1}$ vertical viscosity
$ \kappa_h$ 0 m$ ^2$s$ ^{-1}$ (explicit) horizontal diffusion
$ \kappa_v$ 0 m$ ^2$s$ ^{-1}$ (explicit) vertical diffusion
     
$ \Delta t$ $ 20$ s time step
$ \Delta z$ $ 3.3\dot{3}$ m vertical grid spacing
$ \Delta x$ $ 13.\dot{3}-39.5$ m horizontal grid spacing


The model parameters (Table 3.2) are specified in input/data and if not assume the default values defined in model/src/set_defaults.F. A linear equation of state is used, eosType='LINEAR', but only temperature is active, sBeta=0.E-4. For the given heat flux, $ Q_o$, the buoyancy forcing is $ B_o = \frac{g \alpha Q}{\rho_o c_p} \sim 10^{-7}$ m$ ^2$s$ ^{-3}$. Using $ R=10^3$ m, the shelf width, then this gives a velocity scale of $ U\sim 5 \times 10^{-2}$ m s$ ^-1$ for the initial front but will accelerate by an order of magnitude over the slope. The temperature anomaly will be of order $ \Delta \theta \sim 3 \times 10^{-2}$ K. The viscosity is constant and gives a Reynolds number of $ 100$, using $ h=20$ m for the initial front and will be an order magnitude bigger over the slope. There is no explicit diffusion but a non-linear advection scheme is used for temperature which adds enough diffusion so as to keep the model stable. The time-step is set to $ 20$ s and gives Courant number order one when the flow reaches the bottom of the slope.

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Next: 3.14.5 Build and run Up: 3.14 Gravity Plume On Previous: 3.14.3 Code configuration   Contents
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