Final answer:
The velocity field given by u=xy represents a linear relationship because the velocity scales linearly with each variable when the other is held constant.
Step-by-step explanation:
The question asks to classify the components of a velocity field given by u = xy. To classify this expression, we need to determine how the velocity scales with the variables involved. For variable x, as y is held constant, the change in u is linear with x since multiplying by a constant does not change the linearity. Similarly, for variable y, as x is held constant, the change in u is linear with y. Therefore, the velocity field is a product of two variables that individually lead to a linear change in u. This type of relationship where one variable scales linearly with the product of two other variables indicates that the velocity field is linear. It is not quadratic because the variables are not raised to the second power, nor is it exponential or logarithmic since these involve the variables in the exponent or as part of a log function.