Spring, 2019
Jewett

Test D:  Sinking temperature perturbation in domain center

• Domain and execution:
• 33x33x16 grid - runs quickly for interactive testing
• (note odd dimension for nx,ny; initial bubble at exact X-Y center)
  
• ∆x=∆y=∆z = 500 meters
  
• ∆t = 1.0 seconds
  
• Physics:
• All processes retained and active.
• Sound speed Cs=100 m/s.
• Non-monotonic piecewise linear advection.
  
• Diffusion coefficients = 50 (momentum), 5 (temperature).
• Initial condition: same as Test A
  
• Theta: 1 thermal: -20˚, center (8250,8250,4250) meters (grid point 17,17,9); radius = 4000m in each direction x,y,z
• U,V,W: are all initially zero - no perturbations on U or V
  
• Boundary conditions:
• Usual (symmetric X, periodic Y, 0-gradient Z)
  

Test D1:  Center sinking bubble

• I have used the "www" option from plot3d on test D; the results are online here.
• Cold bubble placed at center at time T=0; run for 400 seconds.
• The negatively buoyant theta perturbation descends to the domain bottom and spreads symmetrically outwards, reaching domain boundaries.  For the X symmetry boundaries, the density current then 'splashes' upwards and climbs the 'wall' since no flow through the boundary is possible.  For Y, the density current moving towards -Y will hit the boundary at the same time the current moving to +Y reaches that boundary.  Due to periodic BCs in Y, the two collide there, with behavior like that seen at the X boundaries.
  
• All plots made with plot3d program; contour intervals are 5 m/s (U,V,W), 20 hPa (P')
• All cross sections are through the center: X-Z at j=(nx-1)/2, or Y-Z at i=(ny-1)/2
  
• 3-D plots use plot3d default "eye", looking toward origin from location in +X, +Y, +Z (so +X is out of page towards you)
• The 3-D plot of theta used a smaller (T' = -5K instead of -10K) isosurface than in earlier tests - to show the T' evolution later in the run.
  
• Note symmetry in the solution; the following should look nearly identical, until perhaps the density current reaches the
  X, Y boundaries with their different BCs:
• X-Z and Y-Z plots of U should look alike, and be nearly identical to X-Z and Y-Z plots of V
• X-Z and Y-Z plots of T should look alike
• X-Z and Y-Z plots of W should look alike
• X-Z and Y-Z plots of P should look nearly alike - small differences are expected
  
• X-Y plots should be nearly symmetric until reaching the boundaries
  
• Text output from running code may be found here.
  
• A slightly longer run (to T=500) was used to prepare animations of 3-D T': GIF, Quicktime

Test D1	T=0	T=100	T=200	T=300	T=400
T X-Z
T Y-Z
T X-Y k=1
T 3-D
U X-Z
U Y-Z
U X-Y k=1
V X-Z
V Y-Z
V X-Y k=1
W X-Z
W Y-Z
W X-Y k=3
P X-Z
P Y-Z
P X-Y k=1

Test D2:  Center sinking bubble but without U,V,W [nonlinear] advection running

• The test case is the same above, except...
• I disabled the U/V/W advection (of U,V,W: the nonlinear advection terms)
• The results are similar but give you a test to see if your nonlinear advection terms are working.
• I used the "www" option from plot3d to plot the fields; the results are online here.
  

Test D3/u:  Center sinking bubble with u nonlinear advection (without v,w)

• The test case is the same as case TestD above, except... no nonlinear advection of v or w (only u).
  
• I used the "www" option from plot3d to plot the fields; the results are online here.

Test D3/v:  Center sinking bubble with v nonlinear advection (without u,w)

• The test case is the same as case TestD above, except... no nonlinear advection of u or w (only v).
  
• I used the "www" option from plot3d to plot the fields; the results are online here.

Test D3/w:  Center sinking bubble with w nonlinear advection (without u,v)

• The test case is the same as case TestD above, except... no nonlinear advection of u or v (only w).
  
• I used the "www" option from plot3d to plot the fields; the results are online here.