Mathematical modeling of the groundwater level depending on the change of groundwater table height

Öz

It is necessary to evaluate the change of the ground water table, the depth and level of groundwater for regulating the amount of
irrigation water in the agricultural areas, preventing salinization in the plant-root region, and planning the drainage system. In this
study, the variation of ground water table and its level depending on solution according to harmonic boundary condition of the
Boussinesq equation (nonlinear diffusion equation), derived from the Dupuit approximation and the Darcy law, were investigated.
It has been theoretically shown that the ground water table and its level depend on distance and time. The maximum variations of
ground water table and its level were calculated as 0.123 m and 2.123 m, at a distance of 0.5 m and at the 2nd hour, respectively. The
minimum changes were determined as -0.006 m and 1.994 m at a distance of 2.5 m and at the 2nd hour, respectively. It has been
determined that the fluctuation amplitude of the groundwater table is exponentially changed and the fluctuation in x> 2 m distance
approaches the "damping" process.

Anahtar Kelimeler

• Groundwater table
• groundwater level
• Boussinesq equation
• amplitude
• distance
• time

Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi

Öz

Tarım alanlarında sulama suyu miktarının düzenlenmesinde, bitki-kök bölgesi tuzlaşmasının önlenmesinde, drenaj sisteminin
planlanmasında taban suyu derinliği ve seviyesinin, taban suyu tablasının değişiminin değerlendirilmesi gerekir. Bu çalışmada,
Dupuit yaklaşımı ve Darcy yasasına bağlı olarak elde edilen Boussinesq denkleminin (doğrusal olmayan difüzyon denklemin),
harmonik sınır koşuluna bağlı çözümüne göre taban suyu tablası ve seviyesinin değişimleri incelenmiştir. Taban suyu tablası ve
seviyesinin mesafe ve zamana bağlı olduğu teorik olarak gösterilmiştir. Taban suyu tablası ve seviyesinin maksimum değişimleri
sırasıyla 0.123 m ve 2.123 m olarak, 0.5 m mesafede ve 2. saatte hesaplanmıştır. Minimum değişimler ise sırasıyla -0.006 m ve 1.994
m olarak 2.5 m mesafede ve 2. saatte belirlenmiştir. Taban suyu tablasının dalgalanma amplitütünün eksponansiyel olarak değiştiği
ve x>2 m mesafede dalgalanmanın “sönme” sürecine yaklaştığı belirlenmiştir.

Anahtar Kelimeler

• Taban suyu tablası
• taban suyu seviyesi
• Boussinesq denklemi
• amplitüt
• mesafe
• zaman

Kaynakça

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