Johns Hopkins Turbulence Databases

### Database Functions

**For detailed formulae used in the functions, DOWNLOAD DOCUMENT**

Isotropic | MHD | Channel | Mixing | Isotropic4096 | Rotstrat4096 | Transitional_bl | Channel5200 | |

GetVelocity | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

GetMagneticField | ✓ | |||||||

GetVectorPotential | ✓ | |||||||

GetPressure | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

GetTemperature | ✓ | |||||||

GetDensity | ✓ | |||||||

GetVelocityAndPressure | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

GetVelocityAndTemperature | ✓ | |||||||

GetForce | ✓ | ✓ | ||||||

GetVelocityGradient* | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

GetMagneticFieldGradient* | ✓ | |||||||

GetVectorPotentialGradient* | ✓ | |||||||

GetPressureGradient | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

GetTemperatureGradient | ✓ | |||||||

GetDensityGradient | ✓ | |||||||

GetVelocityHessian | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

GetMagneticFieldHessian | ✓ | |||||||

GetVectorPotentialHessian | ✓ | |||||||

GetPressureHessian | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

GetTemperatureHessian | ✓ | |||||||

GetDensityHessian | ✓ | |||||||

GetVelocityLaplacian | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

GetMagneticFieldLaplacian | ✓ | |||||||

GetVectorPotentialLaplacian | ✓ | |||||||

GetPosition | ✓ | ✓ | ✓ | ✓ | ✓ | |||

GetBoxFilter | ✓ | ✓ | ✓ | ✓ | ✓ | |||

GetBoxFilterSGSscalar | ✓ | ✓ | ✓ | ✓ | ||||

GetBoxFilterSGSvector | ✓ | ✓ | ✓ | ✓ | ✓ | |||

GetBoxFilterSGSsymtensor | ✓ | ✓ | ✓ | ✓ | ✓ | |||

GetBoxFilterSGStensor | ✓ | |||||||

GetBoxFilterGradient | ✓ | ✓ | ✓ | ✓ | ✓ | |||

GetThreshold | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

GetInvariant | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

**Note: The divergence-free condition in the simulation is enforced based on the spectral representation of the derivatives.
The JHTDB analysis tools for gradients are based on finite differencing of various orders.
Therefore, when evaluating the divergence using these spatially more localized derivative operators, a non-negligible error in the divergence is obtained, as expected.*

### Database Spatial Differentiation Options:

*Options for GetVelocityGradient, GetMagneticFieldGradient, GetVectorPotentialGradient, GetPressureGradient and GetDensityGradient*

*FD4: 4th-order centered finite differencing (can be spatially interpolated)
*

*FD6: 6th-order centered finite differencing (without spatial interpolation)*

*FD8: 8th-order centered finite differencing (without spatial interpolation)*

*M1Q4: Splines with smoothness 1 (3rd order) over 4 data points.*

*M2Q8: Splines with smoothness 2 (5th order) over 8 data points.*

*M2Q14: Splines with smoothness 2 (5th order) over 14 data points.*

*Options for GetPressureHessian, GetVelocityLaplacian, GetMagneticFieldLaplacian, GetVectorPotentialLaplacian,
GetVelocityHessian, GetMagneticFieldHessian and GetVectorPotentialHessian*

*FD4: 4th-order centered finite differencing (can be spatially interpolated)
*

*FD6: 6th-order centered finite differencing (without spatial interpolation)*

*FD8: 8th-order centered finite differencing (without spatial interpolation)*

*M2Q8: Splines with smoothness 2 (5th order) over 8 data points.*

*M2Q14: Splines with smoothness 2 (5th order) over 14 data points.*

### Database Spatial Interpolation Options:

*Interpolation options for GetVelocity, GetMagneticField,
GetVectorPotential, GetPressure, GetVelocityAndPressure, GetDensity and GetPosition*

*NoSInt: No Space interpolation (value at the datapoint closest to each coordinate value)
*

*Lag4: 4th-order Lagrange Polynomial interpolation along each spatial direction|*

