module: lorenz_96 — pydartlab 0.0.1 documentation

# module: lorenz_96

class lorenz_96.Lorenz96(model_size=40, delta_t=0.05, forcing=8)

  This class implements the Lorenz 96 model, a simplified atmospheric model designed by Edward Lorenz. It is commonly used in the study of atmospheric dynamics and chaos theory. The model simulates the behavior of a set of variables that could represent atmospheric quantities over a range of spatial positions on a circular domain. The dynamics of the model are governed by a set of differential equations that exhibit chaotic solutions under certain conditions, making it a useful tool for research in numerical weather prediction and theoretical meteorology.

  model_size

    Specifies the number of spatial points in the model, representing the system’s dimensionality.

    Type:

      int

  delta_t

    The time step used for numerical integration.

    Type:

      float

  forcing

    A constant term in the differential equations that acts as an external forcing, influencing the system’s chaotic behavior.

    Type:

      float

  __init__(self, model_size=36, delta_t=0.01, forcing=8.0)

    Initializes a new instance of the Lorenz96 model with optional parameters for model size, time step, and external forcing.

  step(x)

    Does a single time step advance for Lorenz 96 model using four-step Runge-Kutta time step.

    Parameters: - x: The model_size state.

    self.forcing: The forcing term self.delta_t: The time step.

    Returns: - x_new: The new state vector after the time step.

  comp_dt(x)

    Computes the derivative of the state vector using numpy operations for efficiency.

    Parameters: - x: The state vector.

    self.forcing: The forcing term.

    Returns: - dt: The derivative of the state vector.