Gathering materials on the ocean surface based on forecasting area density

A non-transitory computer readable medium having computer-executable program instructions embodied therein that when executed cause a computer processor to:

• determine an initial distribution of material based on observational sources;
• represent the material by a plurality of particles in a numerical ocean model;
• determine a plurality of trajectories for the numerical ocean model based on modeled surface currents data;
• compute a plurality of velocity gradients along a corresponding trajectory of the plurality of trajectories for each of the plurality of particles based on the initial distribution;
• compute a plurality of deformation tensors for each of the plurality of particles based on the plurality of velocity gradients;
• determine a dilation for each of the plurality of deformation tensors based on a divergence from a corresponding local velocity gradient of the plurality of velocity gradients of a corresponding particle of the plurality of particles, wherein the dilation is determined according to:
• 1
• Δ
• ⁢
• D
• ⁢
• ⁢
• Δ
• D
• ⁢
• ⁢
• t
• =
• ∇
• ·
• v
• ⁡
• (
• x
• ⁡
• (
• t
• )
• )
• ,
• and
• wherein
• D
• D
• ⁢
• ⁢
• t
• is a total derivative along a material trajectory, Δ is the dilation, and ∇•v(x(t)) is a time series of divergence along the corresponding trajectory x(t);
• generate a dilation map for the plurality of particles based on the dilation of a time step tensor of the plurality of deformation tensor for each of the plurality of particles;
• use the dilation map to identify a target area with a higher area density;
• create a recovery path that navigates a recovery ship through the target area;
• and
• use a global positioning system to monitor collection of the material by the recovery ship.

A system comprising:

• a memory to store program code for gathering materials on an ocean surface;
• a global positioning system to determine a location of a recovery ship;
• and
• a computer processor operatively connected to the memory to:
• determine an initial distribution of material based on observational sources;
• represent the material by a plurality of particles in a numerical ocean model;
• determine a plurality of trajectories for the numerical ocean model based on modeled surface currents data;
• compute a plurality of velocity gradients along a corresponding trajectory of the plurality of trajectories for each of the plurality of particles based on the initial distribution;
• compute a plurality of deformation tensors for each of the plurality of particles based on the plurality of velocity gradient;
• determine a dilation for each of the plurality of deformation tensors based on a divergence from a corresponding local velocity gradient of the plurality of velocity gradients of a corresponding particle of the plurality of particles, wherein the dilation is determined according to:
• 1
• Δ
• ⁢
• D
• ⁢
• ⁢
• Δ
• D
• ⁢
• ⁢
• t
• =
• ∇
• ·
• v
• ⁡
• (
• x
• ⁡
• (
• t
• )
• )
• ,
• and
• wherein
• D
• D
• ⁢
• ⁢
• t
• is a total derivative along a material trajectory, Δ is the dilation, and ∇•v(x(t)) is a time series of divergence along the corresponding trajectory x(t);
• generate a dilation map for the plurality of particles based on the dilation of a time step tensor of the plurality of deformation tensor for each of the plurality of particles;
• use the dilation map to identify a target area with a higher area density;
• create a recovery path that navigates a recovery ship through the target area;
• and
• use the global positioning system to monitor collection of the material by the recovery ship.