At what depth is the phase of temperature profile reversed?

In summary, the amplitude of daily temperature is 5 C, and the ground is made of limestone. The phase of temperature profile is reversed at a depth of 7.9 meters where the cosine function switches signs. The circular frequency is equal to 2E-7 per second, and the ratio of the amplitude of temperature variation at 7.9 m to the surface can be found by solving the one-dimensional thermal diffusion equation using the thermal conductivity of limestone.
  • #1
rmjmu507
36
0
The amplitude of daily temperature is dT=5 C. The ground is made of limestone.

At what depth is the phase of temperature profile reversed (cooler at 3 pm and warmer at 3 am)?

Circular frequency is equal to I think 2E-7 per second

The depth at which the profile is reversed is where the cosine function switches signs, i.e. at pi.

So, I find that the profile is reversed at 7.9 meters. Does this seem correct?

How could I find the ratio of the amplitude of temperature variation at 7.9 m vs. the temperature variation at the surface?
 
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  • #2
Replying so that this thread isn't a no-reply, as per Greg's wishes.
If anyone sees this and has knowledge on the subject, feel free to respond.
 
  • #3
rmjmu507 said:
Circular frequency is equal to I think 2E-7 per second
I would question that.
Period T = 24 hours = 24 * 60 * 60 = 86400 sec .
Frequency in Hz = 1 / T ;
Angular freq = 2 * Pi / 86400 = 72.722x10-6 rad/sec.

This problem is a one dimensional thermal diffusion equation.
The depth will depend on the thermal conductivity of the limestone.
 

1. What is the phase of temperature profile reversal?

The phase of temperature profile reversal refers to the point at which the temperature gradient in a body of water shifts from a positive (increasing) slope to a negative (decreasing) slope, or vice versa. This can occur at different depths depending on various factors such as water currents, sunlight exposure, and seasonality.

2. How is the depth of the phase of temperature profile reversal determined?

The depth of the phase of temperature profile reversal is typically determined through temperature measurements taken at various depths in a body of water. The point at which the temperature gradient changes sign is considered the depth of the reversal. This data is often collected using specialized instruments such as thermometers or conductivity-temperature-depth (CTD) probes.

3. What causes the phase of temperature profile reversal?

The phase of temperature profile reversal is primarily caused by changes in water density. As temperature changes, it can affect the density of water, leading to changes in water circulation patterns and the formation of different layers within a body of water. These changes can then impact the temperature gradient and cause the phase of reversal.

4. Is the depth of the phase of temperature profile reversal constant?

No, the depth of the phase of temperature profile reversal is not constant and can vary depending on a variety of factors. It can change depending on the location, season, and local conditions of a particular body of water. It is essential to regularly monitor and collect data on temperature profiles to understand these variations and their potential impacts on the ecosystem.

5. Why is the phase of temperature profile reversal important?

The phase of temperature profile reversal is crucial because it can impact the distribution of nutrients and the growth of organisms in a body of water. It can also affect water circulation patterns and the distribution of oxygen, which can have significant implications for aquatic life. Understanding and monitoring the phase of temperature profile reversal can provide valuable insights into the health and dynamics of a body of water.

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