Newtonian Slab Flow Rate
Evaluate constant-viscosity inclined-slab deformation from supplied maximum basal shear stress; excludes basal sliding.
Description
A constant-viscosity inclined slab has a depth-varying deformation velocity.
A constant-viscosity inclined slab has a depth-varying deformation velocity. Its depth mean is two thirds of the surface deformation velocity.1
Evaluate constant-viscosity inclined-slab deformation from supplied maximum basal shear stress; excludes basal sliding.
When to use Newtonian Slab Flow Rate
Use this for the following task: Evaluate constant-viscosity inclined-slab deformation from supplied maximum basal shear stress; excludes basal sliding.
Prepare the measurements and calibration parameters in the declared units. Keep vector entries aligned and choose a consistent spatial frame and time basis.
How to use Newtonian Slab Flow Rate and understand its results
- Prepare the measurements and calibration parameters in the declared units. Keep vector entries aligned and choose a consistent spatial frame and time basis.
- Enter iceThicknessM, basalShearStressPa, dynamicViscosityPaYears using the field table, then run the tool.
- Read surfaceDeformationVelocityMPerYear, depthMeanDeformationVelocityMPerYear, deformationFluxPerUnitWidthM2PerYear. Interpret flags, units, ordering and placeholder values using the rules below.
- Review any reported issue or failed check, correct the supplied values when appropriate, and verify the result in its intended context.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| iceThicknessM | Ice thickness m | number | Required |
| basalShearStressPa | Basal shear stress pa | number | Required |
| dynamicViscosityPaYears | Dynamic viscosity pa years | number | Required |
Supply positive thickness and viscosity in Pa·years with nonnegative basal shear stress. Return deformation velocities and flux per unit width.2
us = τbH/(2η); umean = 2us/3; q = H umean This summarizes the declared operation. Units, indexing, inclusivity and exceptional cases are explained in the surrounding text.
| Output field | Meaning | Value type |
|---|---|---|
| surfaceDeformationVelocityMPerYear | Surface deformation velocity m per year | number |
| depthMeanDeformationVelocityMPerYear | Depth mean deformation velocity m per year | number |
| deformationFluxPerUnitWidthM2PerYear | Deformation flux per unit width m2 per year | number |
{
"input": {
"iceThicknessM": 2,
"basalShearStressPa": 3,
"dynamicViscosityPaYears": 2
},
"output": {
"surfaceDeformationVelocityMPerYear": 1.5,
"depthMeanDeformationVelocityMPerYear": 1,
"deformationFluxPerUnitWidthM2PerYear": 2
}
}Limitations and assumptions
This Newtonian model excludes basal sliding and nonlinear Glen rheology.
Constants and empirical coefficients are supplied rather than calibrated. Check units and observational applicability before interpreting the model. Malformed requests produce input errors. A successfully evaluated request can still contain false flags, empty result lists or a result outside the supplied threshold; those outcomes have the meanings stated above.
Alternative or Complementary methods
Choose Glen Flow Law Strain Rate for this operation: Evaluate signed scalar Glen shear strain rate A·E·sign(tau)|tau|^n; A units follow n, and shear tensor strain rate differs by a factor two from engineering shear rate. For a complementary task, use Parabolic Channel Discharge for this operation: Analytically integrate local slab Glen flux over a parabolic thickness section plus uniform sliding; excludes lateral stress coupling and uses stress-gradient units Pa/m.
Further background: Ice rheology.
References
-
Ice rheology — PISM
-
Newtonian Slab Flow Rate — tool.io
Similar or alternative tools
- Glen Flow Law Strain Rate
Evaluate signed scalar Glen shear strain rate A·E·sign(tau)|tau|^n; A units follow n, and shear tensor strain rate differs by a factor two from engineering shear rate.
- Parabolic Channel Discharge
Analytically integrate local slab Glen flux over a parabolic thickness section plus uniform sliding; excludes lateral stress coupling and uses stress-gradient units Pa/m.