*Lag6: 6th-order Lagrange Polynomial interpolation along each spatial direction*

*Lag8: 8th-order Lagrange Polynomial interpolation along each spatial direction*

*M1Q4: Splines with smoothness 1 (3rd order) over 4 data points.*

*M2Q8: Splines with smoothness 2 (5th order) over 8 data points.*

*M2Q14: Splines with smoothness 2 (5th order) over 14 data points.*

*Interpolation options for GetVelocityGradient,
GetMagneticFieldGradient, GetVectorPotentialGradient, GetPressureGradient,
GetDensityGradeint,
GetPressureHessian, GetVelocityLaplacian, GetMagneticFieldLaplacian,
GetVectorPotentialLaplacian, GetVelocityHessian, GetMagneticFieldHessian,
GetVectorPotentialHessian and GetDensityHessian*

*FD4NoInt: No interpolation (value of the 4th order finite-difference
evaluations at the datapoint closest to each coordinate value is returned)
FD6NoInt: No interpolation (value of the 6th order finite-difference
evaluations at the datapoint closest to each coordinate value is returned)
FD8NoInt: No interpolation (value of the 8th order finite-difference
evaluations at the datapoint closest to each coordinate value is returned) *

*FD4Lag4: 4th-order Lagrange Polynomial interpolation in each direction,
of the 4th-order finite difference values on the grid.
*

*M2Q8: Splines with smoothness 2 (5th order) over 8 data points.*

*M2Q14: Splines with smoothness 2 (5th order) over 14 data points.*

### Database Time Interpolation Options:

*For all variables and derivatives listed above, the two
options are:*

*NoTInt: No interpolation (the
value at the closest stored time will be returned).*

*PCHIP: Piecewise Cubic Hermite Interpolation
Polynomial method is used, in which
the value from the two nearest
time points is interpolated at time t using Cubic Hermite Interpolation
Polynomial, with centered finite difference evaluation of the end-point
time derivatives (i.e. a total of four temporal points are used).*

### Database Spatial Filtering Options:

*Options for GetBoxFilter, GetBoxFilterSGSscalar, GetBoxFilterSGSvector, GetBoxFilterSGSsymtensor,
GetBoxFilterSGStensor and GetBoxFilterGradient:*

*Field: The field or combination of fields, which should be filtered.
For the GetBoxFilter, GetBoxFilterGradient and
GetBoxFilterSGSsymtensor the valid options are --
"velocity" or "u", "magnetic" or "b", "potential" or "a", "pressure" or "p", density or "d".
For the GetBoxFilterSGSscalar, GetBoxFilterSGSvector, GetBoxFilterSGStensor two fields should be specified
using single characters, such as "pd", "up" or "ub".
GetBoxFilterSGSscalar operates on two scalar fields, e.g. "pp" or "pd".
GetBoxFilterSGSvector operates on a vector and a scalar field, e.g. "up" or "bp".
GetBoxFilterSGStensor operates on two vector fields, e.g. "ub" or "ba".*

*Filter width (odd multiple of the grid resolution): Size of the box filter to be applied along each spatial direction.
NOTE: This value will be rounded to the nearest odd multiple of the grid resolution.*

*Additional option for GetBoxFilterGradient:*

*Spacing (multiple of the grid resolution): The finite differencing spacing that should be used.*

### Database Threshold Options:

*Options for GetThreshold:*

*Field (one of vorticity, Q, velocity, magnetic, potential, pressure, density): The field, which should be thresholded.*

*X, Y, Z, Xwidth, Ywidth, Zwidth: The spatial region to be examined. X, Y and Z specify the grid node to be used as the
bottom left corner of a box, and Xwidth, Ywidth and Zwidth specify the box's dimensions.
NOTE: These options are similar to those used for the GetRawData functions and the cutout service.*

*Returns: All grid locations from the specified region, at which the norm of the given field is above the given threshold, and
the norm of the field at each of these locations.*

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Last update: 12/14/2023 2:00:37 PM