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Comparing $\overline{w'w'}$ and $\overline{w'w'w'}$ tendency terms between ADC and LES #13

Open BrodiePearson opened 3 years ago

BrodiePearson commented 3 years ago

This issue lists the ADC tendency terms for $\overline{w'w'}$ and $\overline{w'w'w'}$, and the analogous LES terms (where possible).

One avenue for diagnosing the skill of the ADC closure scheme is to compare whether the tendency terms in the scheme are comparable to LES data. The tendency terms in the ADC and LES schemes represent similar physical processes, but because the ADC scheme has closure assumptions that are distinct from Reynolds averaging (which is how we analyze LES fields), the tendency terms in the ADC and LES schemes differ in their form.

$\overline{w'w'}$ budget

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L565-L566

$w2tend1=$? (Entrainment/Detrainment; maybe dissipation related or this doesn't have an LES analogy)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L567-L569

$w2tend2=-\frac{\partial \overline{w'w'w'}}{\partial z}$ (Turbulent transport)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L570

$w2tend3=\frac{ \overline{u'u'} + \overline{v'v'} }{3\tau_{slow}}$ (Part of slow pressure; a missing $\overline{w'w'}$ term is added in time-stepping)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L571-L572

$w2tend4= ( 2 - \frac{4}{3}C_2 ) \overline{w'b'} = ( 2 - \frac{4}{3}C_2 ) g ( \alpha_T \overline{w'T'} - \beta_S \overline{w'S'} )$ (Buoyancy plus buoyancy pressure term)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L573-L575

$w2tend5= complicated$ (Rapid pressure & subgrid terms, dissipation too(?))

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L314-L316

$w2tend6= Splatting$ (Effectively a pressure term that converts w2 to u2 and v2 near the surface)

We could add a combined pressure term that is only used for comparison with LES: w2tendpressure $= w2tend3 + w2tend5 + w2tend6 - \frac{2\overline{w'w'}}{3\tau{slow}} - \frac{\frac{4}{3}C_2}{2-\frac{4}{3}C_2} w2tend4$

Then, $w2tend$_$pressure \approx -2\overline{w'\frac{\partial p'}{\partial z}}$

Since $w2tend5$ also contains dissipation, perhaps we go one step further by combining pressure and dissipation terms

$w2tend1 + w2tend$_$pressure = -2\overline{w'\frac{\partial p'}{\partial z}} - \frac{2}{3}\epsilon $

$\overline{w'w'w'}$ budget

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L486

$w3tend1=?$ (Entrainment/Detrainment - perhaps analogous to LES dissipation of $\overline{w'w'w'}$)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L498-L499

$w3tend2=-\frac{\partial \overline{w'w'w'w'}}{\partial z}$ (Turbulent transport, the 4th moment may not be LES output...)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L500

$w3tend3=\frac{3}{2}\frac{\partial \left[ \left(\overline{w'w'}\right)^2 \right]}{\partial z}$ (Source term from w2 gradients)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L504-L505

$w3tend4=complicated$ (Sub-plume scale transport and slow pressure term)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L506-L507

$w3tend5=3(1-C_{11})\overline{w'w'b'}$ (Buoyancy production plus buoyancy pressure term)

https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L303-L305

$w3tend6=Splatting$ (This is effectively a pressure-driven effect)

BrodiePearson commented 3 years ago

@katsmith133 Let me know if you spot anything that's incorrect or doesn't make sense!

katsmith133 commented 3 years ago

@BrodiePearson, I believe I've got correct terms plotted (splatting terms are left out for now as I am comparing to a non-splatting ADC run, the "no-splat, w2 BC off" run at 82 hours in): Cooling2_hour82_nosplat_tendency_terms Note: for the w2tend1 + w2tend_pressure term, the -2*<w'*dp'/dz> term is not available in the saved LES profiles, so I have not plotted that term for the LES. Perhaps something to discuss...

BrodiePearson commented 3 years ago

@katsmith133 These are interesting comparisons. I agree this we should discuss this today

amrapallig commented 3 years ago

LES c2 case: image

katsmith133 commented 3 years ago

@BrodiePearson and @amrapallig, per our discussion yesterday, here is the comparisons for the various terms that go into the w2t term that is used in calculating w3tend5: Coooling2_hour82_nosplat_w3tend5_term_breakdown

w2t panel: black line - diagnosed from LES data as <w'w't'>, blue line - from ADC run, green line - diagnosed from LES data using ADC formulation: https://github.com/vanroekel/MPAS-Model/blob/5dc8d6e40e31fb03492426e324d435637f6edf05/src/core_ocean/shared/mpas_ocn_adcReconstruct.F#L426

Sw - tumd panels: blue lines - from ADC run, green lines - diagnosed from LES using ADC formulations

It looks like using the ADC formulation on the LES data produces a w2t term that is still too small, indicating that something is missing from the ADC approximation of w2t.